@article {3495, title = {Agnostic Phase Estimation}, year = {2024}, month = {2/29/2024}, abstract = {

The goal of quantum metrology is to improve measurements\&$\#$39; sensitivities by harnessing quantum resources. Metrologists often aim to maximize the quantum Fisher information, which bounds the measurement setup\&$\#$39;s sensitivity. In studies of fundamental limits on metrology, a paradigmatic setup features a qubit (spin-half system) subject to an unknown rotation. One obtains the maximal quantum Fisher information about the rotation if the spin begins in a state that maximizes the variance of the rotation-inducing operator. If the rotation axis is unknown, however, no optimal single-qubit sensor can be prepared. Inspired by simulations of closed timelike curves, we circumvent this limitation. We obtain the maximum quantum Fisher information about a rotation angle, regardless of the unknown rotation axis. To achieve this result, we initially entangle the probe qubit with an ancilla qubit. Then, we measure the pair in an entangled basis, obtaining more information about the rotation angle than any single-qubit sensor can achieve. We demonstrate this metrological advantage using a two-qubit superconducting quantum processor. Our measurement approach achieves a quantum advantage, outperforming every entanglement-free strategy.

}, url = {https://arxiv.org/abs/2403.00054}, author = {Xingrui Song and Flavio Salvati and Chandrashekhar Gaikwad and Nicole Yunger Halpern and David R. M. Arvidsson-Shukur and Kater Murch} } @article {3486, title = {Average R{\'e}nyi Entanglement Entropy in Gaussian Boson Sampling}, year = {2024}, month = {3/27/2024}, abstract = {

Recently, many experiments have been conducted with the goal of demonstrating a quantum advantage over classical computation. One popular framework for these experiments is Gaussian Boson Sampling, where quadratic photonic input states are interfered via a linear optical unitary and subsequently measured in the Fock basis. In this work, we study the modal entanglement of the output states in this framework just before the measurement stage. Specifically, we compute Page curves as measured by various R{\'e}nyi-α entropies, where the Page curve describes the entanglement between two partitioned groups of output modes averaged over all linear optical unitaries. We derive these formulas for α=1 (i.e. the von Neumann entropy), and, more generally, for all positive integer α, in the asymptotic limit of infinite number of modes and for input states that are composed of single-mode-squeezed-vacuum state with equal squeezing strength. We then analyze the limiting behaviors when the squeezing is small and large. Having determined the averages, we then explicitly calculate the R{\'e}nyi-α variance for integers α\>1, and we are able to show that these entropies are weakly typical.

}, url = {https://arxiv.org/abs/2403.18890}, author = {Jason Youm and Joseph T. Iosue and Adam Ehrenberg and Yu-Xin Wang and Alexey V. Gorshkov} } @article {3511, title = {Beatty Sequences for a Quadratic Irrational: Decidability and Applications}, year = {2024}, month = {2/13/2024}, abstract = {

Let α and β belong to the same quadratic field. We show that the inhomogeneous Beatty sequence (\⌊nα+β\⌋)n\≥1 is synchronized, in the sense that there is a finite automaton that takes as input the Ostrowski representations of n and y in parallel, and accepts if and only if y=\⌊nα+β\⌋. Since it is already known that the addition relation is computable for Ostrowski representations based on a quadratic number, a consequence is a new and rather simple proof that the first-order logical theory of these sequences with addition is decidable. The decision procedure is easily implemented in the free software Walnut.\ \ As an application, we show that for each r\≥1 it is decidable whether the set {\⌊nα+β\⌋:n\≥1} forms an additive basis (or asymptotic additive basis) of order r. Using our techniques, we also solve some open problems of Reble and Kimberling, and give an explicit characterization of a sequence of Hildebrand et al.

}, url = {https://arxiv.org/abs/2402.08331}, author = {Luke Schaeffer and Jeffrey Shallit and Stefan Zorcic} } @article {3407, title = {A Case for Synthesis of Recursive Quantum Unitary Programs}, journal = {Proceedings of the ACM on Programming Languages}, volume = {8}, year = {2024}, month = {12/5/2023}, pages = {1759{\textendash}1788}, abstract = {

Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be highly desirable. In this paper, we initiate the study of program synthesis for quantum unitary programs that recursively define a family of unitary circuits for different input sizes, which are widely used in existing quantum programming languages. Specifically, we present QSynth, the first quantum program synthesis framework, including a new inductive quantum programming language, its specification, a sound logic for reasoning, and an encoding of the reasoning procedure into SMT instances. By leveraging existing SMT solvers, QSynth successfully synthesizes ten quantum unitary programs including quantum adder circuits, quantum eigenvalue inversion circuits and Quantum Fourier Transformation, which can be readily transpiled to executable programs on major quantum platforms, e.g., Q$\#$, IBM Qiskit, and AWS Braket.

}, issn = {2475-1421}, doi = {10.1145/3632901}, url = {https://arxiv.org/abs/2311.11503}, author = {Deng, Haowei and Tao, Runzhou and Peng, Yuxiang and Wu, Xiaodi} } @article {3506, title = {Clifford-Deformed Surface Codes}, journal = {PRX Quantum}, volume = {5}, year = {2024}, month = {3/19/2024}, abstract = {

Various realizations of Kitaev\&$\#$39;s surface code perform surprisingly well for biased Pauli noise. Attracted by these potential gains, we study the performance of Clifford-deformed surface codes (CDSCs) obtained from the surface code by applying single-qubit Clifford operators. We first analyze CDSCs on the 3\×3 square lattice and find that, depending on the noise bias, their logical error rates can differ by orders of magnitude. To explain the observed behavior, we introduce the effective distance d\′, which reduces to the standard distance for unbiased noise. To study CDSC performance in the thermodynamic limit, we focus on random CDSCs. Using the statistical mechanical mapping for quantum codes, we uncover a phase diagram that describes random CDSC families with 50\% threshold at infinite bias. In the high-threshold region, we further demonstrate that typical code realizations outperform the thresholds and subthreshold logical error rates, at finite bias, of the best-known translationally invariant codes. We demonstrate the practical relevance of these random CDSC families by constructing a translation-invariant CDSC belonging to a high-performance random CDSC family. We also show that our translation-invariant CDSC outperforms well-known translation-invariant CDSCs such as the XZZX and XY codes.

}, issn = {2691-3399}, doi = {http://dx.doi.org/10.1103/PRXQuantum.5.010347}, url = {https://arxiv.org/abs/2201.07802}, author = {Dua, Arpit and Kubica, Aleksander and Jiang, Liang and Flammia, Steven T. and Michael Gullans} } @article {3492, title = {Complexity-constrained quantum thermodynamics}, year = {2024}, month = {3/7/2024}, abstract = {

Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process\&$\#$39;s complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state\&$\#$39;s complexity entropy. The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy. The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer\&$\#$39;s ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy and determine the complexity entropy\&$\#$39;s behavior under random circuits. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a complexity conditional entropy, which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of time, as quantified by complexity.

}, url = {https://arxiv.org/abs/2403.04828}, author = {Anthony Munson and Naga Bhavya Teja Kothakonda and Jonas Haferkamp and Nicole Yunger Halpern and Jens Eisert and Philippe Faist} } @article {3460, title = {Complexity-constrained quantum thermodynamics}, year = {2024}, month = {3/7/2024}, abstract = {

Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process\&$\#$39;s complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state, via a complexity-constrained process, is quantified by the state\&$\#$39;s complexity entropy. The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the complexity relative entropy. The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer\&$\#$39;s ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy and determine the complexity entropy\&$\#$39;s behavior under random circuits. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a complexity conditional entropy, which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of time, as quantified by complexity.

}, url = {https://arxiv.org/abs/2403.04828}, author = {Anthony Munson and Naga Bhavya Teja Kothakonda and Jonas Haferkamp and Nicole Yunger Halpern and Jens Eisert and Philippe Faist} } @article {3514, title = {Continuous-Variable Quantum State Designs: Theory and Applications}, journal = {Phys. Rev. X}, volume = {14}, year = {2024}, month = {2/8/2024}, pages = {011013}, abstract = {

We generalize the notion of quantum state designs to infinite-dimensional spaces. We first prove that, under the definition of continuous-variable (CV) state\ t-designs from [Blume-Kohout et al., Commun. Math. Phys. 326, 755 (2014)], no state designs exist for\ t\≥2. Similarly, we prove that no CV unitary\ t-designs exist for t\≥2. We propose an alternative definition for CV state designs, which we call rigged\ t-designs, and provide explicit constructions for\ t\ =\ 2. As an application of rigged designs, we develop a design-based shadow-tomography protocol for CV states. Using energy-constrained versions of rigged designs, we define an average fidelity for CV quantum channels and relate this fidelity to the CV entanglement fidelity. As an additional result of independent interest, we establish a connection between torus 2-designs and complete sets of mutually unbiased bases.

}, doi = {10.1103/PhysRevX.14.011013}, url = {https://link.aps.org/doi/10.1103/PhysRevX.14.011013}, author = {Iosue, Joseph T. and Sharma, Kunal and Michael Gullans and Albert, Victor V.} } @article {3489, title = {Efficient and practical Hamiltonian simulation from time-dependent product formulas}, year = {2024}, month = {3/13/2024}, abstract = {

In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive application of well-known Trotter formulas, for systems where the evolution is determined by a Hamiltonian with different energy scales (i.e., one part is \"large\" and another part is \"small\"). Our algorithms generate a decomposition of the evolution operator into a product of simple unitaries that are directly implementable on a quantum computer. Although the theoretical scaling is suboptimal compared with state-of-the-art algorithms (e.g., quantum signal processing), the performance of the algorithms we propose is highly competitive in practice. We illustrate this via extensive numerical simulations for several models. For instance, in the strong-field regime of the 1D transverse-field Ising model, our algorithms achieve an improvement of one order of magnitude in both the system size and evolution time that can be simulated with a fixed budget of 1000 arbitrary 2-qubit gates, compared with standard Trotter formulas.

}, url = {https://arxiv.org/abs/2403.08729}, author = {Jan Lukas Bosse and Andrew M. Childs and Charles Derby and Filippo Maria Gambetta and Ashley Montanaro and Raul A. Santos} } @article {3490, title = {Efficiently verifiable quantum advantage on near-term analog quantum simulators}, year = {2024}, month = {3/13/2024}, abstract = {

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an O(λ2)-time classical computation, and the prover need only prepare O(1) samples of a history state and perform O(λ2) single-qubit measurements, for a security parameter λ. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

}, url = {https://arxiv.org/abs/2403.08195}, author = {Zhenning Liu and Dhruv Devulapalli and Dominik Hangleiter and Yi-Kai Liu and Alicia J. Koll{\'a}r and Alexey V. Gorshkov and Andrew M. Childs} } @article {3499, title = {Encoding Majorana codes}, year = {2024}, month = {2/12/2024}, abstract = {

To implement a quantum error correction protocol, we first need a scheme to prepare our state in the correct subspace of the code, and this can be done using a unitary encoding circuit. Majorana codes are special since any gates that transform such codes must preserve fermionic parity. In this paper, we present an algorithm that uses the stabilizer matrix to compute unitary encoding circuits for Majorana codes. We present two approaches, both of which use a version of Gaussian elimination with row operations replaced with elementary fermionic Clifford operations. One approach uses an additional ancilla mode and works for all Majorana stabilizer codes, while the second approach does not use ancilla but does not work if the total parity is inside the stabilizer group.

}, url = {https://arxiv.org/abs/2402.07829}, author = {Maryam Mudassar and Riley W. Chien and Daniel Gottesman} } @article {3494, title = {Error Correction in Dynamical Codes}, year = {2024}, month = {3/7/2024}, abstract = {

We ask what is the general framework for a quantum error correcting code that is defined by a sequence of measurements. Recently, there has been much interest in Floquet codes and space-time codes. In this work, we define and study the distance of a dynamical code. This is a subtle concept and difficult to determine: At any given time, the system will be in a subspace which forms a quantum error-correcting code with a given distance, but the full error correction capability of that code may not be available due to the schedule of measurements associated with the code. We address this challenge by developing an algorithm that tracks information we have learned about the error syndromes through the protocol and put that together to determine the distance of a dynamical code, in a non-fault-tolerant context. We use the tools developed for the algorithm to analyze the initialization and masking properties of a generic Floquet code. Further, we look at properties of dynamical codes under the constraint of geometric locality with a view to understand whether the fundamental limitations on logical gates and code parameters imposed by geometric locality for traditional codes can be surpassed in the dynamical paradigm. We find that codes with a limited number of long range connectivity will not allow non-Clifford gates to be implemented with finite depth circuits in the 2D setting.

}, url = {https://arxiv.org/abs/2403.04163}, author = {Xiaozhen Fu and Daniel Gottesman} } @article {3462, title = {Estimation of Hamiltonian parameters from thermal states}, year = {2024}, month = {1/18/2024}, abstract = {

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term\&$\#$39;s degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/n\−\−\√, beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g. a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.

}, url = {https://arxiv.org/abs/2401.10343}, author = {Luis Pedro Garc{\'\i}a-Pintos and Kishor Bharti and Jacob Bringewatt and Hossein Dehghani and Adam Ehrenberg and Nicole Yunger Halpern and Alexey V. Gorshkov} } @article {3517, title = {Expanding Hardware-Efficiently Manipulable Hilbert Space via Hamiltonian Embedding}, year = {2024}, month = {1/16/2024}, abstract = {

Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although several theoretically appealing quantum algorithms have been proposed for this task, they typically require a black-box query model of the sparse Hamiltonian, rendering them impractical for near-term implementation on quantum devices.
In this paper, we propose a technique named Hamiltonian embedding. This technique simulates a desired sparse Hamiltonian by embedding it into the evolution of a larger and more structured quantum system, allowing for more efficient simulation through hardware-efficient operations. We conduct a systematic study of this new technique and demonstrate significant savings in computational resources for implementing prominent quantum applications. As a result, we can now experimentally realize quantum walks on complicated graphs (e.g., binary trees, glued-tree graphs), quantum spatial search, and the simulation of real-space Schr{\"o}dinger equations on current trapped-ion and neutral-atom platforms. Given the fundamental role of Hamiltonian evolution in the design of quantum algorithms, our technique markedly expands the horizon of implementable quantum advantages in the NISQ era.

}, url = {https://arxiv.org/abs/2401.08550}, author = {Jiaqi Leng and Joseph Li and Yuxiang Peng and Xiaodi Wu} } @article {3498, title = {Experimental roadmap for optimal state transfer and entanglement generation in power-law systems}, year = {2024}, month = {2/12/2024}, abstract = {

Experimental systems with power-law interactions have recently garnered interest as promising platforms for quantum information processing. Such systems are capable of spreading entanglement superballistically and achieving an asymptotic speed-up over locally interacting systems. Recently, protocols developed by Eldredge et al. [Phys. Rev. Lett. 119, 170503 (2017)] and Tran et al. [Phys. Rev. X 11, 031016 (2021)] for the task of transferring a quantum state between distant particles quickly were shown to be optimal and saturate theoretical bounds. However, the implementation of these protocols in physical systems with long-range interactions remains to be fully realized. In this work, we provide an experimental roadmap towards realizing fast state-transfer protocols in three classes of atomic and molecular systems with dipolar interactions: polar molecules composed of alkali-metal dimers, neutral atoms in excited Rydberg states, and atoms with strong magnetic moments (e.g. dysprosium). As a guide to near-term experimental implementation, we numerically evaluate the tradeoffs between the two protocols for small system sizes and develop methods to address potential crosstalk errors that may arise during the execution of the protocols.

}, url = {https://arxiv.org/abs/2402.07974}, author = {Andrew Y. Guo and Jeremy T. Young and Ron Belyansky and Przemyslaw Bienias and Alexey V. Gorshkov} } @article {3510, title = {Fast simulation of planar Clifford circuits}, journal = {Quantum}, volume = {8}, year = {2024}, month = {2/12/2024}, pages = {1251}, abstract = {

A general quantum circuit can be simulated classically in exponential time. If it has a planar layout, then a tensor-network contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more generally exponential in the treewidth of the underlying graph. Separately, Gottesman and Knill showed that if all gates are restricted to be Clifford, then there is a polynomial time simulation. We combine these two ideas and show that treewidth and planarity can be exploited to improve Clifford circuit simulation. Our main result is a classical algorithm with runtime scaling asymptotically as nω/2\<n1.19 which samples from the output distribution obtained by measuring all n qubits of a planar graph state in given Pauli bases. Here ω is the matrix multiplication exponent. We also provide a classical algorithm with the same asymptotic runtime which samples from the output distribution of any constant-depth Clifford circuit in a planar geometry. Our work improves known classical algorithms with cubic runtime. A key ingredient is a mapping which, given a tree decomposition of some graph G, produces a Clifford circuit with a structure that mirrors the tree decomposition and which emulates measurement of the corresponding graph state. We provide a classical simulation of this circuit with the runtime stated above for planar graphs and otherwise ntω\−1 where t is the width of the tree decomposition. Our algorithm incorporates two subroutines which may be of independent interest. The first is a matrix-multiplication-time version of the Gottesman-Knill simulation of multi-qubit measurement on stabilizer states. The second is a new classical algorithm for solving symmetric linear systems over F2 in a planar geometry, extending previous works which only applied to non-singular linear systems in the analogous setting.

}, issn = {2521-327X}, doi = {http://dx.doi.org/10.22331/q-2024-02-12-1251}, url = {https://arxiv.org/abs/2009.03218v3}, author = {Gosset, David and Grier, Daniel and Kerzner, Alex and Luke Schaeffer} } @article {3444, title = {Free Quantum Codes from Twisted Unitary $t$-groups}, year = {2024}, month = {2/2/2024}, abstract = {

We introduce twisted unitary t-groups, a generalization of unitary t-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the Knill-Laflamme error correction conditions to show that twisted unitary t-groups automatically correspond to quantum codes with distance d=t+1. By construction these codes have many transversal gates, which are naturally fault tolerant.

}, url = {https://arxiv.org/abs/2402.01638}, author = {Eric Kubischta and Ian Teixeira} } @article {3503, title = {High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED}, journal = {Physical Review Letters}, volume = {132}, year = {2024}, month = {2/28/2024}, abstract = {

With the aim of studying nonperturbative out-of-equilibrium dynamics of high-energy particle collisions on quantum simulators, we investigate the scattering dynamics of lattice quantum electrodynamics in 1+1 dimensions. Working in the bosonized formulation of the model and in the thermodynamic limit, we use uniform-matrix-product-state tensor networks to construct multi-particle wave-packet states, evolve them in time, and detect outgoing particles post collision. This facilitates the numerical simulation of scattering experiments in both confined and deconfined regimes of the model at different energies, giving rise to rich phenomenology, including inelastic production of quark and meson states, meson disintegration, and dynamical string formation and breaking. We obtain elastic and inelastic scattering cross sections, together with time-resolved momentum and position distributions of the outgoing particles. Furthermore, we propose an analog circuit-QED implementation of the scattering process that is native to the platform, requires minimal ingredients and approximations, and enables practical schemes for particle wave-packet preparation and evolution. This study highlights the role of classical and quantum simulation in enhancing our understanding of scattering processes in quantum field theories in real time.

}, issn = {1079-7114}, doi = {http://dx.doi.org/10.1103/PhysRevLett.132.091903}, url = {https://arxiv.org/abs/2307.02522}, author = {Belyansky, Ron and Whitsitt, Seth and Mueller, Niklas and Fahimniya, Ali and Bennewitz, Elizabeth R. and Davoudi, Zohreh and Gorshkov, Alexey V.} } @article {3482, title = {Integrability of Goldilocks quantum cellular automata}, year = {2024}, month = {4/3/2024}, abstract = {

Goldilocks quantum cellular automata (QCA) have been simulated on quantum hardware and produce emergent small-world correlation networks. In Goldilocks QCA, a single-qubit unitary is applied to each qubit in a one-dimensional chain subject to a balance constraint: a qubit is updated if its neighbors are in opposite basis states. Here, we prove that a subclass of Goldilocks QCA -- including the one implemented experimentally -- map onto free fermions and therefore can be classically simulated efficiently. We support this claim with two independent proofs, one involving a Jordan--Wigner transformation and one mapping the integrable six-vertex model to QCA. We compute local conserved quantities of these QCA and predict experimentally measurable expectation values. These calculations can be applied to test large digital quantum computers against known solutions. In contrast, typical Goldilocks QCA have equilibration properties and quasienergy-level statistics that suggest nonintegrability. Still, the latter QCA conserve one quantity useful for error mitigation. Our work provides a parametric quantum circuit with tunable integrability properties with which to test quantum hardware.

}, url = {https://arxiv.org/abs/2404.02994}, author = {Logan E. Hillberry and Lorenzo Piroli and Eric Vernier and Nicole Yunger Halpern and Toma{\v z} Prosen and Lincoln D. Carr} } @article {3502, title = {Ion trap with in-vacuum high numerical aperture imaging for a dual-species modular quantum computer}, journal = {Review of Scientific Instruments}, volume = {95}, year = {2024}, month = {3/26/2024}, abstract = {

Photonic interconnects between quantum systems will play a central role in both scalable quantum computing and quantum networking. Entanglement of remote qubits via photons has been demonstrated in many platforms; however, improving the rate of entanglement generation will be instrumental for integrating photonic links into modular quantum computers. We present an ion trap system that has the highest reported free-space photon collection efficiency for quantum networking. We use a pair of in-vacuum aspheric lenses, each with a numerical aperture of 0.8, to couple 10\% of the 493 nm photons emitted from a 138Ba+ ion into single-mode fibers. We also demonstrate that proximal effects of the lenses on the ion position and motion can be mitigated.

}, issn = {1089-7623}, doi = {http://dx.doi.org/10.1063/5.0180732}, url = {https://arxiv.org/abs/2310.07058}, author = {Carter, Allison L. and O{\textquoteright}Reilly, Jameson and Toh, George and Saha, Sagnik and Shalaev, Mikhail and Goetting, Isabella and Monroe, Christopher} } @article {3497, title = {Long-Distance Nuclear Matrix Elements for Neutrinoless Double-Beta Decay from Lattice QCD}, year = {2024}, month = {2/14/2024}, abstract = {

Neutrinoless double-beta (0νββ) decay is a heretofore unobserved process which, if observed, would imply that neutrinos are Majorana particles. Interpretations of the stringent experimental constraints on 0νββ-decay half-lives require calculations of nuclear matrix elements. This work presents the first lattice quantum-chromodynamics (LQCD) calculation of the matrix element for 0νββ decay in a multi-nucleon system, specifically the nn\→ppee transition, mediated by a light left-handed Majorana neutrino propagating over nuclear-scale distances. This calculation is performed with quark masses corresponding to a pion mass of mπ=806 MeV at a single lattice spacing and volume. The statistically cleaner Σ\−\→Σ+ee transition is also computed in order to investigate various systematic uncertainties. The prospects for matching the results of LQCD calculations onto a nuclear effective field theory to determine a leading-order low-energy constant relevant for 0νββ decay with a light Majorana neutrino are investigated. This work, therefore, sets the stage for future calculations at physical values of the quark masses that, combined with effective field theory and nuclear many-body studies, will provide controlled theoretical inputs to experimental searches of 0νββ decay.

}, url = {https://arxiv.org/abs/2402.09362}, author = {Zohreh Davoudi and William Detmold and Zhenghao Fu and Anthony V. Grebe and William Jay and David Murphy and Patrick Oare and Phiala E. Shanahan and Michael L. Wagman} } @article {3512, title = {Multi-product Hamiltonian simulation with explicit commutator scaling}, year = {2024}, month = {3/13/2024}, abstract = {

The well-conditioned multi-product formula (MPF), proposed by [Low, Kliuchnikov, and Wiebe, 2019], is a simple high-order time-independent Hamiltonian simulation algorithm that implements a linear combination of standard product formulas of low order. While the MPF aims to simultaneously exploit commutator scaling among Hamiltonians and achieve near-optimal time and precision dependence, its lack of a rigorous error bound on the nested commutators renders its practical advantage ambiguous. In this work, we conduct a rigorous complexity analysis of the well-conditioned MPF, demonstrating explicit commutator scaling and near-optimal time and precision dependence at the same time. Using our improved complexity analysis, we present several applications of practical interest where the MPF based on a second-order product formula can achieve a polynomial speedup in both system size and evolution time, as well as an exponential speedup in precision, compared to second-order and even higher-order product formulas. Compared to post-Trotter methods, the MPF based on a second-order product formula can achieve polynomially better scaling in system size, with only poly-logarithmic overhead in evolution time and precision.

}, url = {https://arxiv.org/abs/2403.08922}, author = {Junaid Aftab and Dong An and Konstantina Trivisa} } @article {3501, title = {Optimal function estimation with photonic quantum sensor networks}, journal = {Physical Review Research}, volume = {6}, year = {2024}, month = {3/6/2024}, abstract = {

The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here, we resolve a number of open questions that arise when extending this framework to Mach-Zehnder interferometers and quadrature displacement sensing. In particular, we derive lower bounds on the achievable mean square error in estimating a linear function of either local phase shifts or quadrature displacements. In the case of local phase shifts, these results prove, and somewhat generalize, a conjecture by Proctor et al. [arXiv:1702.04271 (2017)]. For quadrature displacements, we extend proofs of lower bounds to the case of arbitrary linear functions. We provide optimal protocols achieving these bounds up to small (multiplicative) constants and describe an algebraic approach to deriving new optimal protocols, possibly subject to additional constraints. Using this approach, we prove necessary conditions for the amount of entanglement needed for any optimal protocol for both local phase and displacement sensing.

}, issn = {2643-1564}, doi = {https://doi.org/10.48550/arXiv.2401.16472}, url = {https://arxiv.org/abs/2401.16472}, author = {Bringewatt, Jacob and Ehrenberg, Adam and Goel, Tarushii and Gorshkov, Alexey V.} } @article {3504, title = {Phase transition in magic with random quantum circuits}, year = {2024}, month = {4/11/2024}, abstract = {

Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards efficient and practical fault-tolerant computation. We observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytic, numeric and experimental probes. Below a critical error rate, stabilizer syndrome measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate syndrome measurements concentrate magic. A better understanding of such rich behavior in the resource theory of magic could shed more light on origins of quantum speedup and pave pathways for more efficient magic state generation.

}, url = {https://arxiv.org/abs/2304.10481}, author = {Pradeep Niroula and Christopher David White and Qingfeng Wang and Sonika Johri and Daiwei Zhu and Christopher Monroe and Crystal Noel and Michael Gullans} } @article {3487, title = {Polynomial-Time Classical Simulation of Noisy IQP Circuits with Constant Depth}, year = {2024}, month = {3/21/2024}, abstract = {

Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has become a leading candidate for testing the capabilities of quantum devices. Here we demonstrate that for an arbitrary IQP circuit undergoing dephasing or depolarizing noise, whose depth is greater than a critical O(1) threshold, the output distribution can be efficiently sampled by a classical computer. Unlike other simulation algorithms for quantum supremacy tasks, we do not require assumptions on the circuit\&$\#$39;s architecture, on anti-concentration properties, nor do we require Ω(log(n)) circuit depth. We take advantage of the fact that IQP circuits have deep sections of diagonal gates, which allows the noise to build up predictably and induce a large-scale breakdown of entanglement within the circuit. Our results suggest that quantum supremacy experiments based on IQP circuits may be more susceptible to classical simulation than previously thought.

}, url = {https://arxiv.org/abs/2403.14607}, author = {Joel Rajakumar and James D. Watson and Yi-Kai Liu} } @article {3513, title = {Post-quantum cryptography and the quantum future of cybersecurity}, journal = {Phys. Rev. Appl.}, volume = {21}, year = {2024}, month = {4/9/2024}, pages = {040501}, abstract = {

We review the current status of efforts to develop and deploy post-quantum cryptography on the Internet. Then we suggest specific ways in which quantum technologies might be used to enhance cybersecurity in the near future and beyond. We focus on two goals: protecting the secret keys that are used in classical cryptography, and ensuring the trustworthiness of quantum computations. These goals may soon be within reach, thanks to recent progress in both theory and experiment. This progress includes interactive protocols for testing quantumness as well as for performing uncloneable cryptographic computations; and experimental demonstrations of device-independent random number generators, device-independent quantum key distribution, quantum memories, and analog quantum simulators.

}, doi = {10.1103/PhysRevApplied.21.040501}, url = {https://link.aps.org/doi/10.1103/PhysRevApplied.21.040501}, author = {Liu, Yi-Kai and Moody, Dustin} } @article {3515, title = {Precision Bounds on Continuous-Variable State Tomography Using Classical Shadows}, journal = {PRX Quantum}, volume = {5}, year = {2024}, month = {3/18/2024}, pages = {010346}, abstract = {

Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called \“classical shadows,\” with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon-number-resolving, and photon-parity protocols. To reach a desired precision on the classical shadow of an\ N-photon density matrix with high probability, we show that homodyne detection requires order\ O(N4+1/3) measurements in the worst case, whereas photon-number-resolving and photon-parity detection require\ O\ (N4)measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental analyses of homodyne tomography match closely with our theoretical predictions. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.

}, doi = {10.1103/PRXQuantum.5.010346}, url = {https://link.aps.org/doi/10.1103/PRXQuantum.5.010346}, author = {Gandhari, Srilekha and Albert, Victor V. and Gerrits, Thomas and Taylor, Jacob M. and Michael Gullans} } @article {3485, title = {Properties and Applications of the Kirkwood-Dirac Distribution}, year = {2024}, month = {3/27/2024}, abstract = {

The most famous quasi-probability distribution, the Wigner function, has played a pivotal role in the development of a continuous-variable quantum theory that has clear analogues of position and momentum. However, the Wigner function is ill-suited for much modern quantum-information research, which is focused on finite-dimensional systems and general observables. Instead, recent years have seen the Kirkwood-Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be applied to problems in quantum-information processing. A notable difference to the Wigner function is that the KD distribution can represent a quantum state in terms of arbitrary observables. This paper reviews the KD distribution, in three parts. First, we present definitions and basic properties of the KD distribution and its generalisations. Second, we summarise the KD distribution\&$\#$39;s extensive usage in the study or development of measurement disturbance; quantum metrology; weak values; direct measurements of quantum states; quantum thermodynamics; quantum scrambling and out-of-time-ordered correlators; and the foundations of quantum mechanics, including Leggett-Garg inequalities, the consistent-histories interpretation, and contextuality. We emphasise connections between operational quantum advantages and negative or non-real KD quasi-probabilities. Third, we delve into the KD distribution\&$\#$39;s mathematical structure. We summarise the current knowledge regarding the geometry of KD-positive states (the states for which the KD distribution is a classical probability distribution), describe how to witness and quantify KD non-positivity, and outline relationships between KD non-positivity and observables\&$\#$39; incompatibility.

}, url = {https://arxiv.org/abs/2403.18899}, author = {David R. M. Arvidsson-Shukur and William F. Braasch Jr. and Stephan De Bievre and Justin Dressel and Andrew N. Jordan and Christopher Langrenez and Matteo Lostaglio and Jeff S. Lundeen and Nicole Yunger Halpern} } @article {3496, title = {The Quantum Abstract Machine}, year = {2024}, month = {2/21/2024}, abstract = {

This paper develops a model of quantum behavior that is intended to support the abstract yet accurate design and functional verification of quantum communication protocols. The work is motivated by the need for conceptual tools for the development of quantum-communication systems that are usable by non-specialists in quantum physics while also correctly capturing at a useful abstraction the underlying quantum phenomena. Our approach involves defining a quantum abstract machine (QAM) whose operations correspond to well-known quantum circuits; these operations, however, are given direct abstract semantics in a style similar to that of Berry\&$\#$39;s and Boudol\&$\#$39;s Chemical Abstract Machine. This paper defines the QAM\&$\#$39;s semantics and shows via examples how it may be used to model and reason about existing quantum communication protocols.

}, url = {https://arxiv.org/abs/2402.13469}, author = {Liyi Li and Le Chang and Rance Cleaveland and Mingwei Zhu and Xiaodi Wu} } @article {3516, title = {A Quantum "Lifting Theorem" for Constructions of Pseudorandom Generators from Random Oracles}, year = {2024}, month = {1/30/2024}, abstract = {

We study the (quantum) security of pseudorandom generators (PRGs) constructed from random oracles. We prove a \"lifting theorem\" showing, roughly, that if such a PRG is unconditionally secure against classical adversaries making polynomially many queries to the random oracle, then it is also (unconditionally) secure against quantum adversaries in the same sense. As a result of independent interest, we also show that any pseudo-deterministic quantum-oracle algorithm (i.e., a quantum algorithm that with high probability returns the same value on repeated executions) can be simulated by a computationally unbounded but query bounded classical-oracle algorithm with only a polynomial blowup in the number of queries. This implies as a corollary that our lifting theorem holds even for PRGs that themselves make quantum queries to the random oracle.

}, url = {https://arxiv.org/abs/2401.14319}, author = {Jonathan Katz and Ben Sela} } @article {3507, title = {Quantum One-Wayness of the Single-Round Sponge with Invertible Permutations}, year = {2024}, month = {3/7/2024}, abstract = {

Sponge hashing is a novel class of cryptographic hash algorithms which underlies the current international hash function standard SHA-3. In a nutshell, a sponge function takes as input a bit-stream of any length and processes it via a simple iterative procedure: it repeatedly feeds each block of the input into a so-called block function, and then produces a short digest which consists of a subset of the final output bits. While much is known about the post-quantum security of the sponge construction in the case when the block function is modeled as a random function or permutation, the case of invertible permutations, which more accurately models the construction underlying SHA-3, has so far remained a fundamental open problem.
In this work, we make new progress towards overcoming this barrier and show several results. First, we prove the \"double-sided zero-search\" conjecture proposed by Unruh (eprint\&$\#$39; 2021) and show that finding zero-pairs in a random 2n-bit permutation requires at least Ω(2n/2) many queries -- and this is tight due to Grover\&$\#$39;s algorithm. At the core of our proof lies a novel \"symmetrization argument\" which uses insights from the theory of Young subgroups. Second, we consider more general variants of the double-sided search problem and show similar query lower bounds for them. As an application, we prove the quantum one-wayness of the single-round sponge with invertible permutations in the quantum random oracle model.

}, url = {https://arxiv.org/abs/2403.04740}, author = {Joseph Carolan and Alexander Poremba} } @article {3484, title = {Quantum thermodynamics of nonequilibrium processes in lattice gauge theories}, year = {2024}, month = {4/3/2024}, abstract = {

A key objective in nuclear and high-energy physics is to describe nonequilibrium dynamics of matter, e.g., in the early universe and in particle colliders, starting from the Standard Model. Classical-computing methods, via the framework of lattice gauge theory, have experienced limited success in this mission. Quantum simulation of lattice gauge theories holds promise for overcoming computational limitations. Because of local constraints (Gauss\&$\#$39;s laws), lattice gauge theories have an intricate Hilbert-space structure. This structure complicates the definition of thermodynamic properties of systems coupled to reservoirs during equilibrium and nonequilibrium processes. We show how to define thermodynamic quantities such as work and heat using strong-coupling thermodynamics, a framework that has recently burgeoned within the field of quantum thermodynamics. Our definitions suit instantaneous quenches, simple nonequilibrium processes undertaken in quantum simulators. To illustrate our framework, we compute the work and heat exchanged during a quench in a Z2 lattice gauge theory coupled to matter in 1+1 dimensions. The thermodynamic quantities, as functions of the quench parameter, evidence an expected phase transition. For general thermal states, we derive a simple relation between a quantum many-body system\&$\#$39;s entanglement Hamiltonian, measurable with quantum-information-processing tools, and the Hamiltonian of mean force, used to define strong-coupling thermodynamic quantities.

}, url = {https://arxiv.org/abs/2404.02965}, author = {Zohreh Davoudi and Christopher Jarzynski and Niklas Mueller and Greeshma Oruganti and Connor Powers and Nicole Yunger Halpern} } @article {3508, title = {Randomized measurement protocols for lattice gauge theories}, journal = {Quantum}, volume = {8}, year = {2024}, month = {3/20/2024}, pages = {1300}, abstract = {

Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. This can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments. Crucially, unlike symmetry-blind randomized measurement protocols, these latter tasks can be performed without relearning symmetries via full reconstruction of the density matrix.

}, issn = {2521-327X}, doi = {http://dx.doi.org/10.22331/q-2024-03-27-1300}, url = {https://arxiv.org/abs/2303.15519}, author = {Bringewatt, Jacob and Kunjummen, Jonathan and Mueller, Niklas} } @article {3500, title = {Scattering wave packets of hadrons in gauge theories: Preparation on a quantum computer}, year = {2024}, month = {2/1/2024}, abstract = {

Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the Z2 and U(1) lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the Z2 lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.

}, url = {https://arxiv.org/abs/2402.00840}, author = {Zohreh Davoudi and Chung-Chun Hsieh and Saurabh V. Kadam} } @article {3488, title = {The Second Moment of Hafnians in Gaussian Boson Sampling}, year = {2024}, month = {3/20/2024}, abstract = {

Gaussian Boson Sampling is a popular method for experimental demonstrations of quantum advantage, but many subtleties remain in fully understanding its theoretical underpinnings. An important component in the theoretical arguments for approximate average-case hardness of sampling is anticoncentration, which is a second-moment property of the output probabilities. In Gaussian Boson Sampling these are given by hafnians of generalized circular orthogonal ensemble matrices. In a companion work [arXiv:2312.08433], we develop a graph-theoretic method to study these moments and use it to identify a transition in anticoncentration. In this work, we find a recursive expression for the second moment using these graph-theoretic techniques. While we have not been able to solve this recursion by hand, we are able to solve it numerically exactly, which we do up to Fock sector 2n=80. We further derive new analytical results about the second moment. These results allow us to pinpoint the transition in anticoncentration and furthermore yield the expected linear cross-entropy benchmarking score for an ideal (error-free) device.

}, url = {https://arxiv.org/abs/2403.13878}, author = {Adam Ehrenberg and Joseph T. Iosue and Abhinav Deshpande and Dominik Hangleiter and Alexey V. Gorshkov} } @article {3491, title = {Simulating Meson Scattering on Spin Quantum Simulators}, year = {2024}, month = {3/11/2024}, abstract = {

Studying high-energy collisions of composite particles, such as hadrons and nuclei, is an outstanding goal for quantum simulators. However, preparation of hadronic wave packets has posed a significant challenge, due to the complexity of hadrons and the precise structure of wave packets. This has limited demonstrations of hadron scattering on quantum simulators to date. Observations of confinement and composite excitations in quantum spin systems have opened up the possibility to explore scattering dynamics in spin models. In this article, we develop two methods to create entangled spin states corresponding to wave packets of composite particles in analog quantum simulators of Ising spin Hamiltonians. One wave-packet preparation method uses the blockade effect enabled by beyond-nearest-neighbor Ising spin interactions. The other method utilizes a quantum-bus-mediated exchange, such as the native spin-phonon coupling in trapped-ion arrays. With a focus on trapped-ion simulators, we numerically benchmark both methods and show that high-fidelity wave packets can be achieved in near-term experiments. We numerically study scattering of wave packets for experimentally realizable parameters in the Ising model and find inelastic-scattering regimes, corresponding to particle production in the scattering event, with prominent and distinct experimental signals. Our proposal, therefore, demonstrates the potential of observing inelastic scattering in near-term quantum simulators.

}, url = {https://arxiv.org/abs/2403.07061}, author = {Elizabeth R. Bennewitz and Brayden Ware and Alexander Schuckert and Alessio Lerose and Federica M. Surace and Ron Belyansky and William Morong and De Luo and Arinjoy De and Kate S. Collins and Or Katz and Christopher Monroe and Zohreh Davoudi and Alexey V. Gorshkov} } @article {3416, title = {SimuQ: A Framework for Programming Quantum Hamiltonian Simulation with Analog Compilation}, journal = {Proceedings of the ACM on Programming Languages}, volume = {8}, year = {2024}, month = {11/19/2023}, pages = {2425{\textendash}2455}, abstract = {

Quantum Hamiltonian simulation, which simulates the evolution of quantum systems and probes quantum phenomena, is one of the most promising applications of quantum computing. Recent experimental results suggest that Hamiltonian-oriented analog quantum simulation would be advantageous over circuit-oriented digital quantum simulation in the Noisy Intermediate-Scale Quantum (NISQ) machine era. However, programming analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software. In this paper, we design and implement SimuQ, the first framework for quantum Hamiltonian simulation that supports Hamiltonian programming and pulse-level compilation to heterogeneous analog quantum simulators. Specifically, in SimuQ, front-end users specify the target quantum system with Hamiltonian Modeling Language, and the Hamiltonian-level programmability of analog quantum simulators is specified through a new abstraction called the abstract analog instruction set (AAIS) and programmed in AAIS Specification Language by hardware providers. Through a solver-based compilation, SimuQ generates executable pulse schedules for real devices to simulate the evolution of desired quantum systems, which is demonstrated on superconducting (IBM), neutral-atom (QuEra), and trapped-ion (IonQ) quantum devices. Moreover, we demonstrate the advantages of exposing the Hamiltonian-level programmability of devices with native operations or interaction-based gates and establish a small benchmark of quantum simulation to evaluate SimuQ\&$\#$39;s compiler with the above analog quantum simulators.

}, issn = {2475-1421}, doi = {10.1145/3632923}, url = {https://arxiv.org/abs/2303.02775}, author = {Peng, Yuxiang and Young, Jacob and Liu, Pengyu and Wu, Xiaodi} } @article {3480, title = {Strong interactions between integrated microresonators and alkali atomic vapors: towards single-atom, single-photon operation}, year = {2024}, month = {4/5/2024}, abstract = {

Cavity quantum electrodynamics (cQED), the interaction of a two-level system with a high quality factor (Q) cavity, is a foundational building block in different architectures for quantum computation, communication, and metrology. The strong interaction between the atom and the cavity enables single photon operation which is required for quantum gates and sources. Cold atoms, quantum dots, and color centers in crystals are amongst the systems that have shown single photon operations, but they require significant physical infrastructure. Atomic vapors, on the other hand, require limited experimental infrastructure and are hence much easier to deploy outside a laboratory, but they produce an ensemble of moving atoms that results in short interaction times involving multiple atoms, which can hamper quantum operations. A solution to this issue can be found in nanophotonic cavities, where light-matter interaction is enhanced and the volume of operation is small, so that fast single-atom, single-photon operations are enabled. In this work, we study the interaction of an atomically-clad microring resonator (ACMRR) with different-sized ensembles of Rb atoms. We demonstrate strong coupling between an ensemble of ~50 atoms interacting with a high-quality factor (Q \> 4 x 10^5) ACMRR, yielding a many-atom cooperativity C ~ 5.5. We continue to observe signatures of atom-photon interaction for a few (\< 3) atoms, for which we observe saturation at the level of one intracavity photon. Further development of our platform, which includes integrated thermo-optic heaters to enable cavity tuning and stabilization, should enable the observation of interactions between single photons and single atoms.

}, url = {https://arxiv.org/abs/2404.04372}, author = {Roy Zektzer and Xiyuan Lu and Khoi Tuan Hoang and Rahul Shrestha and Sharoon Austin and Feng Zhou and Ashish Chanana and Glenn Holland and Daron Westly and Paul Lett and Alexey V. Gorshkov and Kartik Srinivasan} } @article {3493, title = {Topology and entanglement of molecular phase space}, year = {2024}, month = {3/7/2024}, abstract = {

We formulate a quantum phase space for molecular rotational and nuclear-spin states. Taking in molecular geometry and nuclear-spin data, our framework yields admissible position and momentum states, inter-convertible via a generalized Fourier transform. We classify molecules into three types -- asymmetric, rotationally symmetric, and perrotationally symmetric -- with the last type having no macroscopic analogue due to nuclear-spin statistics constraints. We identify two features in perrotationally symmetric state spaces that are Hamiltonian-independent and induced solely by symmetry and spin statistics. First, many molecular species are intrinsically rotation-spin entangled in a way that cannot be broken without transitioning to another species or breaking symmetry. Second, each molecular position state houses an internal pseudo-spin or \"fiber\" degree of freedom, and the fiber\&$\#$39;s Berry phase or matrix after adiabatic changes in position yields naturally robust operations, akin to braiding anyonic quasiparticles or realizing fault-tolerant quantum gates. We outline scenarios where these features can be experimentally probed.

}, url = {https://arxiv.org/abs/2403.04572}, author = {Victor V. Albert and Eric Kubischta and Mikhail Lemeshko and Lee R. Liu} } @article {3509, title = {Trainability Barriers in Low-Depth QAOA Landscapes}, year = {2024}, month = {2/15/2024}, abstract = {

The Quantum Alternating Operator Ansatz (QAOA) is a prominent variational quantum algorithm for solving combinatorial optimization problems. Its effectiveness depends on identifying input parameters that yield high-quality solutions. However, understanding the complexity of training QAOA remains an under-explored area. Previous results have given analytical performance guarantees for a small, fixed number of parameters. At the opposite end of the spectrum, barren plateaus are likely to emerge at Ω(n) parameters for n qubits. In this work, we study the difficulty of training in the intermediate regime, which is the focus of most current numerical studies and near-term hardware implementations. Through extensive numerical analysis of the quality and quantity of local minima, we argue that QAOA landscapes can exhibit a superpolynomial growth in the number of low-quality local minima even when the number of parameters scales logarithmically with n. This means that the common technique of gradient descent from randomly initialized parameters is doomed to fail beyond small n, and emphasizes the need for good initial guesses of the optimal parameters.

}, url = {https://arxiv.org/abs/2402.10188}, author = {Joel Rajakumar and John Golden and Andreas B{\"a}rtschi and Stephan Eidenbenz} } @article {3505, title = {Ultrastrong light-matter interaction in a multimode photonic crystal}, year = {2024}, month = {2/21/2024}, abstract = {

Harnessing the interaction between light and matter at the quantum level has been a central theme in atomic physics and quantum optics, with applications from quantum computation to quantum metrology. Combining complex interactions with photonic synthetic materials provides an opportunity to investigate novel quantum phases and phenomena, establishing interesting connections to condensed matter physics. Here we explore many-body phenomena with a single artificial atom coupled to the many discrete modes of a photonic crystal. This experiment reaches the ultrastrong light-matter coupling regime using the circuit quantum electrodynamics paradigm, by galvanically coupling a highly nonlinear fluxonium qubit to a tight-binding lattice of microwave resonators. In this regime, the transport of a single photon becomes a many-body problem, owing to the strong participation of multi-photon bound states arising from interactions that break particle number conservation. Exploiting the effective photon-photon interactions mediated by the qubit, the transport of multiple photons leads to complex multimode dynamics that can be employed for generating a continuous reservoir of strongly-correlated photons, an important resource for quantum networks. This work opens exciting prospects for exploring nonlinear quantum optics at the single-photon level and stabilizing entangled many-body phases of light.

}, url = {https://arxiv.org/abs/2209.14972}, author = {Andrei Vrajitoarea and Ron Belyansky and Rex Lundgren and Seth Whitsitt and Alexey V. Gorshkov and Andrew A. Houck} } @article {3483, title = {Zero-temperature entanglement membranes in quantum circuits}, year = {2024}, month = {4/3/2024}, abstract = {

In chaotic quantum systems, the entanglement of a region A can be described in terms of the surface tension of a spacetime membrane pinned to the boundary of A. Here, we interpret the tension of this entanglement membrane in terms of the rate at which information \"flows\" across it. For any orientation of the membrane, one can define (generically nonunitary) dynamics across the membrane; we explore this dynamics in various space-time translation-invariant (STTI) stabilizer circuits in one and two spatial dimensions. We find that the flux of information across the membrane in these STTI circuits reaches a steady state. In the cases where this dynamics is nonunitary and the steady state flux is nonzero, this occurs because the dynamics across the membrane is unitary in a subspace of extensive entropy. This generalized unitarity is present in a broad class of STTI stabilizer circuits, and is also present in some special non-stabilizer models. The existence of multiple unitary (or generalized unitary) directions forces the entanglement membrane tension to be a piecewise linear function of the orientation of the membrane; in this respect, the entanglement membrane behaves like an interface in a zero-temperature classical lattice model. We argue that entanglement membranes in random stabilizer circuits that produce volume-law entanglement are also effectively at zero temperature.

}, url = {https://arxiv.org/abs/2404.02975}, author = {Grace M. Sommers and Sarang Gopalakrishnan and Michael Gullans and David A. Huse} } @article {3257, title = {Accelerating Progress Towards Practical Quantum Advantage: The Quantum Technology Demonstration Project Roadmap}, year = {2023}, month = {3/20/2023}, abstract = {

Quantum information science and technology (QIST) is a critical and emerging technology with the potential for enormous world impact and is currently invested in by over 40 nations. To bring these large-scale investments to fruition and bridge the lower technology readiness levels (TRLs) of fundamental research at universities to the high TRLs necessary to realize the promise of practical quantum advantage accessible to industry and the public, we present a roadmap for Quantum Technology Demonstration Projects (QTDPs). Such QTDPs, focused on intermediate TRLs, are large-scale public-private partnerships with a high probability of translation from laboratory to practice. They create technology demonstrating a clear \&$\#$39;quantum advantage\&$\#$39; for science breakthroughs that are user-motivated and will provide access to a broad and diverse community of scientific users. Successful implementation of a program of QTDPs will have large positive economic impacts.

}, url = {https://arxiv.org/abs/2210.14757}, author = {Paul Alsing and Phil Battle and Joshua C. Bienfang and Tammie Borders and Tina Brower-Thomas and Lincoln D. Carr and Fred Chong and Siamak Dadras and Brian DeMarco and Ivan Deutsch and Eden Figueroa and Danna Freedman and Henry Everitt and Daniel Gauthier and Ezekiel Johnston-Halperin and Jungsang Kim and Mackillo Kira and Prem Kumar and Paul Kwiat and John Lekki and Anjul Loiacono and Marko Lon{\v c}ar and John R. Lowell and Mikhail Lukin and Celia Merzbacher and Aaron Miller and Christopher Monroe and Johannes Pollanen and David Pappas and Michael Raymer and Ronald Reano and Brandon Rodenburg and Martin Savage and Thomas Searles and Jun Ye} } @article {3409, title = {Accurate and Honest Approximation of Correlated Qubit Noise}, year = {2023}, month = {11/15/2023}, abstract = {

Accurate modeling of noise in realistic quantum processors is critical for constructing fault-tolerant quantum computers. While a full simulation of actual noisy quantum circuits provides information about correlated noise among all qubits and is therefore accurate, it is, however, computationally expensive as it requires resources that grow exponentially with the number of qubits. In this paper, we propose an efficient systematic construction of approximate noise channels, where their accuracy can be enhanced by incorporating noise components with higher qubit-qubit correlation degree. To formulate such approximate channels, we first present a method, dubbed the cluster expansion approach, to decompose the Lindbladian generator of an actual Markovian noise channel into components based on interqubit correlation degree. We then generate a k-th order approximate noise channel by truncating the cluster expansion and incorporating noise components with correlations up to the k-th degree. We require that the approximate noise channels must be accurate and also \"honest\", i.e., the actual errors are not underestimated in our physical models. As an example application, we apply our method to model noise in a three-qubit quantum processor that stabilizes a [[2,0,0]] codeword, which is one of the four Bell states. We find that, for realistic noise strength typical for fixed-frequency superconducting qubits coupled via always-on static interactions, correlated noise beyond two-qubit correlation can significantly affect the code simulation accuracy. Since our approach provides a systematic noise characterization, it enables the potential for accurate, honest and scalable approximation to simulate large numbers of qubits from full modeling or experimental characterizations of small enough quantum subsystems, which are efficient but still retain essential noise features of the entire device.

}, url = {https://arxiv.org/abs/2311.09305}, author = {F. Setiawan and Alexander V. Gramolin and Elisha S. Matekole and Hari Krovi and Jacob M. Taylor} } @article {3056, title = {Advantages and limitations of quantum routing}, journal = {PRX Quantum}, volume = {4}, year = {2023}, month = {2/1/2023}, abstract = {

The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of permuting qubits within an architecture, which we call routing. We consider quantum routing in two models: (1) allowing arbitrary two-qubit unitaries, or (2) allowing Hamiltonians with norm-bounded interactions. We lower bound the circuit depth or time of quantum routing in terms of spectral properties of graphs representing the architecture interaction constraints, and give a generalized upper bound for all simple connected n-vertex graphs. In particular, we give conditions for a superpolynomial classical-quantum routing separation, which exclude graphs with a small spectral gap and graphs of bounded degree. Finally, we provide examples of a quadratic separation between gate-based and Hamiltonian routing models with a constant number of local ancillas per qubit and of an Ω(n) speedup if we also allow fast local interactions.

}, keywords = {Data Structures and Algorithms (cs.DS), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1103/PRXQuantum.4.010313}, url = {https://arxiv.org/abs/2206.01766}, author = {Bapat, Aniruddha and Andrew M. Childs and Alexey V. Gorshkov and Schoute, Eddie} } @article {3246, title = {Analyzing Convergence in Quantum Neural Networks: Deviations from Neural Tangent Kernels}, year = {2023}, month = {3/26/2023}, abstract = {

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based optimizers. Despite the existing empirical and theoretical investigations, the convergence of QNN training is not fully understood. Inspired by the success of the neural tangent kernels (NTKs) in probing into the dynamics of classical neural networks, a recent line of works proposes to study over-parameterized QNNs by examining a quantum version of tangent kernels. In this work, we study the dynamics of QNNs and show that contrary to popular belief it is qualitatively different from that of any kernel regression: due to the unitarity of quantum operations, there is a non-negligible deviation from the tangent kernel regression derived at the random initialization. As a result of the deviation, we prove the at-most sublinear convergence for QNNs with Pauli measurements, which is beyond the explanatory power of any kernel regression dynamics. We then present the actual dynamics of QNNs in the limit of over-parameterization. The new dynamics capture the change of convergence rate during training and implies that the range of measurements is crucial to the fast QNN convergence.

}, url = {https://arxiv.org/abs/2303.14844}, author = {Xuchen You and Shouvanik Chakrabarti and Boyang Chen and Xiaodi Wu} } @article {3365, title = {Bell sampling from quantum circuits}, year = {2023}, month = {10/6/2023}, abstract = {

A central challenge in the verification of quantum computers is benchmarking their performance as a whole and demonstrating their computational capabilities. In this work, we find a universal model of quantum computation, Bell sampling, that can be used for both of those tasks and thus provides an ideal stepping stone towards fault-tolerance. In Bell sampling, we measure two copies of a state prepared by a quantum circuit in the transversal Bell basis. We show that the Bell samples are classically intractable to produce and at the same time constitute what we call a circuit shadow: from the Bell samples we can efficiently extract information about the quantum circuit preparing the state, as well as diagnose circuit errors. In addition to known properties that can be efficiently extracted from Bell samples, we give two new and efficient protocols, a test for the depth of the circuit and an algorithm to estimate a lower bound to the number of T gates in the circuit. With some additional measurements, our algorithm learns a full description of states prepared by circuits with low T-count.

}, url = {https://arxiv.org/abs/2306.00083}, author = {Dominik Hangleiter and Michael Gullans} } @article {3310, title = {Bell sampling from quantum circuits}, year = {2023}, month = {6/19/2023}, abstract = {

A central challenge in the verification of quantum computers is benchmarking their performance as a whole and demonstrating their computational capabilities. In this work, we find a model of quantum computation, Bell sampling, that can be used for both of those tasks and thus provides an ideal stepping stone towards fault-tolerance. In Bell sampling, we measure two copies of a state prepared by a quantum circuit in the transversal Bell basis. We show that the Bell samples are classically intractable to produce and at the same time constitute what we call a circuit shadow: from the Bell samples we can efficiently extract information about the quantum circuit preparing the state, as well as diagnose circuit errors. In addition to known properties that can be efficiently extracted from Bell samples, we give two new and efficient protocols, a test for the depth of the circuit and an algorithm to estimate a lower bound to the number of T gates in the circuit. With some additional measurements, our algorithm learns a full description of states prepared by circuits with low T-count.

}, url = {https://arxiv.org/abs/2306.00083}, author = {Dominik Hangleiter and Michael Gullans} } @article {3360, title = {Bounds on Autonomous Quantum Error Correction}, year = {2023}, month = {8/30/2023}, abstract = {

Autonomous quantum memories are a way to passively protect quantum information using engineered dissipation that creates an \"always-on\&$\#$39;\&$\#$39; decoder. We analyze Markovian autonomous decoders that can be implemented with a wide range of qubit and bosonic error-correcting codes, and derive several upper bounds and a lower bound on the logical error rate in terms of correction and noise rates. For many-body quantum codes, we show that, to achieve error suppression comparable to active error correction, autonomous decoders generally require correction rates that grow with code size. For codes with a threshold, we show that it is possible to achieve faster-than-polynomial decay of the logical error rate with code size by using superlogarithmic scaling of the correction rate. We illustrate our results with several examples. One example is an exactly solvable global dissipative toric code model that can achieve an effective logical error rate that decreases exponentially with the linear lattice size, provided that the recovery rate grows proportionally with the linear lattice size.

}, url = {https://arxiv.org/abs/2308.16233}, author = {Oles Shtanko and Yu-Jie Liu and Simon Lieu and Alexey V. Gorshkov and Victor V. Albert} } @article {3258, title = {Candidate for a passively protected quantum memory in two dimensions}, year = {2023}, month = {3/2/2023}, abstract = {

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a {\textquoteleft}{\textquoteleft}passively protected quantum memory,\&$\#$39;\&$\#$39; defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model, the photonic-Ising model, which appears to passively correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic {\textquoteleft}{\textquoteleft}cat qubits\&$\#$39;\&$\#$39; coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct Z2-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips. We also discuss possible ways to realize the photonic-Ising model.

}, url = {https://arxiv.org/abs/2205.09767}, author = {Simon Lieu and Yu-Jie Liu and Alexey V. Gorshkov} } @article {3410, title = {Clifford operations and homological codes for rotors and oscillators}, year = {2023}, month = {11/13/2023}, abstract = {

We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This n-rotor Clifford group, U(1)n(n+1)/2⋊GLn(Z), is represented by continuous U(1) gates generated by polynomials quadratic in angular momenta, as well as discrete GLn(Z) momentum sign-flip and sum gates. We classify homological rotor error-correcting codes [arXiv:2303.13723] and various rotor states based on equivalence under Clifford operations.
Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes [arXiv:1903.12615].

}, url = {https://arxiv.org/abs/2311.07679}, author = {Yijia Xu and Yixu Wang and Victor V. Albert} } @article {3248, title = {Collision-resolved pressure sensing}, year = {2023}, month = {3/17/2023}, abstract = {

Heat and pressure are ultimately transmitted via quantized degrees of freedom, like gas particles and phonons. While a continuous Brownian description of these noise sources is adequate to model measurements with relatively long integration times, sufficiently precise measurements can resolve the detailed time dependence coming from individual bath-system interactions. We propose the use of nanomechanical devices operated with impulse readout sensitivity around the {\textquoteleft}{\textquoteleft}standard quantum limit\&$\#$39;\&$\#$39; to sense ultra-low gas pressures by directly counting the individual collisions of gas particles on a sensor. We illustrate this in two paradigmatic model systems: an optically levitated nanobead and a tethered membrane system in a phononic bandgap shield.

}, url = {https://arxiv.org/abs/2303.09922}, author = {Daniel S. Barker and Daniel Carney and Thomas W. LeBrun and David C. Moore and Jacob M. Taylor} } @article {3317, title = {Colloquium: Advances in automation of quantum dot devices control}, journal = {Reviews of Modern Physics}, volume = {95}, year = {2023}, month = {2/17/2023}, abstract = {

Arrays of quantum dots (QDs) are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. In such semiconductor quantum systems, devices now have tens of individual electrostatic and dynamical voltages that must be carefully set to localize the system into the single-electron regime and to realize good qubit operational performance. The mapping of requisite QD locations and charges to gate voltages presents a challenging classical control problem. With an increasing number of QD qubits, the relevant parameter space grows sufficiently to make heuristic control unfeasible. In recent years, there has been considerable effort to automate device control that combines script-based algorithms with machine learning (ML) techniques. In this Colloquium, a comprehensive overview of the recent progress in the automation of QD device control is presented, with a particular emphasis on silicon- and GaAs-based QDs formed in two-dimensional electron gases. Combining physics-based modeling with modern numerical optimization and ML has proven effective in yielding efficient, scalable control. Further integration of theoretical, computational, and experimental efforts with computer science and ML holds vast potential in advancing semiconductor and other platforms for quantum computing.

}, doi = {10.1103/revmodphys.95.011006}, url = {https://arxiv.org/abs/2112.09362}, author = {Justyna P. Zwolak and Jacob M. Taylor} } @article {3311, title = {Colloquium: Quantum and Classical Discrete Time Crystals}, year = {2023}, month = {5/15/2023}, abstract = {

The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. We focus on the breaking of ergodicity as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the AC Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there exists a diverse array of strategies to stabilize time crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits will be reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.

}, url = {https://arxiv.org/abs/2305.08904}, author = {Michael P. Zaletel and Mikhail Lukin and Christopher Monroe and Chetan Nayak and Frank Wilczek and Norman Y. Yao} } @article {3353, title = {Complexity and order in approximate quantum error-correcting codes}, year = {2023}, month = {10/7/2023}, abstract = {

We establish rigorous connections between quantum circuit complexity and approximate quantum error correction (AQEC) properties, covering both all-to-all and geometric scenarios including lattice systems. To this end, we introduce a type of code parameter that we call subsystem variance, which is closely related to the optimal AQEC precision. Our key finding is that if the subsystem variance is below an O(k/n) threshold then any state in the code subspace must obey certain circuit complexity lower bounds, which identify nontrivial {\textquoteleft}{\textquoteleft}phases\&$\#$39;\&$\#$39; of codes. Based on our results, we propose O(k/n) as a boundary between subspaces that should and should not count as AQEC codes. This theory of AQEC provides a versatile framework for understanding the quantum complexity and order of many-body quantum systems, offering new insights for wide-ranging physical scenarios, in particular topological order and critical quantum systems which are of outstanding importance in many-body and high energy physics. We observe from various different perspectives that roughly O(1/n) represents a common, physically significant {\textquoteleft}{\textquoteleft}scaling threshold\&$\#$39;\&$\#$39; of subsystem variance for features associated with nontrivial quantum order.

}, url = {https://arxiv.org/abs/2310.04710}, author = {Jinmin Yi and Weicheng Ye and Daniel Gottesman and Zi-Wen Liu} } @article {3415, title = {Compressed gate characterization for quantum devices with time-correlated noise}, year = {2023}, month = {12/22/2023}, abstract = {

As quantum devices make steady progress towards intermediate scale and fault-tolerant quantum computing, it is essential to develop rigorous and efficient measurement protocols that account for known sources of noise. Most existing quantum characterization protocols such as gate set tomography and randomized benchmarking assume the noise acting on the qubits is Markovian. However, this assumption is often not valid, as for the case of 1/f charge noise or hyperfine nuclear spin noise. Here, we present a general framework for quantum process tomography (QPT) in the presence of time-correlated noise. We further introduce fidelity benchmarks that quantify the relative strength of different sources of Markovian and non-Markovian noise. As an application of our method, we perform a comparative theoretical and experimental analysis of silicon spin qubits. We first develop a detailed noise model that accounts for the dominant sources of noise and validate the model against experimental data. Applying our framework for time-correlated QPT, we find that the number of independent parameters needed to characterize one and two-qubit gates can be compressed by 10x and 100x, respectively, when compared to the fully generic case. These compressions reduce the amount of tomographic measurements needed in experiment, while also significantly speeding up numerical simulations of noisy quantum circuit dynamics compared to time-dependent Hamiltonian simulation. Using this compressed noise model, we find good agreement between our theoretically predicted process fidelities and two qubit interleaved randomized benchmarking fidelities of 99.8\% measured in recent experiments on silicon spin qubits. More broadly, our formalism can be directly extended to develop efficient and scalable tuning protocols for high-fidelity control of large-arrays of quantum devices with non-Markovian noise.

}, url = {https://arxiv.org/abs/2307.14432}, author = {Michael Gullans and M. Caranti and A. R. Mills and J. R. Petta} } @article {3367, title = {Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits}, journal = {Physical Review B}, volume = {108}, year = {2023}, month = {8/17/2023}, abstract = {

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry\&$\#$39;s non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a \"spin-sharpening transition.\" On one side is a phase in which the measurements can efficiently identify the system\&$\#$39;s total spin quantum number; on the other side is a phase in which measurements cannot.

}, doi = {10.1103/physrevb.108.054307}, url = {https://arxiv.org/abs/2305.13356}, author = {Shayan Majidy and Utkarsh Agrawal and Sarang Gopalakrishnan and Andrew C. Potter and Romain Vasseur and Nicole Yunger Halpern} } @article {3396, title = {Data Needs and Challenges of Quantum Dot Devices Automation: Workshop Report}, year = {2023}, month = {12/21/2023}, abstract = {

Gate-defined quantum dots are a promising candidate system to realize scalable, coupled qubit systems and serve as a fundamental building block for quantum computers. However, present-day quantum dot devices suffer from imperfections that must be accounted for, which hinders the characterization, tuning, and operation process. Moreover, with an increasing number of quantum dot qubits, the relevant parameter space grows sufficiently to make heuristic control infeasible. Thus, it is imperative that reliable and scalable autonomous tuning approaches are developed. In this report, we outline current challenges in automating quantum dot device tuning and operation with a particular focus on datasets, benchmarking, and standardization. We also present ideas put forward by the quantum dot community on how to overcome them.

}, doi = {https://doi.org/10.48550/arXiv.2312.14322}, url = {https://arxiv.org/abs/2312.14322}, author = {Justyna P. Zwolak and Jacob M. Taylor and Reed Andrews and Jared Benson and Garnett Bryant and Donovan Buterakos and Anasua Chatterjee and Sankar Das Sarma and Mark A. Eriksson and Eli{\v s}ka Greplov{\'a} and Michael Gullans and Fabian Hader and Tyler J. Kovach and Pranav S. Mundada and Mick Ramsey and Torbjoern Rasmussen and Brandon Severin and Anthony Sigillito and Brennan Undseth and Brian Weber} } @article {3074, title = {Decoherence from Long-Range Forces in Atom Interferometry}, journal = {Phys. Rev. A }, volume = {107}, year = {2023}, month = {3/17/2023}, doi = {https://doi.org/10.1103/PhysRevA.107.033319}, url = {https://arxiv.org/abs/2205.03006}, author = {Jonathan Kunjummen and Daniel Carney and Jacob M. Taylor} } @article {3421, title = {Digital quantum simulation of NMR experiments}, journal = {Science Advances}, volume = {9}, year = {2023}, month = {11/29/2023}, abstract = {

Simulations of nuclear magnetic resonance (NMR) experiments can be an important tool for extracting information about molecular structure and optimizing experimental protocols but are often intractable on classical computers for large molecules such as proteins and for protocols such as zero-field NMR. We demonstrate the first quantum simulation of an NMR spectrum, computing the zero-field spectrum of the methyl group of acetonitrile using four qubits of a trapped-ion quantum computer. We reduce the sampling cost of the quantum simulation by an order of magnitude using compressed sensing techniques. We show how the intrinsic decoherence of NMR systems may enable the zero-field simulation of classically hard molecules on relatively near-term quantum hardware and discuss how the experimentally demonstrated quantum algorithm can be used to efficiently simulate scientifically and technologically relevant solid-state NMR experiments on more mature devices. Our work opens a practical application for quantum computation.

}, issn = {2375-2548}, doi = {10.1126/sciadv.adh2594}, url = {https://arxiv.org/abs/2109.13298}, author = {Seetharam, Kushal and Biswas, Debopriyo and Noel, Crystal and Risinger, Andrew and Zhu, Daiwei and Katz, Or and Chattopadhyay, Sambuddha and Cetina, Marko and Monroe, Christopher and Demler, Eugene and Sels, Dries} } @article {3426, title = {The discrete adiabatic quantum linear system solver has lower constant factors than the randomized adiabatic solver}, year = {2023}, month = {12/12/2023}, abstract = {

The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number κ and the allowable error ϵ [PRX Quantum \textbf{3}, 0403003 (2022)]. That work was based on the discrete adiabatic theorem, and worked out an explicit constant factor for an upper bound on the complexity. Here we show via numerical testing on random matrices that the constant factor is in practice about 1,500 times smaller than the upper bound found numerically in the previous results. That means that this approach is far more efficient than might naively be expected from the upper bound. In particular, it is over an order of magnitude more efficient than using a randomised approach from [arXiv:2305.11352] that claimed to be more efficient.

}, url = {https://arxiv.org/abs/2312.07690}, author = {Pedro C. S. Costa and Dong An and Ryan Babbush and Dominic Berry} } @article {3318, title = {DiVincenzo-like criteria for autonomous quantum machines}, year = {2023}, month = {7/17/2023}, abstract = {

Controlled quantum machines have matured significantly. A natural next step is to grant them autonomy, freeing them from timed external control. For example, autonomy could unfetter quantum computers from classical control wires that heat and decohere them; and an autonomous quantum refrigerator recently reset superconducting qubits to near their ground states, as is necessary before a computation. What conditions are necessary for realizing useful autonomous quantum machines? Inspired by recent quantum thermodynamics and chemistry, we posit conditions analogous to DiVincenzo\&$\#$39;s criteria for quantum computing. Our criteria are intended to foment and guide the development of useful autonomous quantum machines.

}, url = {https://arxiv.org/abs/2307.08739}, author = {Jos{\'e} Antonio Mar{\'\i}n Guzm{\'a}n and Paul Erker and Simone Gasparinetti and Marcus Huber and Nicole Yunger Halpern} } @article {3307, title = {Effect of non-unital noise on random circuit sampling}, year = {2023}, month = {6/28/2023}, abstract = {

In this work, drawing inspiration from the type of noise present in real hardware, we study the output distribution of random quantum circuits under practical non-unital noise sources with constant noise rates. We show that even in the presence of unital sources like the depolarizing channel, the distribution, under the combined noise channel, never resembles a maximally entropic distribution at any depth. To show this, we prove that the output distribution of such circuits never anticoncentrates \— meaning it is never too \"flat\" \— regardless of the depth of the circuit. This is in stark contrast to the behavior of noiseless random quantum circuits or those with only unital noise, both of which anticoncentrate at sufficiently large depths. As consequences, our results have interesting algorithmic implications on both the hardness and easiness of noisy random circuit sampling, since anticoncentration is a critical property exploited by both state-of-the-art classical hardness and easiness results.

}, url = {https://arxiv.org/abs/2306.16659}, author = {Bill Fefferman and Soumik Ghosh and Michael Gullans and Kohdai Kuroiwa and Kunal Sharma} } @article {3265, title = {Efficient learning of ground \& thermal states within phases of matter}, year = {2023}, month = {1/30/2023}, abstract = {

We consider two related tasks: (a) estimating a parameterisation of a given Gibbs state and expectation values of Lipschitz observables on this state; and (b) learning the expectation values of local observables within a thermal or quantum phase of matter. In both cases, we wish to minimise the number of samples we use to learn these properties to a given precision.
For the first task, we develop new techniques to learn parameterisations of classes of systems, including quantum Gibbs states of non-commuting Hamiltonians with exponential decay of correlations and the approximate Markov property. We show it is possible to infer the expectation values of all extensive properties of the state from a number of copies that not only scales polylogarithmically with the system size, but polynomially in the observable\&$\#$39;s locality -- an exponential improvement. This set of properties includes expected values of quasi-local observables and entropies.\ \ For the second task, we develop efficient algorithms for learning observables in a phase of matter of a quantum system. By exploiting the locality of the Hamiltonian, we show that M local observables can be learned with probability 1\−δ to precision ϵ with using only N=O(log(Mδ)epolylog(ϵ\−1)) samples -- an exponential improvement on the precision over previous bounds. Our results apply to both families of ground states of Hamiltonians displaying local topological quantum order, and thermal phases of matter with exponential decay of correlations. In addition, our sample complexity applies to the worse case setting whereas previous results only applied on average.
Furthermore, we develop tools of independent interest, such as robust shadow tomography algorithms, Gibbs approximations to ground states, and generalisations of transportation cost inequalities for Gibbs states.

}, url = {https://arxiv.org/abs/2301.12946}, author = {Emilio Onorati and Cambyse Rouz{\'e} and Daniel Stilck Fran{\c c}a and James D. Watson} } @article {3256, title = {Error Mitigation Thresholds in Noisy Quantum Circuits}, year = {2023}, month = {2/8/2023}, abstract = {

Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the performance of such strategies when the noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the existence of an error mitigation threshold for random spatially local circuits in spatial dimensions D\≥2: characterization disorder below the threshold rate allows for error mitigation up to times that scale with the number of qubits. For one-dimensional circuits, by contrast, mitigation fails at an O(1) time for any imperfection in the characterization of disorder. We discuss implications for tests of quantum computational advantage, fault-tolerant probes of measurement-induced phase transitions, and quantum algorithms in near-term devices.

}, url = {https://arxiv.org/abs/2302.04278}, author = {Pradeep Niroula and Sarang Gopalakrishnan and Michael Gullans} } @article {3394, title = {Evaluating the security of CRYSTALS-Dilithium in the quantum random oracle model}, year = {2023}, month = {12/17/2023}, abstract = {

In the wake of recent progress on quantum computing hardware, the National Institute of Standards and Technology (NIST) is standardizing cryptographic protocols that are resistant to attacks by quantum adversaries. The primary digital signature scheme that NIST has chosen is CRYSTALS-Dilithium. The hardness of this scheme is based on the hardness of three computational problems: Module Learning with Errors (MLWE), Module Short Integer Solution (MSIS), and SelfTargetMSIS. MLWE and MSIS have been well-studied and are widely believed to be secure. However, SelfTargetMSIS is novel and, though classically as hard as MSIS, its quantum hardness is unclear. In this paper, we provide the first proof of the hardness of SelfTargetMSIS via a reduction from MLWE in the Quantum Random Oracle Model (QROM). Our proof uses recently developed techniques in quantum reprogramming and rewinding. A central part of our approach is a proof that a certain hash function, derived from the MSIS problem, is collapsing. From this approach, we deduce a new security proof for Dilithium under appropriate parameter settings. Compared to the only other rigorous security proof for a variant of Dilithium, Dilithium-QROM, our proof has the advantage of being applicable under the condition q = 1 mod 2n, where q denotes the modulus and n the dimension of the underlying algebraic ring. This condition is part of the original Dilithium proposal and is crucial for the efficient implementation of the scheme. We provide new secure parameter sets for Dilithium under the condition q = 1 mod 2n, finding that our public key sizes and signature sizes are about 2.5 to 2.8 times larger than those of Dilithium-QROM for the same security levels.

}, url = {https://arxiv.org/abs/2312.16619}, author = {Kelsey A. Jackson and Carl Miller and Daochen Wang} } @article {3261, title = {Ever more optimized simulations of fermionic systems on a quantum computer}, year = {2023}, month = {3/6/2023}, abstract = {

Despite using a novel model of computation, quantum computers break down programs into elementary gates. Among such gates, entangling gates are the most expensive. In the context of fermionic simulations, we develop a suite of compilation and optimization techniques that massively reduce the entangling-gate counts. We exploit the well-studied non-quantum optimization algorithms to achieve up to 24\% savings over the state of the art for several small-molecule simulations, with no loss of accuracy or hidden costs. Our methodologies straightforwardly generalize to wider classes of near-term simulations of the ground state of a fermionic system or real-time simulations probing dynamical properties of a fermionic system.\ 

}, url = {https://arxiv.org/abs/2303.03460}, author = {Qingfeng Wang and Ze-Pei Cian and Ming Li and Igor L. Markov and Yunseong Nam} } @article {3316, title = {Experimental Observation of Thermalization with Noncommuting Charges}, journal = {PRX Quantum}, volume = {4}, year = {2023}, month = {4/28/2023}, abstract = {

Quantum simulators have recently enabled experimental observations of quantum many-body systems\&$\#$39; internal thermalization. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined particle number - in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6-21 spins in an approximate microcanonical subspace, a generalization of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, whose predictions can now be tested.

}, doi = {10.1103/prxquantum.4.020318}, url = {https://arxiv.org/abs/2202.04652}, author = {Florian Kranzl and Aleksander Lasek and Manoj K. Joshi and Amir Kalev and Rainer Blatt and Christian F. Roos and Nicole Yunger Halpern} } @article {3348, title = {A family of permutationally invariant quantum codes}, year = {2023}, month = {10/9/2023}, abstract = {

We construct a new family of permutationally invariant codes that correct t Pauli errors for any t\≥1. We also show that codes in the new family correct spontaneous decay errors as well as deletion errors. In many cases the codes in this family are shorter than the best previously known explicit families of permutationally invariant codes both for Pauli errors, deletions, and for the amplitude damping channel. As a separate result, we generalize the conditions for permutationally invariant codes to correct t Pauli errors from the previously known results for t=1 to any number of errors. For small t, these conditions can be used to construct new examples of codes by computer.

}, url = {https://arxiv.org/abs/2310.05358}, author = {Arda Aydin and Max A. Alekseyev and Alexander Barg} } @article {3296, title = {A Family of Quantum Codes with Exotic Transversal Gates}, year = {2023}, month = {5/11/2023}, abstract = {

Recently it has been shown that the binary icosahedral group 2I together with a certain involution forms the most efficient single-qubit universal gate set. In order for this to be viable, one must construct a quantum code with transversal gate group 2I, however, no such code has ever been demonstrated explicitly. We fill this void by constructing a novel family of quantum codes that all have transversal gate group 2I.

}, url = {https://arxiv.org/abs/2305.07023}, author = {Eric Kubischta and Ian Teixeira} } @article {3126, title = {Fat Pointers for Temporal Memory Safety of C}, journal = {Proceedings of the ACM on Programming Languages}, volume = {7}, year = {2023}, month = {3/20/2023}, pages = {316-347}, abstract = {

Temporal memory safety bugs, especially use-after-free and double free bugs, pose a major security threat to C programs. Real-world exploits utilizing these bugs enable attackers to read and write arbitrary memory locations, causing disastrous violations of confidentiality, integrity, and availability. Many previous solutions retrofit temporal memory safety to C, but they all either incur high performance overhead and/or miss detecting certain types of temporal memory safety bugs.
In this paper, we propose a temporal memory safety solution that is both efficient and comprehensive. Specifically, we extend Checked C, a spatially-safe extension to C, with temporally-safe pointers. These are implemented by combining two techniques: fat pointers and dynamic key-lock checks. We show that the fat-pointer solution significantly improves running time and memory overhead compared to the disjoint-metadata approach that provides the same level of protection. With empirical program data and hands-on experience porting real-world applications, we also show that our solution is practical in terms of backward compatibility -- one of the major complaints about fat pointers.

}, keywords = {Cryptography and Security (cs.CR), FOS: Computer and information sciences}, doi = {10.1145/3586038}, url = {https://arxiv.org/abs/2208.12900}, author = {Zhou, Jie and Criswell, John and Hicks, Michael} } @article {3359, title = {Fault-tolerant hyperbolic Floquet quantum error correcting codes}, year = {2023}, month = {9/18/2023}, abstract = {

A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call \"hyperbolic Floquet codes.\" These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for n qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate (1/8+2/n) and have a depth-3 syndrome extraction circuit. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in n. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1\% in a phenomenological noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a [[400,52,8]] code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.

}, url = {https://arxiv.org/abs/2309.10033}, author = {Ali Fahimniya and Hossein Dehghani and Kishor Bharti and Sheryl Mathew and Alicia J. Koll{\'a}r and Alexey V. Gorshkov and Michael Gullans} } @article {3404, title = {Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes}, year = {2023}, month = {11/29/2023}, abstract = {

Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless. In this work, we design a fault-tolerant distillation protocol for preparing encoded states of one-dimensional random circuit codes even when all gates and measurements are subject to noise. This is sufficient for fault-tolerant quantum memory since these encoded states can then be used as ancillas for Steane error correction. We show through numerical simulations that our protocol can correct erasure errors up to an error rate of 2\%. In addition, we also extend results in the code capacity setting by developing a maximum likelihood decoder for depolarizing noise similar to work by Darmawan et al. As in their work, we formulate the decoding problem as a tensor network contraction and show how to contract the network efficiently by exploiting the low-depth structure. Replacing the tensor network with a so-called \&$\#$39;\&$\#$39;tropical\&$\#$39;\&$\#$39; tensor network, we also show how to perform minimum weight decoding. With these decoders, we are able to numerically estimate the depolarizing error threshold of finite-rate random circuit codes and show that this threshold closely matches the hashing bound even when the decoding is sub-optimal.

}, url = {https://arxiv.org/abs/2311.17985}, author = {Jon Nelson and Gregory Bentsen and Steven T. Flammia and Michael Gullans} } @article {3361, title = {Feasibility of a trapped atom interferometer with accelerating optical traps}, year = {2023}, month = {8/23/2023}, abstract = {

In order to increase the measured phase of an atom interferometer and improve its sensitivity, researchers attempt to increase the enclosed space-time area using two methods: creating larger separations between the interferometer arms and having longer evolution times. However, increasing the evolution time reduces the bandwidth that can be sampled, whereas decreasing the evolution time worsens the sensitivity. In this paper, we attempt to address this by proposing a setup for high-bandwidth applications, with improved overall sensitivity. This is realized by accelerating and holding the atoms using optical dipole traps. We find that accelerations of up to 103-105 m/s2 can be achieved using acousto-optic deflectors (AODs) to move the traps. By comparing the sensitivity of our approach to acceleration as a baseline to traditional atom interferometry, we find a substantial improvement to the state of the art. In the limit of appropriate beam and optics stabilization, sensitivities approaching 10\−14 (m/s2)/Hz\−\−\−\√ may be achievable at 1 Hz, while detection at 1 kHz with a sensitivity an order of magnitude better than traditional free-fall atom interferometers is possible with today\&$\#$39;s systems.

}, url = {https://arxiv.org/abs/2308.12246}, author = {Gayathrini Premawardhana and Jonathan Kunjummen and Sarthak Subhankar and Jacob M. Taylor} } @conference {3370, title = {Fixing and Mechanizing the Security Proof of Fiat-Shamir with Aborts and Dilithium}, booktitle = {Advances in Cryptology {\textendash} CRYPTO 2023}, year = {2023}, month = {8/9/2023}, publisher = {Springer Nature Switzerland}, organization = {Springer Nature Switzerland}, address = {Cham}, abstract = {

We extend and consolidate the security justification for the Dilithium signature scheme. In particular, we identify a subtle but crucial gap that appears in several ROM and QROM security proofs for signature schemes that are based on the Fiat-Shamir with aborts paradigm, including Dilithium. The gap lies in the CMA-to-NMA reduction and was uncovered when trying to formalize a variant of the QROM security proof by Kiltz, Lyubashevsky, and Schaffner (Eurocrypt 2018). The gap was confirmed by the authors, and there seems to be no simple patch for it. We provide new, fixed proofs for the affected CMA-to-NMA reduction, both for the ROM and the QROM, and we perform a concrete security analysis for the case of Dilithium to show that the claimed security level is still valid after addressing the gap. Furthermore, we offer a fully mechanized ROM proof for the CMA-security of Dilithium in the EasyCrypt proof assistant. Our formalization includes several new tools and techniques of independent interest for future formal verification results.

}, isbn = {978-3-031-38554-4}, author = {Barbosa, Manuel and Barthe, Gilles and Doczkal, Christian and Don, Jelle and Fehr, Serge and Gr{\'e}goire, Benjamin and Huang, Yu-Hsuan and H{\"u}lsing, Andreas and Lee, Yi and Wu, Xiaodi}, editor = {Handschuh, Helena and Lysyanskaya, Anna} } @article {3408, title = {A general approach to backaction-evading receivers with magnetomechanical and electromechanical sensors}, year = {2023}, month = {11/16/2023}, abstract = {

Today\&$\#$39;s mechanical sensors are capable of detecting extremely weak perturbations while operating near the standard quantum limit. However, further improvements can be made in both sensitivity and bandwidth when we reduce the noise originating from the process of measurement itself -- the quantum-mechanical backaction of measurement -- and go below this \&$\#$39;standard\&$\#$39; limit, possibly approaching the Heisenberg limit. One of the ways to eliminate this noise is by measuring a quantum nondemolition variable such as the momentum in a free-particle system. Here, we propose and characterize theoretical models for direct velocity measurement that utilize traditional electric and magnetic transducer designs to generate a signal while enabling this backaction evasion. We consider the general readout of this signal via electric or magnetic field sensing by creating toy models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme -- voltage or current -- for each mechanical detector configuration implies access to either the position or velocity of the mechanical sub-system. This in turn suggests a path forward for key fundamental physics experiments such as the direct detection of dark matter particles.

}, url = {https://arxiv.org/abs/2311.09587}, author = {Brittany Richman and Sohitri Ghosh and Daniel Carney and Gerard Higgins and Peter Shawhan and C. J. Lobb and Jacob M. Taylor} } @article {3419, title = {General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory}, journal = {Quantum}, volume = {7}, year = {2023}, month = {12/14/2023}, pages = {1213}, abstract = {

With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple (bosonic and fermionic) quantum numbers with non-trivial functional coefficients. In particular, we analyze diagonalization of Hamiltonian terms using a singular-value decomposition technique, and discuss how the achieved diagonal unitaries in the digitized time-evolution operator can be implemented. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions, for which a complete quantum-resource analysis within different computational models is presented. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories. The example chosen further demonstrates the importance of adopting efficient theoretical formulations: it is shown that an explicitly gauge-invariant formulation using loop, string, and hadron degrees of freedom simplifies the algorithms and lowers the cost compared with the standard formulations based on angular-momentum as well as the Schwinger-boson degrees of freedom. The loop-string-hadron formulation further retains the non-Abelian gauge symmetry despite the inexactness of the digitized simulation, without the need for costly controlled operations. Such theoretical and algorithmic considerations are likely to be essential in quantumly simulating other complex theories of relevance to nature.

}, issn = {2521-327X}, doi = {10.22331/q-2023-12-20-1213}, url = {https://arxiv.org/abs/2212.14030}, author = {Zohreh Davoudi and Shaw, Alexander F. and Stryker, Jesse R.} } @article {3428, title = {Generalized Hybrid Search and Applications to Blockchain and Hash Function Security}, year = {2023}, month = {11/7/2023}, abstract = {

In this work we first examine the hardness of solving various search problems by hybrid quantum-classical strategies, namely, by algorithms that have both quantum and classical capabilities. We then construct a hybrid quantum-classical search algorithm and analyze its success probability. Regarding the former, for search problems that are allowed to have multiple solutions and in which the input is sampled according to arbitrary distributions we establish their hybrid quantum-classical query complexities -- i.e., given a fixed number of classical and quantum queries, determine what is the probability of solving the search task. At a technical level, our results generalize the framework for hybrid quantum-classical search algorithms proposed by Rosmanis. Namely, for an arbitrary distribution D on Boolean functions, the probability an algorithm equipped with τc classical and τq quantum queries succeeds in finding a preimage of 1 for a function sampled from D is at most νD\⋅(2τc\−\−\√+2τq+1)2, where νD captures the average (over D) fraction of preimages of 1. As applications of our hardness results, we first revisit and generalize the security of the Bitcoin protocol called the Bitcoin backbone, to a setting where the adversary has both quantum and classical capabilities, presenting a new hybrid honest majority condition necessary for the protocol to properly operate. Secondly, we examine the generic security of hash functions against hybrid adversaries. Regarding our second contribution, we design a hybrid algorithm which first spends all of its classical queries and in the second stage runs a {\textquoteleft}{\textquoteleft}modified Grover\&$\#$39;\&$\#$39; where the initial state depends on the distribution D. We show how to analyze its success probability for arbitrary target distributions and, importantly, its optimality for the uniform and the Bernoulli distribution cases.

}, url = {arXiv:2311.03723}, author = {Alexandru Cojocaru and Juan Garay and Fang Song} } @article {3356, title = {Hamiltonians whose low-energy states require $\Omega(n)$ T gates}, year = {2023}, month = {10/2/2023}, abstract = {

The recent resolution of the NLTS Conjecture [ABN22] establishes a prerequisite to the Quantum PCP (QPCP) Conjecture through a novel use of newly-constructed QLDPC codes [LZ22]. Even with NLTS now solved, there remain many independent and unresolved prerequisites to the QPCP Conjecture, such as the NLSS Conjecture of [GL22]. In this work we focus on a specific and natural prerequisite to both NLSS and the QPCP Conjecture, namely, the existence of local Hamiltonians whose low-energy states all require ω(logn) T gates to prepare. In fact, we prove a stronger result which is not necessarily implied by either conjecture: we construct local Hamiltonians whose low-energy states require Ω(n) T gates. Following a previous work [CCNN23], we further show that our procedure can be applied to the NLTS Hamiltonians of [ABN22] to yield local Hamiltonians whose low-energy states require both Ω(logn)-depth and Ω(n) T gates to prepare. Our results utilize a connection between T-count and stabilizer groups, which was recently applied in the context of learning low T-count states [GIKL23a, GIKL23b, GIKL23c].

}, url = {https://arxiv.org/abs/2310.01347}, author = {Nolan J. Coble and Matthew Coudron and Jon Nelson and Seyed Sajjad Nezhadi} } @article {3305, title = {High-Energy Collision of Quarks and Hadrons in the Schwinger Model: From Tensor Networks to Circuit QED}, year = {2023}, month = {7/5/2023}, abstract = {

With the aim of studying nonperturbative out-of-equilibrium dynamics of high-energy particle collisions on quantum simulators, we investigate the scattering dynamics of lattice quantum electrodynamics in 1+1 dimensions. Working in the bosonized formulation of the model, we propose an analog circuit-QED implementation that is native to the platform, requires minimal ingredients and approximations, and enables practical schemes for particle wave-packet preparation and evolution. Furthermore, working in the thermodynamic limit, we use uniform-matrix-product-state tensor networks to construct multi-particle wave-packet states, evolve them in time, and detect outgoing particles post collision. This facilitates the numerical simulation of scattering experiments in both confined and deconfined regimes of the model at different energies, giving rise to rich phenomenology, including inelastic production of quark and meson states, meson disintegration, and dynamical string formation and breaking. We obtain elastic and inelastic scattering cross sections, together with time-resolved momentum and position distributions of the outgoing particles. This study highlights the role of classical and quantum simulation in enhancing our understanding of scattering processes in quantum field theories in real time.

}, url = {https://arxiv.org/abs/2307.02522}, author = {Ron Belyansky and Seth Whitsitt and Niklas Mueller and Ali Fahimniya and Elizabeth R. Bennewitz and Zohreh Davoudi and Alexey V. Gorshkov} } @article {3423, title = {Improved Digital Quantum Simulation by Non-Unitary Channels}, year = {2023}, month = {7/24/2023}, abstract = {

Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the randomization of Suzuki-Trotter product formulas have been shown to be a powerful approach to reducing the errors of quantum simulation and lowering the gate count. In this paper, we study the performance of non-unitary simulation channels and consider the error structure of channels constructed from a weighted average of unitary circuits. We show that averaging over just a few simulation circuits can significantly reduce the Trotterization error for both single-step short-time and multi-step long-time simulations. We focus our analysis on two approaches for constructing circuit ensembles for averaging: (i) permuting the order of the terms in the Hamiltonian and (ii) applying a set of global symmetry transformations. We compare our analytical error bounds to empirical performance and show that empirical error reduction surpasses our analytical estimates in most cases. Finally, we test our method on an IonQ trapped-ion quantum computer accessed via the Amazon Braket cloud platform, and benchmark the performance of the averaging approach.

}, url = {https://arxiv.org/abs/2307.13028}, author = {W. Gong and Yaroslav Kharkov and Minh C. Tran and Przemyslaw Bienias and Alexey V. Gorshkov} } @article {3422, title = {Lattice quantum chromodynamics at large isospin density: 6144 pions in a box}, year = {2023}, month = {7/27/2023}, abstract = {

We present an algorithm to compute correlation functions for systems with the quantum numbers of many identical mesons from lattice quantum chromodynamics (QCD). The algorithm is numerically stable and allows for the computation of n-pion correlation functions for n\∈{1,\…,N} using a single N\×N matrix decomposition, improving on previous algorithms. We apply the algorithm to calculations of correlation functions with up to 6144 π+s using two ensembles of gauge field configurations generated with quark masses corresponding to a pion mass mπ=170 MeV and spacetime volumes of (4.43\×8.8) fm4 and (5.83\×11.6) fm4. We also discuss statistical techniques for the analysis of such systems, in which the correlation functions vary over many orders of magnitude. In particular, we observe that the many-pion correlation functions are well approximated by log-normal distributions, allowing the extraction of the energies of these systems. Using these energies, the large-isospin-density, zero-baryon-density region of the QCD phase diagram is explored. A peak is observed in the energy density at an isospin chemical potential μI\∼1.5mπ, signalling the transition into a Bose-Einstein condensed phase. The isentropic speed of sound in the medium is seen to exceed the ideal-gas (conformal) limit (c2s\≤1/3) over a wide range of chemical potential before falling towards the asymptotic expectation at μI\∼15mπ. These, and other thermodynamic observables, indicate that the isospin chemical potential must be large for the system to be well described by an ideal gas or perturbative QCD.

}, url = {https://arxiv.org/abs/2307.15014}, author = {Ryan Abbott and William Detmold and Fernando Romero-L{\'o}pez and Zohreh Davoudi and Marc Illa and Assumpta Parre{\~n}o and Robert J. Perry and Phiala E. Shanahan and Michael L. Wagman} } @article {3267, title = {Linear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost}, journal = {Phys. Rev. Lett.}, volume = {131}, year = {2023}, month = {10/13/2023}, abstract = {

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation (QSVT). The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.

}, doi = {https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.131.150603}, url = {https://arxiv.org/abs/2303.01029}, author = {Dong An and Jin-Peng Liu and Lin Lin} } @article {3252, title = {Local Hamiltonians with no low-energy stabilizer states}, year = {2023}, month = {2/28/2023}, abstract = {

The recently-defined No Low-energy Sampleable States (NLSS) conjecture of Gharibian and Le Gall [GL22] posits the existence of a family of local Hamiltonians where all states of low-enough constant energy do not have succinct representations allowing perfect sampling access. States that can be prepared using only Clifford gates (i.e. stabilizer states) are an example of sampleable states, so the NLSS conjecture implies the existence of local Hamiltonians whose low-energy space contains no stabilizer states. We describe families that exhibit this requisite property via a simple alteration to local Hamiltonians corresponding to CSS codes. Our method can also be applied to the recent NLTS Hamiltonians of Anshu, Breuckmann, and Nirkhe [ABN22], resulting in a family of local Hamiltonians whose low-energy space contains neither stabilizer states nor trivial states. We hope that our techniques will eventually be helpful for constructing Hamiltonians which simultaneously satisfy NLSS and NLTS.

}, url = {https://arxiv.org/abs/2302.14755}, author = {Nolan J. Coble and Matthew Coudron and Jon Nelson and Seyed Sajjad Nezhadi} } @article {3401, title = {Logical quantum processor based on reconfigurable atom arrays}, journal = {Nature}, year = {2023}, month = {12/7/2023}, issn = {1476-4687}, doi = {10.1038/s41586-023-06927-3}, url = {https://arxiv.org/abs/2312.03982}, author = {Bluvstein, Dolev and Evered, Simon J. and Geim, Alexandra A. and Li, Sophie H. and Zhou, Hengyun and Manovitz, Tom and Ebadi, Sepehr and Cain, Madelyn and Kalinowski, Marcin and Dominik Hangleiter and Ataides, J. Pablo Bonilla and Maskara, Nishad and Cong, Iris and Gao, Xun and Rodriguez, Pedro Sales and Karolyshyn, Thomas and Semeghini, Giulia and Michael Gullans and Greiner, Markus and Vuletic, Vladan and Lukin, Mikhail D.} } @article {3185, title = {Lower Bounds on Quantum Annealing Times}, journal = {Phys. Rev. Lett.}, volume = {130}, year = {2023}, month = {4/5/2023}, abstract = {

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p-spin model. Our bounds demonstrate that these schedules have optimal scaling. Our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1103/PhysRevLett.130.140601}, url = {https://arxiv.org/abs/2210.15687}, author = {Garc{\'\i}a-Pintos, Luis Pedro and Brady, Lucas T. and Bringewatt, Jacob and Liu, Yi-Kai} } @article {3247, title = {The maximum refractive index of an atomic crystal - from quantum optics to quantum chemistry}, year = {2023}, month = {3/20/2023}, abstract = {

All known optical materials have an index of refraction of order unity. Despite the tremendous implications that an ultrahigh index could have for optical technologies, little research has been done on why the refractive index of materials is universally small, and whether this observation is fundamental. Here, we investigate the index of an ordered arrangement of atoms, as a function of atomic density. At dilute densities, this problem falls into the realm of quantum optics, where atoms do not interact with one another except via the scattering of light. On the other hand, when the lattice constant becomes comparable to the Bohr radius, the electronic orbitals begin to overlap, giving rise to quantum chemistry. We present a minimal model that allows for a unifying theory of index spanning these two regimes. A key aspect is the treatment of multiple light scattering, which can be highly non-perturbative over a large density range, and which is the reason that conventional theories of the index break down. In the quantum optics regime, we show that ideal light-matter interactions can have a single-mode nature, allowing for a purely real refractive index that grows with density as (N/V)1/3. At the onset of quantum chemistry, we show how two physical mechanisms (excited electron tunneling dynamics and the buildup of electronic density-density correlations) can open up inelastic or spatial multi-mode light scattering processes, which ultimately reduce the index back to order unity while introducing absorption. Around the onset of chemistry, our theory predicts that ultrahigh index (n\∼30), low-loss materials could in principle be allowed by the laws of nature.\ 

}, url = {https://arxiv.org/abs/2303.10998}, author = {Francesco Andreoli and Bennet Windt and Stefano Grava and Gian Marcello Andolina and Michael Gullans and Alexander A. High and Darrick E. Chang} } @article {3395, title = {Microwave signal processing using an analog quantum reservoir computer}, year = {2023}, month = {12/26/2023}, abstract = {

Quantum reservoir computing (QRC) has been proposed as a paradigm for performing machine learning with quantum processors where the training is efficient in the number of required runs of the quantum processor and takes place in the classical domain, avoiding the issue of barren plateaus in parameterized-circuit quantum neural networks. It is natural to consider using a quantum processor based on superconducting circuits to classify microwave signals that are analog -- continuous in time. However, while theoretical proposals of analog QRC exist, to date QRC has been implemented using circuit-model quantum systems -- imposing a discretization of the incoming signal in time, with each time point input by executing a gate operation. In this paper we show how a quantum superconducting circuit comprising an oscillator coupled to a qubit can be used as an analog quantum reservoir for a variety of classification tasks, achieving high accuracy on all of them. Our quantum system was operated without artificially discretizing the input data, directly taking in microwave signals. Our work does not attempt to address the question of whether QRCs could provide a quantum computational advantage in classifying pre-recorded classical signals. However, beyond illustrating that sophisticated tasks can be performed with a modest-size quantum system and inexpensive training, our work opens up the possibility of achieving a different kind of advantage than a purely computational advantage: superconducting circuits can act as extremely sensitive detectors of microwave photons; our work demonstrates processing of ultra-low-power microwave signals in our superconducting circuit, and by combining sensitive detection with QRC processing within the same system, one could achieve a quantum sensing-computational advantage, i.e., an advantage in the overall analysis of microwave signals comprising just a few photons.

}, url = {https://arxiv.org/abs/2312.16166}, author = {Alen Senanian and Sridhar Prabhu and Vladimir Kremenetski and Saswata Roy and Yingkang Cao and Jeremy Kline and Tatsuhiro Onodera and Logan G. Wright and Xiaodi Wu and Valla Fatemi and Peter L. McMahon} } @article {3369, title = {Minimum-entanglement protocols for function estimation}, journal = {Physical Review Research}, volume = {5}, year = {2023}, month = {9/29/2023}, abstract = {

We derive a family of optimal protocols, in the sense of saturating the quantum Cram{\'e}r-Rao bound, for measuring a linear combination of d field amplitudes with quantum sensor networks, a key subprotocol of general quantum sensor network applications. We demonstrate how to select different protocols from this family under various constraints. Focusing primarily on entanglement-based constraints, we prove the surprising result that highly entangled states are not necessary to achieve optimality in many cases. Specifically, we prove necessary and sufficient conditions for the existence of optimal protocols using at most k-partite entanglement. We prove that the protocols which satisfy these conditions use the minimum amount of entanglement possible, even when given access to arbitrary controls and ancilla. Our protocols require some amount of time-dependent control, and we show that a related class of time-independent protocols fail to achieve optimal scaling for generic functions.

}, doi = {10.1103/physrevresearch.5.033228}, url = {https://arxiv.org/abs/2110.07613}, author = {Adam Ehrenberg and Jacob Bringewatt and Alexey V. Gorshkov} } @article {3055, title = {Non-Abelian eigenstate thermalization hypothesis}, journal = {Phys. Rev. Lett.}, volume = {130}, year = {2023}, month = {4/6/2023}, chapter = {140402}, abstract = {

The eigenstate thermalization hypothesis (ETH) explains why chaotic quantum many-body systems thermalize internally if the Hamiltonian lacks symmetries. If the Hamiltonian conserves one quantity (\"charge\"), the ETH implies thermalization within a charge sector -- in a microcanonical subspace. But quantum systems can have charges that fail to commute with each other and so share no eigenbasis; microcanonical subspaces may not exist. Furthermore, the Hamiltonian will have degeneracies, so the ETH need not imply thermalization. We adapt the ETH to noncommuting charges by positing a non-Abelian ETH and invoking the approximate microcanonical subspace introduced in quantum thermodynamics. Illustrating with SU(2) symmetry, we apply the non-Abelian ETH in calculating local observables\&$\#$39; time-averaged and thermal expectation values. In many cases, we prove, the time average thermalizes. However, we also find cases in which, under a physically reasonable assumption, the time average converges to the thermal average unusually slowly as a function of the global-system size. This work extends the ETH, a cornerstone of many-body physics, to noncommuting charges, recently a subject of intense activity in quantum thermodynamics.

}, keywords = {FOS: Physical sciences, High Energy Physics - Theory (hep-th), Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.140402}, url = {https://arxiv.org/abs/2206.05310}, author = {Murthy, Chaitanya and Babakhani, Arman and Iniguez, Fernando and Srednicki, Mark and Nicole Yunger Halpern} } @article {3194, title = {Non-Abelian symmetry can increase entanglement entropy}, journal = {Physical Review B}, volume = {107}, year = {2023}, month = {1/3/2023}, abstract = {

The pillars of quantum theory include entanglement and operators\&$\#$39; failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian {\textquoteleft}{\textquoteleft}charges\&$\#$39;\&$\#$39;). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum thermodynamics to many-body physics, we quantify the effects of charges\&$\#$39; noncommutation -- of a symmetry\&$\#$39;s non-Abelian nature -- on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that the noncommuting-charge case has more entanglement. Hence charges\&$\#$39; noncommutation can promote entanglement.

}, doi = {10.1103/physrevb.107.045102}, url = {https://arxiv.org/abs/2209.14303}, author = {Shayan Majidy and Aleksander Lasek and David A. Huse and Nicole Yunger Halpern} } @article {3371, title = {Nonclassical Advantage in Metrology Established via Quantum Simulations of Hypothetical Closed Timelike Curves}, journal = {Phys. Rev. Lett.}, volume = {131}, year = {2023}, month = {10/12/2023}, pages = {150202}, abstract = {

We construct a metrology experiment in which the metrologist can sometimes amend the input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical. Nevertheless, they can be simulated probabilistically by quantum-teleportation circuits. We leverage such simulations to pinpoint a counterintuitive nonclassical advantage achievable with entanglement. Our experiment echoes a common information-processing task: A metrologist must prepare probes to input into an unknown quantum interaction. The goal is to infer as much information per probe as possible. If the input is optimal, the information gained per probe can exceed any value achievable classically. The problem is that, only after the interaction does the metrologist learn which input would have been optimal. The metrologist can attempt to change the input by effectively teleporting the optimal input back in time, via entanglement manipulation. The effective time travel sometimes fails but ensures that, summed over trials, the metrologist\’s winnings are positive. Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.

}, doi = {10.1103/PhysRevLett.131.150202}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.131.150202}, author = {Arvidsson-Shukur, David R. M. and McConnell, Aidan G. and Yunger Halpern, Nicole} } @article {3366, title = {Noncommuting conserved charges in quantum thermodynamics and beyond}, journal = {Nature Reviews Physics}, year = {2023}, month = {9/7/2023}, abstract = {

Thermodynamic systems typically conserve quantities (\"charges\") such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on observables\&$\#$39; failure to commute. How do noncommuting charges affect thermodynamic phenomena? This question, upon arising at the intersection of quantum information theory and thermodynamics, spread recently across many-body physics. Charges\&$\#$39; noncommutation has been found to invalidate derivations of the thermal state\&$\#$39;s form, decrease entropy production, conflict with the eigenstate thermalization hypothesis, and more. This Perspective surveys key results in, opportunities for, and work adjacent to the quantum thermodynamics of noncommuting charges. Open problems include a conceptual puzzle: Evidence suggests that noncommuting charges may hinder thermalization in some ways while enhancing thermalization in others.

}, doi = {10.1038/s42254-023-00641-9}, url = {https://arxiv.org/abs/2306.00054}, author = {Shayan Majidy and William F. Braasch and Aleksander Lasek and Twesh Upadhyaya and Amir Kalev and Nicole Yunger Halpern} } @article {3358, title = {Non-equilibrium critical scaling and universality in a quantum simulator}, year = {2023}, month = {9/19/2023}, abstract = {

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-ion resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents. While a generic quench can lead to thermal critical behaviour, we find that a second quench from one critical state to another (i.e. a double quench) results in critical behaviour that does not have an equilibrium counterpart. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond the equilibrium paradigm.

}, url = {https://arxiv.org/abs/2309.10856}, author = {A. De and P. Cook and K. Collins and W. Morong and D. Paz and P. Titum and G. Pagano and Alexey V. Gorshkov and M. Maghrebi and C. Monroe} } @article {3398, title = {Non-invertible symmetry-protected topological order in a group-based cluster state}, year = {2023}, month = {12/14/2023}, abstract = {

Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic level. We introduce a one-dimensional stabilizer Hamiltonian composed of group-based Pauli operators whose ground state is a G\×Rep(G)-symmetric state: the G cluster state introduced in Brell, New Journal of Physics 17, 023029 (2015) [at this http URL]. We show that this state lies in a symmetry-protected topological (SPT) phase protected by G\×Rep(G) symmetry, distinct from the symmetric product state by a duality argument. We identify several signatures of SPT order, namely protected edge modes, string order parameters, and topological response. We discuss how G cluster states may be used as a universal resource for measurement-based quantum computation, explicitly working out the case where G is a semidirect product of abelian groups.

}, url = {https://arxiv.org/abs/2312.09272}, author = {Christopher Fechisin and Nathanan Tantivasadakarn and Victor V. Albert} } @article {3413, title = {Observation of a finite-energy phase transition in a one-dimensional quantum simulator}, year = {2023}, month = {10/30/2023}, abstract = {

One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out that a phase transition in 1D can occur in the presence of long-range interactions, but an experimental realization has so far not been achieved due to the requirement to both prepare equilibrium states and realize sufficiently long-range interactions. Here we report on the first experimental demonstration of a finite-energy phase transition in 1D. We use the simple observation that finite-energy states can be prepared by time-evolving product initial states and letting them thermalize under the dynamics of a many-body Hamiltonian. By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system. We observe a ferromagnetic equilibrium phase transition as well as a crossover from a low-energy polarized paramagnet to a high-energy unpolarized paramagnet in a system of up to 23 spins, in excellent agreement with numerical simulations. Our work demonstrates the ability of quantum simulators to realize and study previously inaccessible phases at finite energy density.

}, url = {https://arxiv.org/abs/2310.19869}, author = {Alexander Schuckert and Or Katz and Lei Feng and Eleanor Crane and Arinjoy De and Mohammad Hafezi and Alexey V. Gorshkov and Christopher Monroe} } @article {3315, title = {Page curves and typical entanglement in linear optics}, journal = {Quantum}, volume = {7}, year = {2023}, month = {5/18/2023}, pages = {1017}, abstract = {

Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the R{\'e}nyi-2 Page curve (the average R{\'e}nyi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the R{\'e}nyi-2 entropy by studying its variance. Using the aforementioned results for the R{\'e}nyi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity.

}, doi = {10.22331/q-2023-05-23-1017}, url = {https://arxiv.org/abs/2209.06838}, author = {Joseph T. Iosue and Adam Ehrenberg and Dominik Hangleiter and Abhinav Deshpande and Alexey V. Gorshkov} } @article {3271, title = {Parallel self-testing of EPR pairs under computational assumptions}, year = {2023}, month = {3/29/2023}, abstract = {

Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ϵ must be poly(N,ϵ)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.

}, url = {https://arxiv.org/abs/2201.13430}, author = {Honghao Fu and Daochen Wang and Qi Zhao} } @article {3272, title = {Parallel self-testing of EPR pairs under computational assumptions}, year = {2023}, month = {3/29/2023}, abstract = {

Self-testing is a fundamental feature of quantum mechanics that allows a classical verifier to force untrusted quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under computational assumptions. In this work, we generalize their results to give the first parallel self-test of N EPR pairs and measurements on them in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ϵ must be poly(N,ϵ)-close to being honest in the appropriate sense. In particular, our protocol can test any distribution over tensor products of computational or Hadamard basis measurements, making it suitable for applications such as device-independent quantum key distribution under computational assumptions. Moreover, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a single cloud quantum computer using only classical communication.

}, url = {https://arxiv.org/abs/2201.13430}, author = {Honghao Fu and Daochen Wang and Qi Zhao} } @article {3262, title = {Parallelization techniques for quantum simulation of fermionic systems}, year = {2023}, month = {3/30/2023}, abstract = {

Mapping fermionic operators to qubit operators is an essential step for simulating fermionic systems on a quantum computer. We investigate how the choice of such a mapping interacts with the underlying qubit connectivity of the quantum processor to enable (or impede) parallelization of the resulting Hamiltonian-simulation algorithm. It is shown that this problem can be mapped to a path coloring problem on a graph constructed from the particular choice of encoding fermions onto qubits and the fermionic interactions onto paths. The basic version of this problem is called the weak coloring problem. Taking into account the fine-grained details of the mapping yields what is called the strong coloring problem, which leads to improved parallelization performance. A variety of illustrative analytical and numerical examples are presented to demonstrate the amount of improvement for both weak and strong coloring-based parallelizations. Our results are particularly important for implementation on near-term quantum processors where minimizing circuit depth is necessary for algorithmic feasibility.

}, url = {https://arxiv.org/abs/2207.12470}, author = {Jacob Bringewatt and Zohreh Davoudi} } @article {3364, title = {Partial Syndrome Measurement for Hypergraph Product Codes}, year = {2023}, month = {9/26/2023}, abstract = {

Hypergraph product codes are a promising avenue to achieving fault-tolerant quantum computation with constant overhead. When embedding these and other constant-rate qLDPC codes into 2D, a significant number of nonlocal connections are required, posing difficulties for some quantum computing architectures. In this work, we introduce a fault-tolerance scheme that aims to alleviate the effects of implementing this nonlocality by measuring generators acting on spatially distant qubits less frequently than those which do not. We investigate the performance of a simplified version of this scheme, where the measured generators are randomly selected. When applied to hypergraph product codes and a modified small-set-flip decoding algorithm, we prove that for a sufficiently high percentage of generators being measured, a threshold still exists. We also find numerical evidence that the logical error rate is exponentially suppressed even when a large constant fraction of generators are not measured.

}, url = {https://arxiv.org/abs/2306.17122}, author = {Noah Berthusen and Daniel Gottesman} } @article {3405, title = {Projective toric designs, difference sets, and quantum state designs}, year = {2023}, month = {11/22/2023}, abstract = {

Trigonometric cubature rules of degree t are sets of points on the torus over which sums reproduce integrals of degree t monomials over the full torus. They can be thought of as t-designs on the torus. Motivated by the projective structure of quantum mechanics, we develop the notion of t-designs on the projective torus, which, surprisingly, have a much more restricted structure than their counterparts on full tori. We provide various constructions of these projective toric designs and prove some bounds on their size and characterizations of their structure. We draw connections between projective toric designs and a diverse set of mathematical objects, including difference and Sidon sets from the field of additive combinatorics, symmetric, informationally complete positive operator valued measures (SIC-POVMs) and complete sets of mutually unbiased bases (MUBs) (which are conjectured to relate to finite projective geometry) from quantum information theory, and crystal ball sequences of certain root lattices. Using these connections, we prove bounds on the maximal size of dense Btmodm sets. We also use projective toric designs to construct families of quantum state designs. Finally, we discuss many open questions about the properties of these projective toric designs and how they relate to other questions in number theory, geometry, and quantum information.

}, url = {https://arxiv.org/abs/2311.13479}, author = {Joseph T. Iosue and T. C. Mooney and Adam Ehrenberg and Alexey V. Gorshkov} } @article {3427, title = {Provably Efficient Learning of Phases of Matter via Dissipative Evolutions}, year = {2023}, month = {11/13/2023}, abstract = {

The combination of quantum many-body and machine learning techniques has recently proved to be a fertile ground for new developments in quantum computing. Several works have shown that it is possible to classically efficiently predict the expectation values of local observables on all states within a phase of matter using a machine learning algorithm after learning from data obtained from other states in the same phase. However, existing results are restricted to phases of matter such as ground states of gapped Hamiltonians and Gibbs states that exhibit exponential decay of correlations. In this work, we drop this requirement and show how it is possible to learn local expectation values for all states in a phase, where we adopt the Lindbladian phase definition by Coser \& P{\'e}rez-Garc{\'\i}a [Coser \& P{\'e}rez-Garc{\'\i}a, Quantum 3, 174 (2019)], which defines states to be in the same phase if we can drive one to other rapidly with a local Lindbladian. This definition encompasses the better-known Hamiltonian definition of phase of matter for gapped ground state phases, and further applies to any family of states connected by short unitary circuits, as well as non-equilibrium phases of matter, and those stable under external dissipative interactions. Under this definition, we show that N=O(log(n/δ)2polylog(1/ϵ)) samples suffice to learn local expectation values within a phase for a system with n qubits, to error ϵ with failure probability δ. This sample complexity is comparable to previous results on learning gapped and thermal phases, and it encompasses previous results of this nature in a unified way. Furthermore, we also show that we can learn families of states which go beyond the Lindbladian definition of phase, and we derive bounds on the sample complexity which are dependent on the mixing time between states under a Lindbladian evolution.

}, url = {arXiv:2311.07506 Search...}, author = {Emilio Onorati and Cambyse Rouz{\'e} and Daniel Stilck Fran{\c c}a and James D. Watson} } @article {3314, title = {Qafny: Quantum Program Verification Through Type-guided Classical Separation Logic}, year = {2023}, month = {7/12/2023}, abstract = {

Formal verification has been proven instrumental to ensure that quantum programs implement their specifications but often requires a significant investment of time and labor. To address this challenge, we present Qafny, an automated proof system designed for verifying quantum programs. At its core, Qafny uses a type-guided quantum proof system that translates quantum operations to classical array operations. By modeling these operations as proof rules within a classical separation logic framework, Qafny provides automated support for the reasoning process that would otherwise be tedious and time-consuming. We prove the soundness and completeness of our proof system and implement a prototype compiler that transforms Qafny programs both into the Dafny programming language and into executable quantum circuits. Using Qafny, we demonstrate how to efficiently verify prominent quantum algorithms, including quantum-walk algorithms, Grover\&$\#$39;s search algorithm, and Shor\&$\#$39;s factoring algorithm, with significantly reduced human efforts.

}, url = {https://arxiv.org/abs/2211.06411}, author = {Liyi Li and Mingwei Zhu and Rance Cleaveland and Yi Lee and Le Chang and Xiaodi Wu} } @article {2448, title = {Quantum algorithm for estimating volumes of convex bodies}, journal = {ACM Transactions on Quantum Computing}, volume = {4}, year = {2023}, month = {4/2023}, chapter = {20}, abstract = {

Estimating the volume of a convex body is a central problem in convex geometry and can be viewed as a continuous version of counting. We present a quantum algorithm that estimates the volume of an n-dimensional convex body within multiplicative error ε using O~(n3.5+n2.5/ε) queries to a membership oracle and O~(n5.5+n4.5/ε) additional arithmetic operations. For comparison, the best known classical algorithm uses O~(n4+n3/ε2) queries and O~(n6+n5/ε2) additional arithmetic operations. To the best of our knowledge, this is the first quantum speedup for volume estimation. Our algorithm is based on a refined framework for speeding up simulated annealing algorithms that might be of independent interest. This framework applies in the setting of \"Chebyshev cooling\", where the solution is expressed as a telescoping product of ratios, each having bounded variance. We develop several novel techniques when implementing our framework, including a theory of continuous-space quantum walks with rigorous bounds on discretization error.

}, url = {https://arxiv.org/abs/1908.03903}, author = {Shouvanik Chakrabarti and Andrew M. Childs and Shih-Han Hung and Tongyang Li and Chunhao Wang and Xiaodi Wu} } @article {3402, title = {Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters}, year = {2023}, month = {12/6/2023}, abstract = {

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

}, url = {https://arxiv.org/abs/2312.03916}, author = {Dong An and Andrew M. Childs and Lin Lin} } @article {3269, title = {Quantum Algorithms and the Power of Forgetting}, journal = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, volume = {251}, year = {2023}, pages = {37:1--37:22}, abstract = {

The so-called welded tree problem provides an example of a black-box problem that can be solved exponentially faster by a quantum walk than by any classical algorithm [Andrew M. Childs et al., 2003]. Given the name of a special entrance vertex, a quantum walk can find another distinguished exit vertex using polynomially many queries, though without finding any particular path from entrance to exit. It has been an open problem for twenty years whether there is an efficient quantum algorithm for finding such a path, or if the path-finding problem is hard even for quantum computers. We show that a natural class of efficient quantum algorithms provably cannot find a path from entrance to exit. Specifically, we consider algorithms that, within each branch of their superposition, always store a set of vertex labels that form a connected subgraph including the entrance, and that only provide these vertex labels as inputs to the oracle. While this does not rule out the possibility of a quantum algorithm that efficiently finds a path, it is unclear how an algorithm could benefit by deviating from this behavior. Our no-go result suggests that, for some problems, quantum algorithms must necessarily forget the path they take to reach a solution in order to outperform classical computation.

}, isbn = {978-3-95977-263-1}, doi = {10.4230/LIPIcs.ITCS.2023.37}, url = {https://drops.dagstuhl.de/opus/volltexte/2023/17540}, author = {Andrew M. Childs and Coudron, Matthew and Gilani, Amin Shiraz}, editor = {Tauman Kalai, Yael} } @article {3400, title = {Quantum Algorithms for Simulating Nuclear Effective Field Theories}, year = {2023}, month = {12/8/2023}, abstract = {

Quantum computers offer the potential to simulate nuclear processes that are classically intractable. With the goal of understanding the necessary quantum resources, we employ state-of-the-art Hamiltonian-simulation methods, and conduct a thorough algorithmic analysis, to estimate the qubit and gate costs to simulate low-energy effective field theories (EFTs) of nuclear physics. In particular, within the framework of nuclear lattice EFT, we obtain simulation costs for the leading-order pionless and pionful EFTs. We consider both static pions represented by a one-pion-exchange potential between the nucleons, and dynamical pions represented by relativistic bosonic fields coupled to non-relativistic nucleons. We examine the resource costs for the tasks of time evolution and energy estimation for physically relevant scales. We account for model errors associated with truncating either long-range interactions in the one-pion-exchange EFT or the pionic Hilbert space in the dynamical-pion EFT, and for algorithmic errors associated with product-formula approximations and quantum phase estimation. Our results show that the pionless EFT is the least costly to simulate and the dynamical-pion theory is the costliest. We demonstrate how symmetries of the low-energy nuclear Hamiltonians can be utilized to obtain tighter error bounds on the simulation algorithm. By retaining the locality of nucleonic interactions when mapped to qubits, we achieve reduced circuit depth and substantial parallelization. We further develop new methods to bound the algorithmic error for classes of fermionic Hamiltonians that preserve the number of fermions, and demonstrate that reasonably tight Trotter error bounds can be achieved by explicitly computing nested commutators of Hamiltonian terms. This work highlights the importance of combining physics insights and algorithmic advancement in reducing quantum-simulation costs.

}, url = {https://arxiv.org/abs/2312.05344}, author = {James D. Watson and Jacob Bringewatt and Alexander F. Shaw and Andrew M. Childs and Alexey V. Gorshkov and Zohreh Davoudi} } @article {3411, title = {A quantum central path algorithm for linear optimization}, year = {2023}, month = {11/7/2023}, abstract = {

We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive linearizations of the perturbed KKT conditions, we perform a single simulation working directly with the nonlinear complementarity equations. Combining our approach with iterative refinement techniques, we obtain an exact solution to a linear optimization problem involving m constraints and n variables using at most O((m+n)nnz(A)κ(M)L\⋅polylog(m,n,κ(M))) elementary gates and O(nnz(A)L) classical arithmetic operations, where nnz(A) is the total number of non-zero elements found in the constraint matrix, L denotes binary input length of the problem data, and κ(M) is a condition number that depends only on the problem data.

}, url = {https://arxiv.org/abs/2311.03977}, author = {Brandon Augustino and Jiaqi Leng and Giacomo Nannicini and Tam{\'a}s Terlaky and Xiaodi Wu} } @article {3368, title = {Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory}, year = {2023}, month = {10/6/2023}, abstract = {

Strongly-coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with classical-simulation methods, but is a natural application of quantum simulation. To demonstrate this prospect, we quantum compute non-equal time correlation functions and perform entanglement tomography of non-equilibrium states of a simple lattice gauge theory, the Schwinger model, using a trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term devices, a recently-predicted [Zache et al., Phys. Rev. Lett. 122, 050403 (2019)] dynamical quantum phase transition in this model is studied by preparing, quenching, and tracking the subsequent non-equilibrium dynamics in three ways: i) overlap echos signaling dynamical transitions, ii) non-equal time correlation functions with an underlying topological nature, and iii) the entanglement structure of non-equilibrium states, including entanglement Hamiltonians. These results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer, and are a first step toward investigating topological phenomena in nuclear and high-energy physics using quantum technologies.

}, url = {https://arxiv.org/abs/2210.03089}, author = {Niklas Mueller and Joseph Carolan and Andrew Connelly and Zohreh Davoudi and Eugene F. Dumitrescu and K{\"u}bra Yeter-Aydeniz} } @article {3250, title = {Quantum Hamiltonian Descent}, year = {2023}, month = {3/2/2023}, abstract = {

Gradient descent is a fundamental algorithm in both theory and practice for continuous optimization. Identifying its quantum counterpart would be appealing to both theoretical and practical quantum applications. A conventional approach to quantum speedups in optimization relies on the quantum acceleration of intermediate steps of classical algorithms, while keeping the overall algorithmic trajectory and solution quality unchanged. We propose Quantum Hamiltonian Descent (QHD), which is derived from the path integral of dynamical systems referring to the continuous-time limit of classical gradient descent algorithms, as a truly quantum counterpart of classical gradient methods where the contribution from classically-prohibited trajectories can significantly boost QHD\&$\#$39;s performance for non-convex optimization. Moreover, QHD is described as a Hamiltonian evolution efficiently simulatable on both digital and analog quantum computers. By embedding the dynamics of QHD into the evolution of the so-called Quantum Ising Machine (including D-Wave and others), we empirically observe that the D-Wave-implemented QHD outperforms a selection of state-of-the-art gradient-based classical solvers and the standard quantum adiabatic algorithm, based on the time-to-solution metric, on non-convex constrained quadratic programming instances up to 75 dimensions. Finally, we propose a \"three-phase picture\" to explain the behavior of QHD, especially its difference from the quantum adiabatic algorithm.

}, url = {https://arxiv.org/abs/2303.01471}, author = {Jiaqi Leng and Ethan Hickman and Joseph Li and Xiaodi Wu} } @article {3362, title = {Quantum Lego Expansion Pack: Enumerators from Tensor Networks}, year = {2023}, month = {8/9/2023}, abstract = {

We provide the first tensor network method for computing quantum weight enumerator polynomials in the most general form. As a corollary, if a quantum code has a known tensor network construction of its encoding map, our method produces an algorithm that computes its distance. For non-(Pauli)-stabilizer codes, this constitutes the current best algorithm for computing the code distance. For degenerate stabilizer codes, it can provide up to an exponential speed up compared to the current methods. We also introduce a few novel applications of different weight enumerators. In particular, for any code built from the quantum lego method, we use enumerators to construct its (optimal) decoders under any i.i.d. single qubit or qudit error channels and discuss their applications for computing logical error rates. As a proof of principle, we perform exact analyses of the deformed surface codes, the holographic pentagon code, and the 2d Bacon-Shor code under (biased) Pauli noise and limited instances of coherent error at sizes that are inaccessible by brute force.

}, url = {https://arxiv.org/abs/2308.05152}, author = {ChunJun Cao and Michael Gullans and Brad Lackey and Zitao Wang} } @article {3355, title = {Quantum Sensing with Erasure Qubits}, year = {2023}, month = {10/2/2023}, abstract = {

The dominant noise in an \"erasure qubit\" is an erasure -- a type of error whose occurrence and location can be detected. Erasure qubits have potential to reduce the overhead associated with fault tolerance. To date, research on erasure qubits has primarily focused on quantum computing and quantum networking applications. Here, we consider the applicability of erasure qubits to quantum sensing and metrology. We show theoretically that, for the same level of noise, an erasure qubit acts as a more precise sensor or clock compared to its non-erasure counterpart. We experimentally demonstrate this by artificially injecting either erasure errors (in the form of atom loss) or dephasing errors into a differential optical lattice clock comparison, and observe enhanced precision in the case of erasure errors for the same injected error rate. Similar benefits of erasure qubits to sensing can be realized in other quantum platforms like Rydberg atoms and superconducting qubits

}, url = {https://arxiv.org/abs/2310.01512}, author = {Pradeep Niroula and Jack Dolde and Xin Zheng and Jacob Bringewatt and Adam Ehrenberg and Kevin C. Cox and Jeff Thompson and Michael Gullans and Shimon Kolkowitz and Alexey V. Gorshkov} } @article {3479, title = {Quantum Simulating Nature{\textquoteright}s Fundamental Fields}, journal = {Nature Reviews Physics}, volume = {5}, year = {2023}, month = {4/9/2024}, pages = {420{\textendash}432}, abstract = {

Simulating key static and dynamic properties of matter -- from creation in the Big Bang to evolution into sub-atomic and astrophysical environments -- arising from the underlying fundamental quantum fields of the Standard Model and their effective descriptions, lies beyond the capabilities of classical computation alone. Advances in quantum technologies have improved control over quantum entanglement and coherence to the point where robust simulations are anticipated to be possible in the foreseeable future. We discuss the emerging area of quantum simulations of Standard-Model physics, challenges that lie ahead, and opportunities for progress in the context of nuclear and high-energy physics.

}, issn = {2522-5820}, doi = {https://doi.org/10.1038/s42254-023-00599-8}, url = {https://arxiv.org/abs/2404.06298}, author = {Christian W. Bauer and Zohreh Davoudi and Natalie Klco and Martin J. Savage} } @article {3425, title = {Quantum simulations of time travel can power nonclassical metrology}, journal = {Phys. Rev. Lett.}, volume = {131}, year = {2023}, month = {11/3/2023}, abstract = {

We construct a metrology experiment in which the metrologist can sometimes amend her input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical. Nevertheless, they can be simulated probabilistically by quantum-teleportation circuits. We leverage such simulations to pinpoint a counterintuitive nonclassical advantage achievable with entanglement. Our experiment echoes a common information-processing task: A metrologist must prepare probes to input into an unknown quantum interaction. The goal is to infer as much information per probe as possible. If the input is optimal, the information gained per probe can exceed any value achievable classically. The problem is that, only after the interaction does the metrologist learn which input would have been optimal. The metrologist can attempt to change her input by effectively teleporting the optimal input back in time, via entanglement manipulation. The effective time travel sometimes fails but ensures that, summed over trials, the metrologist\&$\#$39;s winnings are positive. Our Gedankenexperiment demonstrates that entanglement can generate operational advantages forbidden in classical chronology-respecting theories.

}, doi = {https://doi.org/10.48550/arXiv.2207.07666}, url = {arXiv:2207.07666}, author = {David R. M. Arvidsson-Shukur and Aidan G. McConnell and Nicole Yunger Halpern} } @article {3417, title = {Quantum spherical codes}, year = {2023}, month = {12/7/2023}, abstract = {

We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, obtaining multimode extensions of the cat codes that can outperform previous constructions while requiring a similar type of overhead. Our polytope-based cat codes consist of sets of points with large separation that at the same time form averaging sets known as spherical designs. We also recast concatenations of CSS codes with cat codes as quantum spherical codes, revealing a new way to autonomously protect against dephasing noise

}, url = {https://arxiv.org/abs/2302.11593}, author = {Shubham P. Jain and Joseph T. Iosue and Alexander Barg and Victor V. Albert} } @article {3397, title = {Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions}, year = {2023}, month = {12/14/2023}, abstract = {

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.

}, url = {https://arxiv.org/abs/2312.09733}, author = {Yuri Alexeev and Maximilian Amsler and Paul Baity and Marco Antonio Barroca and Sanzio Bassini and Torey Battelle and Daan Camps and David Casanova and Young jai Choi and Frederic T. Chong and Charles Chung and Chris Codella and Antonio D. Corcoles and James Cruise and Alberto Di Meglio and Jonathan Dubois and Ivan Duran and Thomas Eckl and Sophia Economou and Stephan Eidenbenz and Bruce Elmegreen and Clyde Fare and Ismael Faro and Cristina Sanz Fern{\'a}ndez and Rodrigo Neumann Barros Ferreira and Keisuke Fuji and Bryce Fuller and Laura Gagliardi and Giulia Galli and Jennifer R. Glick and Isacco Gobbi and Pranav Gokhale and Salvador de la Puente Gonzalez and Johannes Greiner and Bill Gropp and Michele Grossi and Emmanuel Gull and Burns Healy and Benchen Huang and Travis S. Humble and Nobuyasu Ito and Artur F. Izmaylov and Ali Javadi-Abhari and Douglas Jennewein and Shantenu Jha and Liang Jiang and Barbara Jones and Wibe Albert de Jong and Petar Jurcevic and William Kirby and Stefan Kister and Masahiro Kitagawa and Joel Klassen and Katherine Klymko and Kwangwon Koh and Masaaki Kondo and Doga Murat Kurkcuoglu and Krzysztof Kurowski and Teodoro Laino and Ryan Landfield and Matt Leininger and Vicente Leyton-Ortega and Ang Li and Meifeng Lin and Junyu Liu and Nicolas Lorente and Andre Luckow and Simon Martiel and Francisco Martin-Fernandez and Margaret Martonosi and Claire Marvinney and Arcesio Castaneda Medina and Dirk Merten and Antonio Mezzacapo and Kristel Michielsen and Abhishek Mitra and Tushar Mittal and Kyungsun Moon and Joel Moore and Mario Motta and Young-Hye Na and Yunseong Nam and Prineha Narang and Yu-ya Ohnishi and Daniele Ottaviani and Matthew Otten and Scott Pakin and Vincent R. Pascuzzi and Ed Penault and Tomasz Piontek and Jed Pitera and Patrick Rall and Gokul Subramanian Ravi and Niall Robertson and Matteo Rossi and Piotr Rydlichowski and Hoon Ryu and Georgy Samsonidze and Mitsuhisa Sato and Nishant Saurabh and Vidushi Sharma and Kunal Sharma and Soyoung Shin and George Slessman and Mathias Steiner and Iskandar Sitdikov and In-Saeng Suh and Eric Switzer and Wei Tang and Joel Thompson and Synge Todo and Minh Tran and Dimitar Trenev and Christian Trott and Huan-Hsin Tseng and Esin Tureci and David Garc{\'\i}a Valinas and Sofia Vallecorsa and Christopher Wever and Konrad Wojciechowski and Xiaodi Wu and Shinjae Yoo and Nobuyuki Yoshioka and Victor Wen-zhe Yu and Seiji Yunoki and Sergiy Zhuk and Dmitry Zubarev} } @article {3412, title = {A quantum-classical performance separation in nonconvex optimization}, year = {2023}, month = {11/1/2023}, abstract = {

In this paper, we identify a family of nonconvex continuous optimization instances, each d-dimensional instance with 2d local minima, to demonstrate a quantum-classical performance separation. Specifically, we prove that the recently proposed Quantum Hamiltonian Descent (QHD) algorithm [Leng et al., arXiv:2303.01471] is able to solve any d-dimensional instance from this family using O\˜(d3) quantum queries to the function value and O\˜(d4) additional 1-qubit and 2-qubit elementary quantum gates. On the other side, a comprehensive empirical study suggests that representative state-of-the-art classical optimization algorithms/solvers (including Gurobi) would require a super-polynomial time to solve such optimization instances.

}, url = {https://arxiv.org/abs/2311.00811}, author = {Jiaqi Leng and Yufan Zheng and Xiaodi Wu} } @article {3295, title = {Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison}, journal = {PRX Quantum}, volume = {4}, year = {2023}, month = {6/14/2023}, pages = {020342}, abstract = {

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP)\ \–\ stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog or Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing and formulate qudit versions of GKP-stabilizer codes.

}, doi = {10.1103/PRXQuantum.4.020342}, url = {https://arxiv.org/abs/2209.04573}, author = {Xu, Yijia and Wang, Yixu and Kuo, En-Jui and Victor V. Albert} } @article {3251, title = {Random Pulse Sequences for Qubit Noise Spectroscopy}, year = {2023}, month = {3/2/2023}, abstract = {

Qubit noise spectroscopy is an important tool for the experimental investigation of open quantum systems. However, conventional techniques for implementing noise spectroscopy are time-consuming, because they require multiple measurements of the noise spectral density at different frequencies. Here we describe an alternative method for quickly characterizing the spectral density. Our method utilizes random pulse sequences, with carefully-controlled correlations among the pulses, to measure arbitrary linear functionals of the noise spectrum. Such measurements allow us to estimate k\&$\#$39;th-order moments of the noise spectrum, as well as to reconstruct sparse noise spectra via compressed sensing. Our simulations of the performance of the random pulse sequences on a realistic physical system, self-assembled quantum dots, reveal a speedup of an order of magnitude in extracting the noise spectrum compared to conventional dynamical decoupling approaches.

}, url = {https://arxiv.org/abs/2303.00909}, author = {Kaixin Huang and Demitry Farfurnik and Alireza Seif and Mohammad Hafezi and Yi-Kai Liu} } @article {3429, title = {On the Rational Degree of Boolean Functions and Applications}, year = {2023}, month = {10/12/2023}, abstract = {

We study a natural complexity measure of Boolean functions known as the (exact) rational degree. For total functions f, it is conjectured that rdeg(f) is polynomially related to deg(f), where deg(f) is the Fourier degree. Towards this conjecture, we show that symmetric functions have rational degree at least deg(f)/2 and monotone functions have rational degree at least deg(f)\−\−\−\−\−\√. We observe that both of these lower bounds are tight. In addition, we show that all read-once depth-d Boolean formulae have rational degree at least Ω(deg(f)1/d). Furthermore, we show that almost every Boolean function on n variables has rational degree at least n/2\−O(n\−\−\√).
In contrast to total functions, we exhibit partial functions that witness unbounded separations between rational and approximate degree, in both directions. As a consequence, we show that for quantum computers, post-selection and bounded-error are incomparable resources in the black-box model.

}, url = {arXiv:2310.08004}, author = {Vishnu Iyer and Siddhartha Jain and Matt Kovacs-Deak and Vinayak M. Kumar and Luke Schaeffer and Daochen Wang and Michael Whitmeyer} } @article {3309, title = {Realization of 1D Anyons with Arbitrary Statistical Phase}, year = {2023}, month = {6/2/2023}, abstract = {

Low-dimensional quantum systems can host anyons, particles with exchange statistics that are neither bosonic nor fermionic. Despite indications of a wealth of exotic phenomena, the physics of anyons in one dimension (1D) remains largely unexplored. Here, we realize Abelian anyons in 1D with arbitrary exchange statistics using ultracold atoms in an optical lattice, where we engineer the statistical phase via a density-dependent Peierls phase. We explore the dynamical behavior of two anyons undergoing quantum walks, and observe the anyonic Hanbury Brown-Twiss effect, as well as the formation of bound states without on-site interactions. Once interactions are introduced, we observe spatially asymmetric transport in contrast to the symmetric dynamics of bosons and fermions. Our work forms the foundation for exploring the many-body behavior of 1D anyons.

}, url = {https://arxiv.org/abs/2306.01737}, author = {Joyce Kwan and Perrin Segura and Yanfei Li and Sooshin Kim and Alexey V. Gorshkov and Andr{\'e} Eckardt and Brice Bakkali-Hassani and Markus Greiner} } @article {3518, title = {Secret extraction attacks against obfuscated IQP circuits}, year = {2023}, month = {12/15/2023}, abstract = {

Quantum computing devices can now perform sampling tasks which, according to complexity-theoretic and numerical evidence, are beyond the reach of classical computers. This raises the question of how one can efficiently verify that a quantum computer operating in this regime works as intended. In 2008, Shepherd and Bremner proposed a protocol in which a verifier constructs a unitary from the comparatively easy-to-implement family of so-called IQP circuits, and challenges a prover to execute it on a quantum computer. The challenge problem is designed to contain an obfuscated secret, which can be turned into a statistical test that accepts samples from a correct quantum implementation. It was conjectured that extracting the secret from the challenge problem is NP-hard, so that the ability to pass the test constitutes strong evidence that the prover possesses a quantum device and that it works as claimed. Unfortunately, about a decade later, Kahanamoku-Meyer found an efficient classical secret extraction attack. Bremner, Cheng, and Ji very recently followed up by constructing a wide-ranging generalization of the original protocol. Their IQP Stabilizer Scheme has been explicitly designed to circumvent the known weakness. They also suggested that the original construction can be made secure by adjusting the problem parameters. In this work, we develop a number of secret extraction attacks which are effective against both new approaches in a wide range of problem parameters. The important problem of finding an efficient and reliable verification protocol for sampling-based proofs of quantum supremacy thus remains open.

}, url = {https://arxiv.org/abs/2312.10156}, author = {David Gross and Dominik Hangleiter} } @article {3264, title = {Self-dual quasiperiodic percolation}, journal = {Phys. Rev. E}, volume = {107}, year = {2023}, month = {2/27/2023}, pages = {024137}, abstract = {

How does the percolation transition behave in the absence of quenched randomness? To address this question, we study two nonrandom self-dual quasiperiodic models of square-lattice bond percolation. In both models, the critical point has emergent discrete scale invariance, but none of the additional emergent conformal symmetry of critical random percolation. From the discrete sequences of critical clusters, we find fractal dimensions of Df=1.911943(1) and Df=1.707234(40) for the two models, significantly different from Df=91/48=1.89583... of random percolation. The critical exponents ν, determined through a numerical study of cluster sizes and wrapping probabilities on a torus, are also well below the ν=4/3 of random percolation. While these new models do not appear to belong to a universality class, they demonstrate how the removal of randomness can fundamentally change the critical behavior.

}, doi = {10.1103/PhysRevE.107.024137}, url = {https://arxiv.org/abs/2206.11290}, author = {Sommers, Grace M. and Michael Gullans and Huse, David A.} } @article {2859, title = {Shadow process tomography of quantum channels}, journal = {Phys. Rev. A}, volume = {107}, year = {2023}, month = {4/4/2023}, abstract = {

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scale exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.

}, doi = {https://doi.org/10.1103/PhysRevA.107.042403}, url = {https://arxiv.org/abs/2110.03629}, author = {Jonathan Kunjummen and Minh C. Tran and Daniel Carney and Jacob M. Taylor} } @article {3312, title = {A sharp phase transition in linear cross-entropy benchmarking}, year = {2023}, month = {5/8/2023}, abstract = {

Demonstrations of quantum computational advantage and benchmarks of quantum processors via quantum random circuit sampling are based on evaluating the linear cross-entropy benchmark (XEB). A key question in the theory of XEB is whether it approximates the fidelity of the quantum state preparation. Previous works have shown that the XEB generically approximates the fidelity in a regime where the noise rate per qudit ε satisfies εN<<1 for a system of N qudits and that this approximation breaks down at large noise rates. Here, we show that the breakdown of XEB as a fidelity proxy occurs as a sharp phase transition at a critical value of εN that depends on the circuit architecture and properties of the two-qubit gates, including in particular their entangling power. We study the phase transition using a mapping of average two-copy quantities to statistical mechanics models in random quantum circuit architectures with full or one-dimensional connectivity. We explain the phase transition behavior in terms of spectral properties of the transfer matrix of the statistical mechanics model and identify two-qubit gate sets that exhibit the largest noise robustness.

}, url = {https://arxiv.org/abs/2305.04954}, author = {Brayden Ware and Abhinav Deshpande and Dominik Hangleiter and Pradeep Niroula and Bill Fefferman and Alexey V. Gorshkov and Michael Gullans} } @article {3249, title = {SimuQ: A Domain-Specific Language For Quantum Simulation With Analog Compilation}, year = {2023}, month = {3/5/2023}, abstract = {

Hamiltonian simulation is one of the most promising applications of quantum computing. Recent experimental results suggest that continuous-time analog quantum simulation would be advantageous over gate-based digital quantum simulation in the Noisy Intermediate-Size Quantum (NISQ) machine era. However, programming such analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software, and the only few known examples are all hardware-specific. In this paper, we design and implement SimuQ, the first domain-specific language for Hamiltonian simulation that supports pulse-level compilation to heterogeneous analog quantum simulators. Specifically, in SimuQ, front-end users will specify the target Hamiltonian evolution with a Hamiltonian modeling language, and the programmability of analog simulators is specified through a new abstraction called the abstract analog instruction set by hardware providers. Through a solver-based compilation, SimuQ will generate the pulse-level instruction schedule on the target analog simulator for the desired Hamiltonian evolution, which has been demonstrated on pulse-controlled superconducting (Qiskit Pulse) and neutral-atom (QuEra Bloqade) quantum systems, as well as on normal circuit-based digital quantum machines. Moreover, we also demonstrate the advantage of analog compilation over digital compilation on IBM machines, the use of SimuQ for resource estimation for hypothetical machines, and a scalability test of SimuQ\&$\#$39;s compilation.

}, url = {https://arxiv.org/abs/2303.02775}, author = {Yuxiang Peng and Jacob Young and Pengyu Liu and Xiaodi Wu} } @article {3255, title = {Spin-selective strong light-matter coupling in a 2D hole gas-microcavity system}, year = {2023}, month = {2/12/2023}, abstract = {

The interplay between time-reversal symmetry breaking and strong light-matter coupling in 2D gases brings intriguing aspects to polariton physics. This combination can lead to polarization/spin selective light-matter interaction in the strong coupling regime. In this work, we report such a selective strong light-matter interaction by harnessing a 2D gas in the quantum Hall regime coupled to a microcavity. Specifically, we demonstrate circular-polarization dependence of the vacuum Rabi splitting, as a function of magnetic field and hole density. We provide a quantitative understanding of the phenomenon by modeling the coupling of optical transitions between Landau levels to the microcavity. This method introduces a control tool over the spin degree of freedom in polaritonic semiconductor systems, paving the way for new experimental possibilities in light-matter hybrids.

}, url = {https://arxiv.org/abs/2302.06023}, author = {Daniel G. Suarez-Forero and Deric Weston Session and Mahmoud Jalali Mehrabad and Patrick Knuppel and Stefan Faelt and Werner Wegscheider and Mohammad Hafezi} } @article {3260, title = {On the stability of solutions to Schr{\"o}dinger{\textquoteright}s equation short of the adiabatic limit}, year = {2023}, month = {3/23/2023}, abstract = {

We prove an adiabatic theorem that applies at timescales short of the adiabatic limit. Our proof analyzes the stability of solutions to Schrodinger\&$\#$39;s equation under perturbation. We directly characterize cross-subspace effects of perturbation, which are typically significantly less than suggested by the perturbation\&$\#$39;s operator norm. This stability has numerous consequences: we can (1) find timescales where the solution of Schrodinger\&$\#$39;s equation converges to the ground state of a block, (2) lower bound the convergence to the global ground state by demonstrating convergence to some other known quantum state, (3) guarantee faster convergence than the standard adiabatic theorem when the ground state of the perturbed Hamiltonian (H) is close to that of the unperturbed H, and (4) bound tunneling effects in terms of the global spectral gap when H is {\textquoteleft}{\textquoteleft}stoquastic\&$\#$39;\&$\#$39; (a Z-matrix). Our results apply to quantum annealing protocols with faster convergence than usually guaranteed by a standard adiabatic theorem. Our upper and lower bounds demonstrate that at timescales short of the adiabatic limit, subspace dynamics can dominate over global dynamics. Thus, we see that convergence to particular target states can be understood as the result of otherwise local dynamics.

}, url = {https://arxiv.org/abs/2303.13478}, author = {Jacob Bringewatt and Michael Jarret and T. C. Mooney} } @article {3357, title = {Streaming quantum state purification}, year = {2023}, month = {9/28/2023}, abstract = {

Quantum state purification is the task of recovering a nearly pure copy of an unknown pure quantum state using multiple noisy copies of the state. This basic task has applications to quantum communication over noisy channels and quantum computation with imperfect devices, but has only been studied previously for the case of qubits. We derive an efficient purification procedure based on the swap test for qudits of any dimension, starting with any initial error parameter. Treating the initial error parameter and the dimension as constants, we show that our procedure has sample complexity asymptotically optimal in the final error parameter. Our protocol has a simple recursive structure that can be applied when the states are provided one at a time in a streaming fashion, requiring only a small quantum memory to implement.

}, url = {https://arxiv.org/abs/2309.16387}, author = {Andrew M. Childs and Honghao Fu and Debbie Leung and Zhi Li and Maris Ozols and Vedang Vyas} } @article {3266, title = {Strongly incoherent gravity}, year = {2023}, month = {1/20/2023}, abstract = {

While most fundamental interactions in nature are known to be mediated by quantized fields, the possibility has been raised that gravity may behave differently. Making this concept precise enough to test requires consistent models. Here we construct an explicit example of a theory where a non-entangling version of an arbitrary two-body potential V(r) arises from local measurements and feedback forces. While a variety of such theories exist, our construction causes particularly strong decoherence compared to more subtle approaches. Regardless, expectation values of observables obey the usual classical dynamics, while the interaction generates no entanglement. Applied to the Newtonian potential, this produces a non-relativistic model of gravity with fundamental loss of unitarity. The model contains a pair of free parameters, a substantial range of which is not excluded by observations to date. As an alternative to testing entanglement properties, we show that the entire remaining parameter space can be tested by looking for loss of quantum coherence in small systems like atom interferometers coupled to oscillating source masses.

}, url = {https://arxiv.org/abs/2301.08378}, author = {Daniel Carney and Jacob M. Taylor} } @article {3403, title = {Subsystem CSS codes, a tighter stabilizer-to-CSS mapping, and Goursat{\textquoteright}s Lemma}, year = {2023}, month = {11/29/2023}, abstract = {

The CSS code construction is a powerful framework used to express features of a quantum code in terms of a pair of underlying classical codes. Its subsystem extension allows for similar expressions, but the general case has not been fully explored. Extending previous work of Aly et. al. [quant-ph/0610153], we determine subsystem CSS code parameters, express codewords, and develop a Steane-type decoder using only data from the two underlying classical codes. We show that any subsystem stabilizer code can be {\textquoteleft}{\textquoteleft}doubled\&$\#$39;\&$\#$39; to yield a subsystem CSS code with twice the number of physical, logical, and gauge qudits and up to twice the code distance. This mapping preserves locality and is tighter than the Majorana-based mapping of Bravyi, Leemhuis, and Terhal [New J. Phys. 12 083039 (2010)]. Using Goursat\&$\#$39;s Lemma, we show that every subsystem stabilizer code can be constructed from two nested subsystem CSS codes satisfying certain constraints, and we characterize subsystem stabilizer codes based on the nested codes\&$\#$39; properties.

}, url = {https://arxiv.org/abs/2311.18003}, author = {Michael Liaofan Liu and Nathanan Tantivasadakarn and Victor V. Albert} } @article {3254, title = {Symphony: Expressive Secure Multiparty Computation with Coordination}, journal = {The Art, Science, and Engineering of Programming}, volume = {7}, year = {2023}, month = {2/20/2023}, type = {14}, abstract = {

Context: Secure Multiparty Computation (MPC) refers to a family of cryptographic techniques where mutually untrusting parties may compute functions of their private inputs while revealing only the function output. Inquiry: It can be hard to program MPCs correctly and efficiently using existing languages and frameworks, especially when they require coordinating disparate computational roles. How can we make this easier? Approach: We present Symphony, a new functional programming language for MPCs among two or more parties. Symphony starts from the single-instruction, multiple-data (SIMD) semantics of prior MPC languages, in which each party carries out symmetric responsibilities, and generalizes it using constructs that can coordinate many parties. Symphony introduces **first-class shares** and **first-class party sets** to provide unmatched language-level expressive power with high efficiency. Knowledge: Developing a core formal language called λ-Symphony, we prove that the intuitive, generalized SIMD view of a program coincides with its actual distributed semantics. Thus the programmer can reason about her programs by reading them from top to bottom, even though in reality the program runs in a coordinated fashion, distributed across many machines. We implemented a prototype interpreter for Symphony leveraging multiple cryptographic backends. With it we wrote a variety of MPC programs, finding that Symphony can express optimized protocols that other languages cannot, and that in general Symphony programs operate efficiently. [ full abstract at https://doi.org/10.22152/programming-journal.org/2023/7/14 ]\ 

}, doi = {10.22152/programming-journal.org/2023/7/14}, url = {https://arxiv.org/abs/2302.10076}, author = {Ian Sweet and David Darais and David Heath and William Harris and Ryan Estes and Michael Hicks} } @article {3270, title = {A theory of quantum differential equation solvers: limitations and fast-forwarding}, year = {2023}, month = {3/2/2023}, abstract = {

We study the limitations and fast-forwarding of quantum algorithms for linear ordinary differential equation (ODE) systems with a particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the ODE is inhomogeneous. On the one hand, for generic homogeneous linear ODEs, by proving worst-case lower bounds, we show that quantum algorithms suffer from computational overheads due to two types of {\textquoteleft}{\textquoteleft}non-quantumness\&$\#$39;\&$\#$39;: real part gap and non-normality of the coefficient matrix. We then show that homogeneous ODEs in the absence of both types of {\textquoteleft}{\textquoteleft}non-quantumness\&$\#$39;\&$\#$39; are equivalent to quantum dynamics, and reach the conclusion that quantum algorithms for quantum dynamics work best. We generalize our results to the inhomogeneous case and find that existing generic quantum ODE solvers cannot be substantially improved. To obtain these lower bounds, we propose a general framework for proving lower bounds on quantum algorithms that are amplifiers, meaning that they amplify the difference between a pair of input quantum states. On the other hand, we show how to fast-forward quantum algorithms for solving special classes of ODEs which leads to improved efficiency. More specifically, we obtain quadratic improvements in the evolution time T for inhomogeneous ODEs with a negative semi-definite coefficient matrix, and exponential improvements in both T and the spectral norm of the coefficient matrix for inhomogeneous ODEs with efficiently implementable eigensystems, including various spatially discretized linear evolutionary partial differential equations. We give fast-forwarding algorithms that are conceptually different from existing ones in the sense that they neither require time discretization nor solving high-dimensional linear systems.

}, url = {https://arxiv.org/abs/2211.05246}, author = {Dong An and Jin-Peng Liu and Daochen Wang and Qi Zhao} } @article {3288, title = {Thermally driven quantum refrigerator autonomously resets superconducting qubit}, year = {2023}, month = {5/26/2023}, abstract = {

The first thermal machines steered the industrial revolution, but their quantum analogs have yet to prove useful. Here, we demonstrate a useful quantum absorption refrigerator formed from superconducting circuits. We use it to reset a transmon qubit to a temperature lower than that achievable with any one available bath. The process is driven by a thermal gradient and is autonomous -- requires no external control. The refrigerator exploits an engineered three-body interaction between the target qubit and two auxiliary qudits coupled to thermal environments. The environments consist of microwave waveguides populated with synthesized thermal photons. The target qubit, if initially fully excited, reaches a steady-state excited-level population of 5\×10\−4\±5\×10\−4 (an effective temperature of 23.5~mK) in about 1.6~μs. Our results epitomize how quantum thermal machines can be leveraged for quantum information-processing tasks. They also initiate a path toward experimental studies of quantum thermodynamics with superconducting circuits coupled to propagating thermal microwave fields.

}, url = {https://arxiv.org/abs/2305.16710}, author = {Mohammed Ali Aamir and Paul Jamet Suria and Jos{\'e} Antonio Mar{\'\i}n Guzm{\'a}n and Claudia Castillo-Moreno and Jeffrey M. Epstein and Nicole Yunger Halpern and Simone Gasparinetti} } @article {3418, title = {Thresholds in the Robustness of Error Mitigation in Noisy Quantum Dynamics}, year = {2023}, month = {10/30/2023}, abstract = {

Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the robustness of such strategies when the noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the existence of a threshold in the robustness of error mitigation for random spatially local circuits in spatial dimensions D\≥2: noise characterization disorder below the threshold rate allows for error mitigation up to times that scale with the number of qubits. For one-dimensional circuits, by contrast, mitigation fails at an O(1) time for any imperfection in the characterization of disorder. As a result, error mitigation is only a practical method for sufficiently well-characterized noise. We discuss further implications for tests of quantum computational advantage, fault-tolerant probes of measurement-induced phase transitions, and quantum algorithms in near-term devices.

}, url = {https://arxiv.org/abs/2302.04278}, author = {Pradeep Niroula and Sarang Gopalakrishnan and Michael Gullans} } @article {3206, title = {Time-energy uncertainty relation for noisy quantum metrology}, journal = {PRX Quantum}, volume = {4(4)}, year = {2023}, month = {12/5/2023}, abstract = {

Detection of weak forces and precise measurement of time are two of the many applications of quantum metrology to science and technology. We consider a quantum system initialized in a pure state and whose evolution is goverened by a Hamiltonian H; a measurement can later estimate the time t for which the system has evolved. In this work, we introduce and study a fundamental trade-off which relates the amount by which noise reduces the accuracy of a quantum clock to the amount of information about the energy of the clock that leaks to the environment. Specifically, we consider an idealized scenario in which Alice prepares an initial pure state of the clock, allows the clock to evolve for a time t that is not precisely known, and then transmits the clock through a noisy channel to Bob. The environment (Eve) receives any information that is lost. We prove that Bob\&$\#$39;s loss of quantum Fisher information (QFI) about t is equal to Eve\&$\#$39;s gain of QFI about a complementary energy parameter. We also prove a more general trade-off that applies when Bob and Eve wish to estimate the values of parameters associated with two non-commuting observables. We derive the necessary and sufficient conditions for the accuracy of the clock to be unaffected by the noise. These are a subset of the Knill-Laflamme error-correction conditions; states satisfying these conditions are said to form a metrological code. We provide a scheme to construct metrological codes in the stabilizer formalism. We show that there are metrological codes that cannot be written as a quantum error-correcting code with similar distance in which the Hamiltonian acts as a logical operator, potentially offering new schemes for constructing states that do not lose any sensitivity upon application of a noisy channel. We discuss applications of our results to sensing using a many-body state subject to erasure or amplitude-damping noise.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.4.040336}, url = {https://arxiv.org/abs/2207.13707}, author = {Faist, Philippe and Woods, Mischa P. and Victor V. Albert and Renes, Joseph M. and Eisert, Jens and Preskill, John} } @article {3399, title = {Transition of Anticoncentration in Gaussian Boson Sampling}, year = {2023}, month = {12/13/2023}, abstract = {

Gaussian Boson Sampling is a promising method for experimental demonstrations of quantum advantage because it is easier to implement than other comparable schemes. While most of the properties of Gaussian Boson Sampling are understood to the same degree as for these other schemes, we understand relatively little about the statistical properties of its output distribution. The most relevant statistical property, from the perspective of demonstrating quantum advantage, is the anticoncentration of the output distribution as measured by its second moment. The degree of anticoncentration features in arguments for the complexity-theoretic hardness of Gaussian Boson Sampling, and it is also important to know when using cross-entropy benchmarking to verify experimental performance. In this work, we develop a graph-theoretic framework for analyzing the moments of the Gaussian Boson Sampling distribution. Using this framework, we show that Gaussian Boson Sampling undergoes a transition in anticoncentration as a function of the number of modes that are initially squeezed compared to the number of photons measured at the end of the circuit. When the number of initially squeezed modes scales sufficiently slowly with the number of photons, there is a lack of anticoncentration. However, if the number of initially squeezed modes scales quickly enough, the output probabilities anticoncentrate weakly.

}, url = {https://arxiv.org/abs/2312.08433}, author = {Adam Ehrenberg and Joseph T. Iosue and Abhinav Deshpande and Dominik Hangleiter and Alexey V. Gorshkov} } @article {3308, title = {On the Two-sided Permutation Inversion Problem}, year = {2023}, month = {6/23/2023}, abstract = {

In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This is a fundamental problem in query complexity, and appears in many contexts, particularly cryptography. In this work, we examine the setting in which the oracle allows for quantum queries to both the forward and the inverse direction of the permutation -- except that the challenge value cannot be submitted to the latter. Within that setting, we consider two options for the inversion algorithm: whether it can get quantum advice about the permutation, and whether it must produce the entire preimage (search) or only the first bit (decision). We prove several theorems connecting the hardness of the resulting variations of the inversion problem, and establish a number of lower bounds. Our results indicate that, perhaps surprisingly, the inversion problem does not become significantly easier when the adversary is granted oracle access to the inverse, provided it cannot query the challenge itself.

}, url = {https://arxiv.org/abs/2306.13729}, author = {Gorjan Alagic and Chen Bai and Alexander Poremba and Kaiyan Shi} } @article {3354, title = {An Uncertainty Principle for the Curvelet Transform, and the Infeasibility of Quantum Algorithms for Finding Short Lattice Vectors}, year = {2023}, month = {10/5/2023}, abstract = {

The curvelet transform is a special type of wavelet transform, which is useful for estimating the locations and orientations of waves propagating in Euclidean space. We prove an uncertainty principle that lower-bounds the variance of these estimates, for radial wave functions in n dimensions.
As an application of this uncertainty principle, we show the infeasibility of one approach to constructing quantum algorithms for solving lattice problems, such as the approximate shortest vector problem (approximate-SVP), and bounded distance decoding (BDD). This gives insight into the computational intractability of approximate-SVP, which plays an important role in algorithms for integer programming, and in post-quantum cryptosystems.
In this approach to solving lattice problems, one prepares quantum superpositions of Gaussian-like wave functions centered at lattice points. A key step in this procedure requires finding the center of each Gaussian-like wave function, using the quantum curvelet transform. We show that, for any choice of the Gaussian-like wave function, the error in this step will be above the threshold required to solve BDD and approximate-SVP.

}, url = {https://arxiv.org/abs/2310.03735}, author = {Yi-Kai Liu} } @article {3414, title = {An Uncertainty Principle for the Curvelet Transform, and the Infeasibility of Quantum Algorithms for Finding Short Lattice Vectors}, year = {2023}, month = {11/7/2023}, abstract = {

The curvelet transform is a special type of wavelet transform, which is useful for estimating the locations and orientations of waves propagating in Euclidean space. We prove an uncertainty principle that lower-bounds the variance of these estimates, for radial wave functions in n dimensions.\ \ As an application of this uncertainty principle, we show the infeasibility of one approach to constructing quantum algorithms for solving lattice problems, such as the approximate shortest vector problem (approximate-SVP), and bounded distance decoding (BDD). This gives insight into the computational intractability of approximate-SVP, which plays an important role in algorithms for integer programming, and in post-quantum cryptosystems.
In this approach to solving lattice problems, one prepares quantum superpositions of Gaussian-like wave functions centered at lattice points. A key step in this procedure requires finding the center of each Gaussian-like wave function, using the quantum curvelet transform. We show that, for any choice of the Gaussian-like wave function, the error in this step will be above the threshold required to solve BDD and approximate-SVP.\ \ 

}, url = {https://arxiv.org/abs/2310.03735}, author = {Yi-Kai Liu} } @article {3363, title = {Verifiable measurement-based quantum random sampling with trapped ions}, year = {2023}, month = {7/26/2023}, abstract = {

Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing tools for verifying that a quantum device indeed performed the classically intractable sampling task are either impractical or not scalable to the quantum advantage regime. The verification problem thus remains an outstanding challenge. Here, we experimentally demonstrate efficiently verifiable quantum random sampling in the measurement-based model of quantum computation on a trapped-ion quantum processor. We create random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. Moreover, by exploiting the structure of these states, we are able to recycle qubits during the computation to sample from entangled cluster states that are larger than the qubit register. We then efficiently estimate the fidelity to verify the prepared states--in single instances and on average--and compare our results to cross-entropy benchmarking. Finally, we study the effect of experimental noise on the certificates. Our results and techniques provide a feasible path toward a verified demonstration of a quantum advantage.

}, doi = {https://doi.org/10.48550/arXiv.2307.14424}, url = {https://arxiv.org/abs/2307.14424}, author = {Martin Ringbauer and Marcel Hinsche and Thomas Feldker and Paul K. Faehrmann and Juani Bermejo-Vega and Claire Edmunds and Lukas Postler and Roman Stricker and Christian D. Marciniak and Michael Meth and Ivan Pogorelov and Rainer Blatt and Philipp Schindler and Jens Eisert and Thomas Monz and Dominik Hangleiter} } @article {3313, title = {A Watermark for Large Language Models}, year = {2023}, month = {6/6/2023}, abstract = {

Potential harms of large language models can be mitigated by watermarking model output, i.e., embedding signals into generated text that are invisible to humans but algorithmically detectable from a short span of tokens. We propose a watermarking framework for proprietary language models. The watermark can be embedded with negligible impact on text quality, and can be detected using an efficient open-source algorithm without access to the language model API or parameters. The watermark works by selecting a randomized set of \"green\" tokens before a word is generated, and then softly promoting use of green tokens during sampling. We propose a statistical test for detecting the watermark with interpretable p-values, and derive an information-theoretic framework for analyzing the sensitivity of the watermark. We test the watermark using a multi-billion parameter model from the Open Pretrained Transformer (OPT) family, and discuss robustness and security.

}, url = {https://arxiv.org/abs/2301.10226}, author = {John Kirchenbauer and Jonas Geiping and Yuxin Wen and Jonathan Katz and Ian Miers and Tom Goldstein} } @article {3289, title = {What happens to entropy production when conserved quantities fail to commute with each other}, year = {2023}, month = {5/24/2023}, abstract = {

We extend entropy production to a deeply quantum regime involving noncommuting conserved quantities. Consider a unitary transporting conserved quantities (\"charges\") between two systems initialized in thermal states. Three common formulae model the entropy produced. They respectively cast entropy as an extensive thermodynamic variable, as an information-theoretic uncertainty measure, and as a quantifier of irreversibility. Often, the charges are assumed to commute with each other (e.g., energy and particle number). Yet quantum charges can fail to commute. Noncommutation invites generalizations, which we posit and justify, of the three formulae. Charges\&$\#$39; noncommutation, we find, breaks the formulae\&$\#$39;s equivalence. Furthermore, different formulae quantify different physical effects of charges\&$\#$39; noncommutation on entropy production. For instance, entropy production can signal contextuality - true nonclassicality - by becoming nonreal. This work opens up stochastic thermodynamics to noncommuting - and so particularly quantum - charges.

}, url = {https://arxiv.org/abs/2305.15480}, author = {Twesh Upadhyaya and William F. Braasch, Jr. and Gabriel T. Landi and Nicole Yunger Halpern} } @article {3406, title = {{\AE} codes}, year = {2023}, month = {11/21/2023}, abstract = {

Diatomic molecular codes [{arXiv:1911.00099}] are designed to encode quantum information in the orientation of a diatomic molecule, allowing error correction from small torques and changes in angular momentum. Here, we directly study noise native to atomic and molecular platforms -- spontaneous emission, stray electromagnetic fields, and Raman scattering -- and derive simple necessary and sufficient conditions for codes to protect against such noise. We identify existing and develop new absorption-emission ({\AE}) codes that are more practical than molecular codes, require lower average momentum, can directly protect against photonic processes up to arbitrary order, and are applicable to a broader set of atomic and molecular systems.

}, url = {https://arxiv.org/abs/2311.12324}, author = {Shubham P. Jain and Eric R. Hudson and Wesley C. Campbell and Victor V. Albert} } @article {3078, title = {Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {5/28/2022}, pages = {020360}, abstract = {

Although quantum computation (QC) is regarded as a promising numerical method for computational quantum chemistry, current applications of quantum-chemistry calculations on quantum computers are limited to small molecules. This limitation can be ascribed to technical problems in building and manipulating more qubits and the associated complicated operations of quantum gates in a quantum circuit when the size of the molecular system becomes large. As a result, reducing the number of required qubits is necessary to make QC practical. Currently, the minimal STO-3G basis set is commonly used in benchmark studies because it requires the minimum number of spin orbitals. Nonetheless, the accuracy of using STO-3G is generally low and thus cannot provide useful predictions. We propose to adopt Daubechies wavelet functions as an accurate and efficient method for QCs of molecular electronic properties. We demonstrate that a minimal basis set constructed from Daubechies wavelet basis can yield accurate results through a better description of the molecular Hamiltonian, while keeping the number of spin orbitals minimal. With the improved Hamiltonian through Daubechies wavelets, we calculate vibrational frequencies for H2 and LiH using quantum-computing algorithm to show that the results are in excellent agreement with experimental data. As a result, we achieve quantum calculations in which accuracy is comparable with that of the full configuration interaction calculation using the cc-pVDZ basis set, whereas the computational cost is the same as that of a STO-3G calculation. Thus, our work provides a more efficient and accurate representation of the molecular Hamiltonian for efficient QCs of molecular systems, and for the first time demonstrates that predictions in agreement with experimental measurements are possible to be achieved with quantum resources available in near-term quantum computers.

}, doi = {https://doi.org/10.1103/PRXQuantum.3.020360}, url = {https://arxiv.org/abs/2205.14476}, author = {Cheng-Lin Hong and Ting Tsai and Jyh-Pin Chou and Peng-Jen Chen and Pei-Kai Tsai and Yu-Cheng Chen and En-Jui Kuo and David Srolovitz and Alice Hu and Yuan-Chung Cheng and Hsi-Sheng Goan} } @book {2982, title = {Analogue Quantum Simulation: A New Instrument for Scientific Understanding}, year = {2022}, pages = {83-102}, publisher = {Springer Nature}, organization = {Springer Nature}, abstract = {

Analyzes analogue quantum simulation philosophically.\ Provides a framework to support the goals of scientists.\ Useful to both working scientists and philosophers of science.

}, doi = {https://doi.org/10.1007/978-3-030-87216-8_6}, author = {Dominik Hangleiter and Jacques Carolan and Karim P. Y. Th{\'e}bault} } @article {3001, title = {Approximating Output Probabilities of Shallow Quantum Circuits which are Geometrically-local in any Fixed Dimension}, journal = {Leibniz International Proceedings in Informatics (LIPIcs)}, volume = {232}, year = {2022}, month = {4/7/2022}, pages = {9:1--9:17}, type = {17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022)}, abstract = {

We present a classical algorithm that, for any D-dimensional geometrically-local, quantum circuit C of polylogarithmic-depth, and any bit string x\∈0,1n, can compute the quantity |\<x|C|0\⊗n\>|2 to within any inverse-polynomial additive error in quasi-polynomial time, for any fixed dimension D. This is an extension of the result [CC21], which originally proved this result for D=3. To see why this is interesting, note that, while the D=1 case of this result follows from standard use of Matrix Product States, known for decades, the D=2 case required novel and interesting techniques introduced in [BGM19]. Extending to the case D=3 was even more laborious and required further new techniques introduced in [CC21]. Our work here shows that, while handling each new dimension has historically required a new insight, and fixed algorithmic primitive, based on known techniques for D\≤3, we can now handle any fixed dimension D\>3.
Our algorithm uses the Divide-and-Conquer framework of [CC21] to approximate the desired quantity via several instantiations of the same problem type, each involving D-dimensional circuits on about half the number of qubits as the original. This division step is then applied recursively, until the width of the recursively decomposed circuits in the Dth dimension is so small that they can effectively be regarded as (D\−1)-dimensional problems by absorbing the small width in the Dth dimension into the qudit structure at the cost of a moderate increase in runtime. The main technical challenge lies in ensuring that the more involved portions of the recursive circuit decomposition and error analysis from [CC21] still hold in higher dimensions, which requires small modifications to the analysis in some places.

}, keywords = {Computational Complexity (cs.CC), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, isbn = {978-3-95977-237-2}, issn = {1868-8969}, doi = {10.48550/ARXIV.2202.08349}, url = {https://arxiv.org/abs/2202.08349}, author = {Dontha, Suchetan and Tan, Shi Jie Samuel and Smith, Stephen and Choi, Sangheon and Matthew Coudron} } @article {2715, title = {Approximating the two-mode two-photon Rabi model}, journal = {Physics Letters A}, volume = {422}, year = {2022}, month = {01/17/2022}, chapter = {127779}, abstract = {

The Rabi model describes the simplest nontrivial interaction between a few-level system and a bosonic mode, featuring in multiple seemingly unrelated systems of importance to quantum science and technology. While exact expressions for the energies of this model and its few-mode extensions have been obtained, they involve roots of transcendental functions and are thus cumbersome and unintuitive. Utilizing the symmetric generalized rotating wave approximation (S-GRWA), we develop a family of approximations to the energies of the two-mode two-photon Rabi model. The simplest elements of the family are analytically tractable, providing good approximations in regimes of interest such as ultra- and deep-strong coupling. Higher-order approximate energies can be used if more accuracy is required.\ 

}, doi = {https://doi.org/10.1016/j.physleta.2021.127779}, url = {https://arxiv.org/abs/2012.06994}, author = {David H. Wu and Victor V. Albert} } @article {3010, title = {Arline Benchmarks: Automated Benchmarking Platform for Quantum Compilers}, year = {2022}, month = {3/28/2022}, abstract = {

Efficient compilation of quantum algorithms is vital in the era of Noisy Intermediate-Scale Quantum (NISQ) devices. While multiple open-source quantum compilation and circuit optimization frameworks are available, e.g. IBM Qiskit, CQC Tket, Google Cirq, Rigetti Quilc, PyZX, their relative performance is not always clear to a quantum programmer. The growth of complexity and diversity of quantum circuit compilation algorithms creates a demand for a dedicated tool for cross-benchmarking and profiling of inner workflow of the quantum compilation stack. We present an open-source software package, Arline Benchmarks, that is designed to perform automated benchmarking of quantum compilers with the focus on NISQ applications. The name \"Arline\" was given in honour of Arline Greenbaum Feynman, the first wife of Richard Feynman, the pioneer of quantum computing. We compared several quantum compilation frameworks based on a set of important metrics such as post-optimization gate counts, circuit depth, hardware-dependent circuit cost function, compiler run time etc. with a detailed analysis of metrics for each compilation stage. We performed a variety of compiler tests for random circuits and structured quantum algorithms (VQE, Trotter decomposition, Grover search, Option Pricing via Amplitude Estimation) for several popular quantum hardware architectures. Leveraging cross-platform functionality of Arline, we propose a concept of composite compilation pipeline that combines compiler-specific circuit optimization subroutines in a single compilation stack and finds an optimized sequence of compilation passes. By providing detailed insights into the compilation flow of quantum compilers, Arline Benchmarks offers a valuable toolkit for quantum computing researchers and software developers to gain additional insights into compilers\&$\#$39; characteristics.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph), Software Engineering (cs.SE)}, doi = {10.48550/ARXIV.2202.14025}, url = {https://arxiv.org/abs/2202.14025}, author = {Kharkov, Y. and Ivanova, A. and Mikhantiev, E. and Kotelnikov, A.} } @article {3067, title = {Boson Sampling for Generalized Bosons}, year = {2022}, month = {5/2/2022}, abstract = {

We introduce the notion of \"generalized bosons\" whose exchange statistics resemble those of bosons, but the local bosonic commutator [ai,a\†i]=1 is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analogue of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so that the results regarding hardness of sampling directly carry over. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms.

}, url = {https://arxiv.org/abs/2204.08389}, author = {En-Jui Kuo and Yijia Xu and Dominik Hangleiter and Andrey Grankin and Mohammad Hafezi} } @article {3181, title = {Bosonic coding: introduction and use cases}, year = {2022}, month = {11/10/2022}, abstract = {

Bosonic or continuous-variable coding is a field concerned with robust quantum information processing and communication with electromagnetic signals or mechanical modes. I review bosonic quantum memories, characterizing them as either bosonic stabilizer or bosonic Fock-state codes. I then enumerate various applications of bosonic encodings, four of which circumvent no-go theorems due to the intrinsic infinite-dimensionality of bosonic systems.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Information Theory (cs.IT), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.05714}, url = {https://arxiv.org/abs/2211.05714}, author = {Victor V. Albert} } @article {3143, title = {Bosonic Qiskit}, year = {2022}, month = {9/22/2022}, abstract = {

The practical benefits of hybrid quantum information processing hardware that contains continuous-variable objects (bosonic modes such as mechanical or electromagnetic oscillators) in addition to traditional (discrete-variable) qubits have recently been demonstrated by experiments with bosonic codes that reach the break-even point for quantum error correction and by efficient Gaussian boson sampling simulation of the Franck-Condon spectra of triatomic molecules that is well beyond the capabilities of current qubit-only hardware. The goal of this Co-design Center for Quantum Advantage (C2QA) project is to develop an instruction set architecture (ISA) for hybrid qubit/bosonic mode systems that contains an inventory of the fundamental operations and measurements that are possible in such hardware. The corresponding abstract machine model (AMM) would also contain a description of the appropriate error models associated with the gates, measurements and time evolution of the hardware. This information has been implemented as an extension of Qiskit. Qiskit is an opensource software development toolkit (SDK) for simulating the quantum state of a quantum circuit on a system with Python 3.7+ and for running the same circuits on prototype hardware within the IBM Quantum Lab. We introduce the Bosonic Qiskit software to enable the simulation of hybrid qubit/bosonic systems using the existing Qiskit software development kit. This implementation can be used for simulating new hybrid systems, verifying proposed physical systems, and modeling systems larger than can currently be constructed. We also cover tutorials and example use cases included within the software to study Jaynes- Cummings models, bosonic Hubbard models, plotting Wigner functions and animations, and calculating maximum likelihood estimations using Wigner functions.

}, keywords = {Emerging Technologies (cs.ET), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.11153}, url = {https://arxiv.org/abs/2209.11153}, author = {Stavenger, Timothy J and Crane, Eleanor and Smith, Kevin and Kang, Christopher T and Girvin, Steven M and Wiebe, Nathan} } @article {3152, title = {Bounding the Minimum Time of a Quantum Measurement}, year = {2022}, month = {9/13/2022}, abstract = {

Measurements take a singular role in quantum theory. While they are often idealized as an instantaneous process, this is in conflict with all other physical processes in nature. In this Letter, we adopt a standpoint where the interaction with an environment is a crucial ingredient for the occurrence of a measurement. Within this framework, we derive lower bounds on the time needed for a measurement to occur. Our bound scales proportionally to the change in entropy of the measured system, and inversely proportional to the number of possible measurement outcomes and the interaction strength driving the measurement. We evaluate our bound in two examples where the environment is modelled by bosonic modes and the measurement apparatus is modelled by spins or bosons.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.06248}, url = {https://arxiv.org/abs/2209.06248}, author = {Shettell, Nathan and Centrone, Federico and Garc{\'\i}a-Pintos, Luis Pedro} } @article {3073, title = {Candidate for a self-correcting quantum memory in two dimensions}, year = {2022}, month = {5/19/2022}, abstract = {

An interesting problem in the field of quantum error correction involves finding a physical system that hosts a \"self-correcting quantum memory,\" defined as an encoded qubit coupled to an environment that naturally wants to correct errors. To date, a quantum memory stable against finite-temperature effects is only known in four spatial dimensions or higher. Here, we take a different approach to realize a stable quantum memory by relying on a driven-dissipative environment. We propose a new model which appears to self correct against both bit-flip and phase-flip errors in two dimensions: A square lattice composed of photonic \"cat qubits\" coupled via dissipative terms which tend to fix errors locally. Inspired by the presence of two distinct Z2-symmetry-broken phases, our scheme relies on Ising-like dissipators to protect against bit flips and on a driven-dissipative photonic environment to protect against phase flips.\ 

}, url = {https://arxiv.org/abs/2205.09767}, author = {Simon Lieu and Yu-Jie Liu and Alexey V. Gorshkov} } @article {3075, title = {Certifying Temporal Correlations}, year = {2022}, month = {6/13/2022}, abstract = {

Self-testing has been established as a major approach for quantum device certification based on experimental statistics under minimal assumptions. However, despite more than 20 years of research effort most of the self-testing protocols are restricted to spatial scenarios (Bell scenarios), without any temporal generalisations known. Under the scenario of sequential measurements performed on a single quantum system, we build upon previous works which used semi-definite programming (SDP) based methods to bound sequential measurement inequalities. For such SDPs, we show that the optimiser matrix is unique and moreover this uniqueness is robust to small deviations from the quantum bound. Further, we consider a generalised scenario in presence of quantum channels and draw analogies in the structure of Bell and sequential inequalities using the pseudo-density matrix formalism. These analogies allow us to show a practical use of maximal violations of sequential inequalities in the form of certification of quantum channels up to isometries.\ 

}, url = {https://arxiv.org/abs/2206.06092}, author = {Harshank Shrotriya and Leong-Chuan Kwek, Kishor Bharti and Kishor Bharti} } @article {2945, title = {Chiral central charge from a single bulk wave function}, journal = {Phys. Rev. Lett. }, volume = {128}, year = {2022}, month = {4/28/2022}, pages = {176402}, abstract = {

A (2+1)-dimensional gapped quantum many-body system can have a topologically protected energy current at its edge. The magnitude of this current is determined entirely by the temperature and the chiral central charge, a quantity associated with the effective field theory of the edge. We derive a formula for the chiral central charge that, akin to the topological entanglement entropy, is completely determined by the many-body ground state wave function in the bulk. According to our formula, nonzero chiral central charge gives rise to a topological obstruction that prevents the ground state wave function from being real-valued in any local product basis.

}, doi = {10.1103/PhysRevLett.128.176402}, url = {https://arxiv.org/abs/2110.06932}, author = {Isaac H. Kim and Bowen Shi and Kohtaro Kato and Victor V. Albert} } @article {2930, title = {Classification of (2+1)D invertible fermionic topological phases with symmetry}, journal = {Phys. Rev. B}, volume = {105}, year = {2022}, month = {5/30/2022}, abstract = {

We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups Gf and general values of the chiral central charge c\−. Here Gf is a central extension of a bosonic symmetry group Gb by fermion parity, (\−1)F, specified by a second cohomology class [ω2]\∈H2(Gb,Z2). Our approach proceeds by gauging fermion parity and classifying the resulting Gb symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c\−)1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c\−=0. We show how the 10-fold way classification of topological insulators and superconductors fits into our scheme, along with general non-perturbative constraints due to certain choices of c\− and Gf. Mathematically, our results also suggest an explicit general parameterization of deformation classes of (2+1)D invertible topological quantum field theories with Gf symmetry.\ 

}, doi = {https://doi.org/10.1103/PhysRevB.105.235143}, url = {https://arxiv.org/abs/2109.11039}, author = {Maissam Barkeshli and Yu-An Chen and Po-Shen Hsin and Naren Manjunath} } @article {3082, title = {Closing the Locality and Detection Loopholes in Multiparticle Entanglement Self-Testing}, journal = {Physical Review Letters}, volume = {128}, year = {2022}, month = {06/23/2022}, pages = {250401}, abstract = {

First proposed by Mayers and Yao, self-testing provides a certification method to infer the underlying physics of quantum experiments in a black-box scenario. Numerous demonstrations have been reported to self-test various types of entangled states. However, all the multiparticle self-testing experiments reported so far suffer from both detection and locality loopholes. Here, we report the first experimental realization of multiparticle entanglement self-testing closing the locality loophole in a photonic system, and the detection loophole in a superconducting system, respectively. We certify three-party and four-party GHZ states with at least 0.84 (1) and 0.86 (3) fidelities in a device-independent way. These results can be viewed as a meaningful advance in multiparticle loophole-free self-testing, and also significant progress on the foundations of quantum entanglement certification.

}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.250401}, url = {https://www.researchgate.net/profile/Dian-Wu/publication/361497881_Closing_the_Locality_and_Detection_Loopholes_in_Multiparticle_Entanglement_Self-Testing/links/62b55a8c1010dc02cc57530c/Closing-the-Locality-and-Detection-Loopholes-in-Multiparticle-Entangl}, author = {Dian Wu and Qi Zhao and Can Wang and Liang Huang and Yang-Fan Jiang and Bing Bai and You Zhou and Xue-Mei Gu and Feng-Ming Liu and Ying-Qiu Mao and Qi-Chao Sun and Ming-Cheng Chen and Jun Zhang and Cheng-Zhi Peng and Xiao-Bo Zhu and Qiang Zhang and Chao-Yang Lu and Jian-Wei Pan} } @article {3144, title = {Codimension-2 defects and higher symmetries in (3+1)D topological phases}, year = {2022}, month = {8/15/2022}, abstract = {

(3+1)D topological phases of matter can host a broad class of non-trivial topological defects of codimension-1, 2, and 3, of which the well-known point charges and flux loops are special cases. The complete algebraic structure of these defects defines a higher category, and can be viewed as an emergent higher symmetry. This plays a crucial role both in the classification of phases of matter and the possible fault-tolerant logical operations in topological quantum error correcting codes. In this paper, we study several examples of such higher codimension defects from distinct perspectives. We mainly study a class of invertible codimension-2 topological defects, which we refer to as twist strings. We provide a number of general constructions for twist strings, in terms of gauging lower dimensional invertible phases, layer constructions, and condensation defects. We study some special examples in the context of Z2 gauge theory with fermionic charges, in Z2\×Z2 gauge theory with bosonic charges, and also in non-Abelian discrete gauge theories based on dihedral (Dn) and alternating (A6) groups. The intersection between twist strings and Abelian flux loops sources Abelian point charges, which defines an H4 cohomology class that characterizes part of an underlying 3-group symmetry of the topological order. The equations involving background gauge fields for the 3-group symmetry have been explicitly written down for various cases. We also study examples of twist strings interacting with non-Abelian flux loops (defining part of a non-invertible higher symmetry), examples of non-invertible codimension-2 defects, and examples of interplay of codimension-2 defects with codimension-1 defects. We also find an example of geometric, not fully topological, twist strings in (3+1)D A6 gauge theory.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, High Energy Physics - Theory (hep-th), Mathematical Physics (math-ph), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2208.07367}, url = {https://arxiv.org/abs/2208.07367}, author = {Barkeshli, Maissam and Chen, Yu-An and Huang, Sheng-Jie and Kobayashi, Ryohei and Tantivasadakarn, Nathanan and Zhu, Guanyu} } @article {3080, title = {Combining machine learning with physics: A framework for tracking and sorting multiple dark solitons}, journal = {Phys. Rev. Research}, volume = {4}, year = {2022}, month = {06/01/2022}, pages = {023163 }, abstract = {

In ultracold-atom experiments, data often comes in the form of images which suffer information loss inherent in the techniques used to prepare and measure the system. This is particularly problematic when the processes of interest are complicated, such as interactions among excitations in Bose-Einstein condensates (BECs). In this paper, we describe a framework combining machine learning (ML) models with physics-based traditional analyses to identify and track multiple solitonic excitations in images of BECs. We use an ML-based object detector to locate the solitonic excitations and develop a physics-informed classifier to sort solitonic excitations into physically motivated subcategories. Lastly, we introduce a quality metric quantifying the likelihood that a specific feature is a longitudinal soliton. Our trained implementation of this framework, SolDet, is publicly available as an open-source python package. SolDet is broadly applicable to feature identification in cold-atom images when trained on a suitable user-provided dataset.

}, doi = {https://doi.org/10.1103/PhysRevResearch.4.023163}, url = {https://arxiv.org/abs/2111.04881}, author = {Shangjie Guo and Sophia M. Koh and Amilson R. Fritsch and I. B. Spielman and Justyna P. Zwolak} } @article {3066, title = {Computational advantage of quantum random sampling}, year = {2022}, month = {6/8/2022}, abstract = {

Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. In this article, we comprehensively review the theoretical underpinning of quantum random sampling in terms of computational complexity and verifiability, as well as the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. We discuss in detail open questions in the field and provide perspectives for the road ahead, including potential applications of quantum random sampling.

}, url = {https://arxiv.org/abs/2206.04079}, author = {Dominik Hangleiter and Jens Eisert} } @article {3021, title = {Computational self-testing of multi-qubit states and measurements}, year = {2022}, month = {1/31/2022}, abstract = {

Self-testing is a fundamental technique within quantum information theory that allows a classical verifier to force (untrusted) quantum devices to prepare certain states and perform certain measurements on them. The standard approach assumes at least two spatially separated devices. Recently, Metger and Vidick [Quantum, 2021] showed that a single EPR pair of a single quantum device can be self-tested under standard computational assumptions. In this work, we generalize their techniques to give the first protocol that self-tests N EPR pairs and measurements in the single-device setting under the same computational assumptions. We show that our protocol can be passed with probability negligibly close to 1 by an honest quantum device using poly(N) resources. Moreover, we show that any quantum device that fails our protocol with probability at most ϵ must be poly(N,ϵ)-close to being honest in the appropriate sense. In particular, a simplified version of our protocol is the first that can efficiently certify an arbitrary number of qubits of a cloud quantum computer, on which we cannot enforce spatial separation, using only classical communication.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2201.13430}, url = {https://arxiv.org/abs/2201.13430}, author = {Fu, Honghao and Daochen Wang and Zhao, Qi} } @article {2488, title = {Constant-sized correlations are sufficient to robustly self-test maximally entangled states with unbounded dimension}, journal = {Quantum}, volume = {6}, year = {2022}, month = {01/03/2022}, pages = {614}, abstract = {

We show that for any prime odd integer d, there exists a correlation of size Θ(r) that can robustly self-test a maximally entangled state of dimension 4d\−4, where r is the smallest multiplicative generator of Z\∗d. The construction of the correlation uses the embedding procedure proposed by Slofstra (Forum of Mathematics, Pi. Vol. 7, (2019)). Since there are infinitely many prime numbers whose smallest multiplicative generator is at most 5 (M. Murty The Mathematical Intelligencer 10.4 (1988)), our result implies that constant-sized correlations are sufficient for robust self-testing of maximally entangled states with unbounded local dimension.

}, doi = {https://doi.org/10.22331/q-2022-01-03-614}, url = {https://arxiv.org/abs/1911.01494}, author = {Honghao Fu} } @article {3184, title = {Continuous Symmetry Breaking in a Trapped-Ion Spin Chain}, year = {2022}, month = {11/2/2022}, abstract = {

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to 23 spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.

}, keywords = {FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2211.01275}, url = {https://arxiv.org/abs/2211.01275}, author = {Feng, Lei and Katz, Or and Haack, Casey and Maghrebi, Mohammad and Alexey V. Gorshkov and Gong, Zhexuan and Cetina, Marko and Monroe, Christopher} } @article {3182, title = {Continuous-Variable Shadow Tomography}, year = {2022}, month = {11/9/2022}, abstract = {

Shadow tomography is a framework for constructing succinct descriptions of quantum states, called classical shadows, with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable tomography in the classical-shadow framework, obtaining rigorous bounds on the sample complexity for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon number resolving (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with a high probability, we show that homodyne detection requires an order O(N5) measurements in the worst case, whereas PNR and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in N. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.05149}, url = {https://arxiv.org/abs/2211.05149}, author = {Gandhari, Srilekha and Victor V. Albert and Gerrits, Thomas and Taylor, Jacob M. and Michael Gullans} } @article {3072, title = {A Convergence Theory for Over-parameterized Variational Quantum Eigensolvers}, year = {2022}, month = {5/25/2022}, abstract = {

The Variational Quantum Eigensolver (VQE) is a promising candidate for quantum applications on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. Despite a lot of empirical studies and recent progress in theoretical understanding of VQE\&$\#$39;s optimization landscape, the convergence for optimizing VQE is far less understood. We provide the first rigorous analysis of the convergence of VQEs in the over-parameterization regime. By connecting the training dynamics with the Riemannian Gradient Flow on the unit-sphere, we establish a threshold on the sufficient number of parameters for efficient convergence, which depends polynomially on the system dimension and the spectral ratio, a property of the problem Hamiltonian, and could be resilient to gradient noise to some extent. We further illustrate that this overparameterization threshold could be vastly reduced for specific VQE instances by establishing an ansatz-dependent threshold paralleling our main result. We showcase that our ansatz-dependent threshold could serve as a proxy of the trainability of different VQE ansatzes without performing empirical experiments, which hence leads to a principled way of evaluating ansatz design. Finally, we conclude with a comprehensive empirical study that supports our theoretical findings

}, url = {https://arxiv.org/abs/2205.12481}, author = {Xuchen You and Shouvanik Chakrabarti and Xiaodi Wu} } @article {3007, title = {Convex optimization for non-equilibrium steady states on a hybrid quantum processor}, year = {2022}, month = {4/7/2022}, abstract = {

Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics. By reformulating the problem of finding the fixed point of Lindblad dynamics as a feasibility semi-definite program, we bypass several well known issues with variational quantum approaches to solving for steady states. We demonstrate that our hybrid approach allows us to estimate the steady states of higher dimensional open quantum systems and discuss how our method can find multiple steady states for systems with symmetries.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.48550/arXiv.2204.03203}, url = {https://arxiv.org/abs/2204.03203}, author = {Lau, Jonathan Wei Zhong and Lim, Kian Hwee and Bharti, Kishor and Kwek, Leong-Chuan and Vinjanampathy, Sai} } @article {3128, title = {CoVault: A Secure Analytics Platform}, year = {2022}, month = {8/7/2022}, abstract = {

In a secure analytics platform, data sources consent to the exclusive use of their data for a pre-defined set of analytics queries performed by a specific group of analysts, and for a limited period. If the platform is secure under a sufficiently strong threat model, it can provide the missing link to enabling powerful analytics of sensitive personal data, by alleviating data subjects\&$\#$39; concerns about leakage and misuse of data. For instance, many types of powerful analytics that benefit public health, mobility, infrastructure, finance, or sustainable energy can be made differentially private, thus alleviating concerns about privacy. However, no platform currently exists that is sufficiently secure to alleviate concerns about data leakage and misuse; as a result, many types of analytics that would be in the interest of data subjects and the public are not done. CoVault uses a new multi-party implementation of functional encryption (FE) for secure analytics, which relies on a unique combination of secret sharing, multi-party secure computation (MPC), and different trusted execution environments (TEEs). CoVault is secure under a very strong threat model that tolerates compromise and side-channel attacks on any one of a small set of parties and their TEEs. Despite the cost of MPC, we show that CoVault scales to very large data sizes using map-reduce based query parallelization. For example, we show that CoVault can perform queries relevant to epidemic analytics at scale.

}, keywords = {and Cluster Computing (cs.DC), Cryptography and Security (cs.CR), Distributed, FOS: Computer and information sciences, Parallel}, doi = {10.48550/ARXIV.2208.03784}, url = {https://arxiv.org/abs/2208.03784}, author = {De Viti, Roberta and Sheff, Isaac and Glaeser, Noemi and Dinis, Baltasar and Rodrigues, Rodrigo and Katz, Jonathan and Bhattacharjee, Bobby and Hithnawi, Anwar and Garg, Deepak and Druschel, Peter} } @article {3079, title = {Dark Solitons in Bose-Einstein Condensates: A Dataset for Many-body Physics Research}, year = {2022}, month = {05/17/2022}, abstract = {

We establish a dataset of over 1.6\×104 experimental images of Bose-Einstein condensates containing solitonic excitations to enable machine learning (ML) for many-body physics research. About 33 \% of this dataset has manually assigned and carefully curated labels. The remainder is automatically labeled using SolDet -- an implementation of a physics-informed ML data analysis framework -- consisting of a convolutional-neural-network-based classifier and object detector as well as a statistically motivated physics-informed classifier and a quality metric. This technical note constitutes the definitive reference of the dataset, providing an opportunity for the data science community to develop more sophisticated analysis tools, to further understand nonlinear many-body physics, and even advance cold atom experiments.

}, url = {https://arxiv.org/abs/2205.09114}, author = {Amilson R. Fritsch and Shangjie Guo and Sophia M. Koh and I. B. Spielman and Justyna P. Zwolak} } @article {3013, title = {Deconfinement and Error Thresholds in Holography}, year = {2022}, month = {2/9/2022}, abstract = {

We study the error threshold properties of holographic quantum error-correcting codes. We demonstrate that holographic CFTs admit an algebraic threshold, which is related to the confinement-deconfinement phase transition. We then apply geometric intuition from holography and the Hawking-Page phase transition to motivate the CFT result, and comment on potential extensions to other confining theories.

}, keywords = {FOS: Physical sciences, High Energy Physics - Theory (hep-th), Nuclear Theory (nucl-th), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2202.04710}, url = {https://arxiv.org/abs/2202.04710}, author = {Bao, Ning and Cao, Charles and Zhu, Guanyu} } @article {3140, title = {Demonstration of three- and four-body interactions between trapped-ion spins}, year = {2022}, month = {9/12/2022}, abstract = {

Quantum processors use the native interactions between effective spins to simulate Hamiltonians or execute quantum gates. In most processors, the native interactions are pairwise, limiting the efficiency of controlling entanglement between many qubits. Here we experimentally demonstrate a new class of native interactions between trapped-ion qubits, extending conventional pairwise interactions to higher order. We realize three- and four-body spin interactions as examples, showing that high-order spin polynomials may serve as a new toolbox for quantum information applications.

}, keywords = {Atomic Physics (physics.atom-ph), FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.05691}, url = {https://arxiv.org/abs/2209.05691}, author = {Katz, Or and Feng, Lei and Risinger, Andrew and Monroe, Christopher and Cetina, Marko} } @article {3195, title = {Differentiable Quantum Programming with Unbounded Loops}, year = {2022}, month = {11/8/2022}, abstract = {

The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Recently, Zhu et al. (PLDI 2020) have formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q$\#$, and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Machine Learning (cs.LG), Programming Languages (cs.PL), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.04507}, url = {https://arxiv.org/abs/2211.04507}, author = {Fang, Wang and Ying, Mingsheng and Wu, Xiaodi} } @article {3127, title = {Disordered Lieb-Robinson bounds in one dimension}, year = {2022}, month = {8/10/2022}, abstract = {

By tightening the conventional Lieb-Robinson bounds to better handle systems which lack translation invariance, we determine the extent to which \"weak links\" suppress operator growth in disordered one-dimensional spin chains. In particular, we prove that ballistic growth is impossible when the distribution of coupling strengths μ(J) has a sufficiently heavy tail at small J, and identify the correct dynamical exponent to use instead. Furthermore, through a detailed analysis of the special case in which the couplings are genuinely random and independent, we find that the standard formulation of Lieb-Robinson bounds is insufficient to capture the complexity of the dynamics -- we must distinguish between bounds which hold for all sites of the chain and bounds which hold for a subsequence of sites, and we show by explicit example that these two can have dramatically different behaviors. All the same, our result for the dynamical exponent is tight, in that we prove by counterexample that there cannot exist any Lieb-Robinson bound with a smaller exponent. We close by discussing the implications of our results, both major and minor, for numerous applications ranging from quench dynamics to the structure of ground states.

}, keywords = {Disordered Systems and Neural Networks (cond-mat.dis-nn), FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2208.05509}, url = {https://arxiv.org/abs/2208.05509}, author = {Baldwin, Christopher L. and Ehrenberg, Adam and Guo, Andrew Y. and Alexey V. Gorshkov} } @article {3205, title = {Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning}, year = {2022}, month = {4/14/2022}, abstract = {

Efficient quantum compiling tactics greatly enhance the capability of quantum computers to execute complicated quantum algorithms. Due to its fundamental importance, a plethora of quantum compilers has been designed in past years. However, there are several caveats to current protocols, which are low optimality, high inference time, limited scalability, and lack of universality. To compensate for these defects, here we devise an efficient and practical quantum compiler assisted by advanced deep reinforcement learning (RL) techniques, i.e., data generation, deep Q-learning, and AQ* search. In this way, our protocol is compatible with various quantum machines and can be used to compile multi-qubit operators. We systematically evaluate the performance of our proposal in compiling quantum operators with both inverse-closed and inverse-free universal basis sets. In the task of single-qubit operator compiling, our proposal outperforms other RL-based quantum compilers in the measure of compiling sequence length and inference time. Meanwhile, the output solution is near-optimal, guaranteed by the Solovay-Kitaev theorem. Notably, for the inverse-free universal basis set, the achieved sequence length complexity is comparable with the inverse-based setting and dramatically advances previous methods. These empirical results contribute to improving the inverse-free Solovay-Kitaev theorem. In addition, for the first time, we demonstrate how to leverage RL-based quantum compilers to accomplish two-qubit operator compiling. The achieved results open an avenue for integrating RL with quantum compiling to unify efficiency and practicality and thus facilitate the exploration of quantum advantages.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Machine Learning (cs.LG), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2204.06904}, url = {https://arxiv.org/abs/2204.06904}, author = {Chen, Qiuhao and Du, Yuxuan and Zhao, Qi and Jiao, Yuling and Lu, Xiliang and Wu, Xingyao} } @article {2910, title = {Efficient Product Formulas for Commutators and Applications to Quantum Simulation}, journal = {Physical Review Research}, volume = {4}, year = {2022}, month = {03/10/2022}, chapter = {013191}, abstract = {

We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator differential method. We then derive higher-order product formulas recursively from the third-order formula. We improve over previous recursive constructions, reducing the number of gates required to achieve the same accuracy. In addition, we demonstrate that the constituent linear terms in the commutator can be included at no extra cost. As an application, we show how to use the product formulas in a digital protocol for counterdiabatic driving, which increases the fidelity for quantum state preparation. We also discuss applications to quantum simulation of one-dimensional fermion chains with nearest- and next-nearest-neighbor hopping terms, and two-dimensional fractional quantum Hall phases.

}, doi = {https://doi.org/10.1103/PhysRevResearch.4.013191}, url = {https://arxiv.org/abs/2111.12177}, author = {Yu-An Chen and Andrew M. Childs and Mohammad Hafezi and Zhang Jiang and Hwanmun Kim and Yijia Xu} } @article {3064, title = {Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation}, year = {2022}, month = {5/2/2022}, abstract = {

Nonlinear differential equations exhibit rich phenomena in many fields but are notoriously challenging to solve. Recently, Liu et al. [1] demonstrated the first efficient quantum algorithm for dissipative quadratic differential equations under the condition R\<1, where R measures the ratio of nonlinearity to dissipation using the l2 norm. Here we develop an efficient quantum algorithm based on [1] for reaction-diffusion equations, a class of nonlinear partial differential equations (PDEs). To achieve this, we improve upon the Carleman linearization approach introduced in [1] to obtain a faster convergence rate under the condition RD\<1, where RD measures the ratio of nonlinearity to dissipation using the l\∞ norm. Since RD is independent of the number of spatial grid points n while R increases with n, the criterion RD\<1 is significantly milder than R\<1 for high-dimensional systems and can stay convergent under grid refinement for approximating PDEs. As applications of our quantum algorithm we consider the Fisher-KPP and Allen-Cahn equations, which have interpretations in classical physics. In particular, we show how to estimate the mean square kinetic energy in the solution by postprocessing the quantum state that encodes it to extract derivative information.

}, url = {https://arxiv.org/abs/2205.01141}, author = {Dong An and Di Fang and Stephen Jordan and Jin-Peng Liu and Guang Hao Low and Jiasu Wang} } @article {3153, title = {Error-correcting codes for fermionic quantum simulation}, year = {2022}, month = {10/16/2022}, abstract = {

We provide ways to simulate fermions by qubits on 2d lattices using Z2 gauge theories (stabilizer codes). By studying the symplectic automorphisms of the Pauli module over the Laurent polynomial ring, we develop a systematic way to increase the code distances of stabilizer codes. We identify a family of stabilizer codes that can be used to simulate fermions with code distances of d=2,3,4,5,6,7 such that any \⌊d\−12\⌋-qubit error can be corrected. In particular, we demonstrate three stabilizer codes with code distances of d=3, d=4, and d=5, respectively, with all stabilizers and logical operators shown explicitly. The syndromes for all Pauli errors are provided. Finally, we introduce a syndrome-matching method to compute code distances numerically.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2210.08411}, url = {https://arxiv.org/abs/2210.08411}, author = {Chen, Yu-An and Alexey V. Gorshkov and Xu, Yijia} } @article {3081, title = {Estimating gate complexities for the site-by-site preparation of fermionic vacua}, year = {2022}, month = {07/04/2022}, abstract = {

An important aspect of quantum simulation is the preparation of physically interesting states on a quantum computer, and this task can often be costly or challenging to implement. A digital, {\textquoteleft}{\textquoteleft}site-by-site\&$\#$39;\&$\#$39; scheme of state preparation was introduced in arXiv:1911.03505 as a way to prepare the vacuum state of certain fermionic field theory Hamiltonians with a mass gap. More generally, this algorithm may be used to prepare ground states of Hamiltonians by adding one site at a time as long as successive intermediate ground states share a non-zero overlap and the Hamiltonian has a non-vanishing spectral gap at finite lattice size. In this paper, we study the ground state overlap as a function of the number of sites for a range of quadratic fermionic Hamiltonians. Using analytical formulas known for free fermions, we are able to explore the large-N behavior and draw conclusions about the state overlap. For all models studied, we find that the overlap remains large (e.g. \>0.1) up to large lattice sizes (N=64,72) except near quantum phase transitions or in the presence of gapless edge modes. For one-dimensional systems, we further find that two N/2-site ground states also share a large overlap with the N-site ground state everywhere except a region near the phase boundary. Based on these numerical results, we additionally propose a recursive alternative to the site-by-site state preparation algorithm.

}, url = {https://arxiv.org/abs/2207.01692}, author = {Troy Sewell and Aniruddha Bapat and Stephen Jordan} } @article {3016, title = {Euler-obstructed Cooper pairing: Nodal superconductivity and hinge Majorana zero modes}, journal = {Physical Review B}, volume = {105}, year = {2022}, month = {3/29/2022}, abstract = {

Since the proposal of monopole Cooper pairing in [Phys. Rev. Lett. 120, 067003 (2018)], considerable research efforts have been dedicated to the study of Cooper pairing order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces in 3D systems. In the current work, we generalize the topologically obstructed pairings between Chern states (like the monopole Cooper pairing) by proposing Euler obstructed Cooper pairing in 3D systems. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterized by nonzero Euler numbers; such Fermi surfaces can exist in 3D PT-protected spinless-Dirac/nodal-line semimetals with negligible spin-orbit coupling, where PT is the space-time inversion symmetry. An Euler obstructed pairing channel must have pairing nodes on the pairing-relevant Fermi surfaces, and the total winding number of the pairing nodes is determined by the sum or difference of the Euler numbers on the Fermi surfaces. In particular, we find that when the normal state is time-reversal invariant and the pairing is weak, a sufficiently-dominant Euler obstructed pairing channel with zero total momentum leads to nodal superconductivity. If the Fermi surface splitting is small, the resultant nodal superconductor hosts hinge Majorana zero modes. The possible dominance of the Euler obstructed pairing channel near the superconducting transition and the robustness of the hinge Majorana zero modes against disorder are explicitly demonstrated using effective or tight-binding models. Our work presents the first class of higher-order nodal superconductivity originating from the topologically obstructed Cooper pairing.

}, doi = {https://doi.org/10.1103\%2Fphysrevb.105.104515}, url = {https://arxiv.org/abs/2109.02685}, author = {Jiabin Yu and Yu-An Chen and Sankar Das Sarma} } @article {3139, title = {Experimental Implementation of an Efficient Test of Quantumness}, year = {2022}, month = {9/28/2022}, abstract = {

A test of quantumness is a protocol where a classical user issues challenges to a quantum device to determine if it exhibits non-classical behavior, under certain cryptographic assumptions. Recent attempts to implement such tests on current quantum computers rely on either interactive challenges with efficient verification, or non-interactive challenges with inefficient (exponential time) verification. In this paper, we execute an efficient non-interactive test of quantumness on an ion-trap quantum computer. Our results significantly exceed the bound for a classical device\&$\#$39;s success.

}, keywords = {FOS: Physical sciences, Other Condensed Matter (cond-mat.other), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.14316}, url = {https://arxiv.org/abs/2209.14316}, author = {Lewis, Laura and Zhu, Daiwei and Gheorghiu, Alexandru and Noel, Crystal and Katz, Or and Harraz, Bahaa and Wang, Qingfeng and Risinger, Andrew and Feng, Lei and Biswas, Debopriyo and Egan, Laird and Vidick, Thomas and Cetina, Marko and Monroe, Christopher} } @article {3002, title = {Experimental observation of thermalisation with noncommuting charges}, year = {2022}, month = {2/9/2022}, abstract = {

Quantum simulators have recently enabled experimental observations of quantum many-body systems\&$\#$39; internal thermalisation. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined particle number - in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6-15 spins in an approximate microcanonical subspace, a generalisation of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, whose predictions can now be tested.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech)}, doi = {10.48550/ARXIV.2202.04652}, url = {https://arxiv.org/abs/2202.04652}, author = {Kranzl, Florian and Lasek, Aleksander and Joshi, Manoj K. and Kalev, Amir and Blatt, Rainer and Roos, Christian F. and Nicole Yunger Halpern} } @article {3077, title = {Experimentally Measuring Rolling and Sliding in Three-Dimensional Dense Granular Packings}, journal = {Phys. Rev. Lett.}, volume = {129}, year = {2022}, month = {06/18/2022}, pages = {048001}, abstract = {

We experimentally measure a three-dimensional (3D) granular system\’s reversibility under cyclic compression. We image the grains using a refractive-index-matched fluid, then analyze the images using the artificial intelligence of variational autoencoders. These techniques allow us to track all the grains\’ translations and 3D rotations with accuracy sufficient to infer sliding and rolling displacements. Our observations reveal unique roles played by 3D rotational motions in granular flows. We find that rotations and contact-point motion dominate the dynamics in the bulk, far from the perturbation\’s source. Furthermore, we determine that 3D rotations are irreversible under cyclic compression. Consequently, contact-point sliding, which is dissipative, accumulates throughout the cycle. Using numerical simulations whose accuracy our experiment supports, we discover that much of the dissipation occurs in the bulk, where grains rotate more than they translate. Our observations suggest that the analysis of 3D rotations is needed for understanding granular materials\’ unique and powerful ability to absorb and dissipate energy.

}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.048001}, url = {https://arxiv.org/abs/2108.11975}, author = {Zackery A. Benson and Anton Peshkov and Nicole Yunger Halpern and Derek C. Richardson and Wolfgang Losert} } @article {3122, title = {Extracting Wilson loop operators and fractional statistics from a single bulk ground state}, year = {2022}, month = {9/28/2022}, abstract = {

An essential aspect of topological phases of matter is the existence of Wilson loop operators that keep the ground state subspace invariant. Here we present and implement an unbiased numerical optimization scheme to systematically find the Wilson loop operators given a single ground state wave function of a gapped Hamiltonian on a disk. We then show how these Wilson loop operators can be cut and glued through further optimization to give operators that can create, move, and annihilate anyon excitations. We subsequently use these operators to determine the braiding statistics and topological twists of the anyons, yielding a way to fully extract topological order from a single wave function. We apply our method to the ground state of the perturbed toric code and doubled semion models with a magnetic field that is up to a half of the critical value. From a contemporary perspective, this can be thought of as a machine learning approach to discover emergent 1-form symmetries of a ground state wave function. From an application perspective, our approach can be relevant to find Wilson loop operators in current quantum simulators.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2209.14302}, url = {https://arxiv.org/abs/2209.14302}, author = {Cian, Ze-Pei and Hafezi, Mohammad and Barkeshli, Maissam} } @article {3198, title = {FIPS Compliant Quantum Secure Communication using Quantum Permutation Pad}, year = {2022}, month = {12/30/2022}, abstract = {

Quantum computing has entered fast development track since Shor\&$\#$39;s algorithm was proposed in 1994. Multi-cloud services of quantum computing farms are currently available. One of which, IBM quantum computing, presented a road map showing their Kookaburra system with over 4158 qubits will be available in 2025. For the standardization of Post-Quantum Cryptography or PQC, the National Institute of Standards and Technology or NIST recently announced the first candidates for standardization with one algorithm for key encapsulation mechanism (KEM), Kyber, and three algorithms for digital signatures. NIST has also issued a new call for quantum-safe digital signature algorithms due June 1, 2023. This timeline shows that FIPS-certified quantum-safe TLS protocol would take a predictably long time. However, \"steal now, crack later\" tactic requires protecting data against future quantum threat actors today. NIST recommended the use of a hybrid mode of TLS 1.3 with its extensions to support PQC. The hybrid mode works for certain cases but FIPS certification for the hybridized cryptomodule might still be required. This paper proposes to take a nested mode to enable TLS 1.3 protocol with quantum-safe data, which can be made available today and is FIPS compliant. We discussed the performance impacts of the handshaking phase of the nested TLS 1.3 with PQC and the symmetric encryption phase. The major impact on performance using the nested mode is in the data symmetric encryption with AES. To overcome this performance reduction, we suggest using quantum encryption with a quantum permutation pad for the data encryption with a minor performance reduction of less than 10 percent.

}, keywords = {Cryptography and Security (cs.CR), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2301.00062}, url = {https://arxiv.org/abs/2301.00062}, author = {He, Alex and Lou, Dafu and She, Eric and Guo, Shangjie and Watson, Hareesh and Weng, Sibyl and Perepechaenko, Maria and Kuang, Rand} } @article {3179, title = {Group coset monogamy games and an application to device-independent continuous-variable QKD}, year = {2022}, month = {12/7/2022}, abstract = {

We develop an extension of a recently introduced subspace coset state monogamy-of-entanglement game [Coladangelo, Liu, Liu, and Zhandry; Crypto\&$\#$39;21] to general group coset states, which are uniform superpositions over elements of a subgroup to which has been applied a group-theoretic generalization of the quantum one-time pad. We give a general bound on the winning probability of a monogamy game constructed from subgroup coset states that applies to a wide range of finite and infinite groups. To study the infinite-group case, we use and further develop a measure-theoretic formalism that allows us to express continuous-variable measurements as operator-valued generalizations of probability measures.
We apply the monogamy game bound to various physically relevant groups, yielding realizations of the game in continuous-variable modes as well as in rotational states of a polyatomic molecule. We obtain explicit strong bounds in the case of specific group-space and subgroup combinations. As an application, we provide the first proof of one sided-device independent security of a squeezed-state continuous-variable quantum key distribution protocol against general coherent attacks.

}, keywords = {Cryptography and Security (cs.CR), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2212.03935}, url = {https://arxiv.org/abs/2212.03935}, author = {Culf, Eric and Vidick, Thomas and Victor V. Albert} } @article {2913, title = {Hamiltonian simulation with random inputs}, journal = {Phys. Rev. Lett. 129, 270502}, volume = {129}, year = {2022}, month = {12/30/2022}, abstract = {

The algorithmic error of digital quantum simulations is usually explored in terms of the spectral norm distance between the actual and ideal evolution operators. In practice, this worst-case error analysis may be unnecessarily pessimistic. To address this, we develop a theory of average-case performance of Hamiltonian simulation with random initial states. We relate the average-case error to the Frobenius norm of the multiplicative error and give upper bounds for the product formula (PF) and truncated Taylor series methods. As applications, we estimate average-case error for digital Hamiltonian simulation of general lattice Hamiltonians and k-local Hamiltonians. In particular, for the nearest-neighbor Heisenberg chain with n spins, the error is quadratically reduced from O(n) in the worst case to O(n\−\−\√) on average for both the PF method and the Taylor series method. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models. We also apply our results to error analysis in the simulation of quantum scrambling.

}, doi = {https://doi.org/10.1103/PhysRevLett.129.270502}, url = {https://arxiv.org/abs/2111.04773}, author = {Qi Zhao and You Zhou and Alexander F. Shaw and Tongyang Li and Andrew M. Childs} } @article {3190, title = {Higher-group symmetry in finite gauge theory and stabilizer codes}, year = {2022}, month = {11/21/2022}, abstract = {

A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper, we derive the d-group global symmetry and its \&$\#$39;t Hooft anomaly for topological finite group gauge theories in (d+1) space-time dimensions, including non-Abelian gauge groups and Dijkgraaf-Witten twists. We focus on the 1-form symmetry generated by invertible (Abelian) magnetic defects and the higher-form symmetries generated by invertible topological defects decorated with lower dimensional gauged symmetry-protected topological (SPT) phases. We show that due to a generalization of the Witten effect and charge-flux attachment, the 1-form symmetry generated by the magnetic defects mixes with other symmetries into a higher group. We describe such higher-group symmetry in various lattice model examples. We discuss several applications, including the classification of fermionic SPT phases in (3+1)D for general fermionic symmetry groups, where we also derive a simpler formula for the [O5]\∈H5(BG,U(1)) obstruction than has appeared in previous work. We also show how the d-group symmetry is related to fault-tolerant non-Pauli logical gates and a refined Clifford hierarchy in stabilizer codes. We construct new logical gates in stabilizer codes using the d-group symmetry, such as the control-Z gate in (3+1)D Z2 toric code.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, High Energy Physics - Theory (hep-th), Quantum Algebra (math.QA), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2211.11764}, url = {https://arxiv.org/abs/2211.11764}, author = {Barkeshli, Maissam and Chen, Yu-An and Hsin, Po-Shen and Kobayashi, Ryohei} } @article {2944, title = {How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics}, journal = {npj Quantum Inf}, volume = {8}, year = {2022}, month = {01/27/2022}, abstract = {

Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and a bath exchange quantities -- energy, particles, electric charge, etc. -- that are globally conserved and are represented by Hermitian operators. These operators were implicitly assumed to commute with each other, until a few years ago. Freeing the operators to fail to commute has enabled many theoretical discoveries -- about reference frames, entropy production, resource-theory models, etc. Little work has bridged these results from abstract theory to experimental reality. This paper provides a methodology for building this bridge systematically: We present an algorithm for constructing Hamiltonians that conserve noncommuting quantities globally while transporting the quantities locally. The Hamiltonians can couple arbitrarily many subsystems together and can be integrable or nonintegrable. Special cases of our construction have appeared in quantum chromodynamics (QCD). Our Hamiltonians may be realized physically with superconducting qudits, with ultracold atoms, with trapped ions, and in QCD.

}, doi = {https://doi.org/10.1038/s41534-022-00516-4}, url = {https://arxiv.org/abs/2103.14041v1}, author = {Nicole Yunger Halpern and Shayan Majidy} } @article {2607, title = {Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions}, journal = {Phys. Rev. Research}, volume = {4}, year = {2022}, month = {10/27/2022}, abstract = {

The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as 1/rα in the distance r provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor\&$\#$39;s algorithm to be performed on a D-dimensional lattice in time logarithmic in the number of qubits for interactions with α\≤D. As a corollary, we show that power-law systems with α\≤D are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a new technique to give a general lower bound, linear in the size of the system, on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than is possible with previously available techniques.\ 

}, doi = {https://doi.org/10.1103/PhysRevResearch.4.L042016}, url = {https://arxiv.org/abs/2007.00662}, author = {Andrew Y. Guo and Abhinav Deshpande and Su-Kuan Chu and Zachary Eldredge and Przemyslaw Bienias and Dhruv Devulapalli and Yuan Su and Andrew M. Childs and Alexey V. Gorshkov} } @article {3188, title = {Importance of the Spectral gap in Estimating Ground-State Energies}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {12/9/2022}, abstract = {

The field of quantum Hamiltonian complexity lies at the intersection of quantum many-body physics and computational complexity theory, with deep implications to both fields. The main object of study is the LocalHamiltonian problem, which is concerned with estimating the ground-state energy of a local Hamiltonian and is complete for the class QMA, a quantum generalization of the class NP. A major challenge in the field is to understand the complexity of the LocalHamiltonian problem in more physically natural parameter regimes. One crucial parameter in understanding the ground space of any Hamiltonian in many-body physics is the spectral gap, which is the difference between the smallest two eigenvalues. Despite its importance in quantum many-body physics, the role played by the spectral gap in the complexity of the LocalHamiltonian is less well-understood. In this work, we make progress on this question by considering the precise regime, in which one estimates the ground-state energy to within inverse exponential precision. Computing ground-state energies precisely is a task that is important for quantum chemistry and quantum many-body physics.
In the setting of inverse-exponential precision, there is a surprising result that the complexity of LocalHamiltonian is magnified from QMA to PSPACE, the class of problems solvable in polynomial space. We clarify the reason behind this boost in complexity. Specifically, we show that the full complexity of the high precision case only comes about when the spectral gap is exponentially small. As a consequence of the proof techniques developed to show our results, we uncover important implications for the representability and circuit complexity of ground states of local Hamiltonians, the theory of uniqueness of quantum witnesses, and techniques for the amplification of quantum witnesses in the presence of postselection.

}, doi = {10.1103/prxquantum.3.040327}, url = {https://arxiv.org/abs/2007.11582}, author = {Abhinav Deshpande and Alexey V. Gorshkov and Bill Fefferman} } @article {3070, title = {Infinite-randomness criticality in monitored quantum dynamics with static disorder}, year = {2022}, month = {5/27/2022}, abstract = {

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In particular, at the critical measurement rate, we find that the entanglement of a subsystem of size l scales as S\∼l\√; moreover, the dynamical critical exponent z=\∞. The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents. We argue for this infinite-randomness scenario on general grounds and present numerical evidence that it captures some features of the universal critical properties of MIPT using large-scale simulations of Clifford circuits. These findings demonstrate that the relevance and irrelevance of perturbations to the MIPT can naturally be interpreted using a powerful heuristic known as the Harris criterion.\ 

}, url = {https://arxiv.org/abs/2205.14002}, author = {Aidan Zabalo and Justin H. Wilson and Michael Gullans and Romain Vasseur and Sarang Gopalakrishnan and David A. Huse and J. H. Pixley} } @article {3135, title = {Isolation and manipulation of a single-donor detector in a silicon quantum dot}, journal = {Phys. Rev. B}, volume = {106}, year = {2022}, month = {9/27/2022}, pages = {125423}, abstract = {

We demonstrate the isolation and electrostatic control of a single phosphorus donor in a silicon quantum dot by making use of source-drain bias during cooldown and biases applied to capacitively coupled gates. Characterization of the device at low temperatures and in magnetic fields shows single donors can be electrostatically isolated near one of the quantum dot\&$\#$39;s tunnel barriers with either single or double occupancy. This model is well supported by capacitance-based simulations. The ability to use the\ D\ 0\ state of such isolated donors as a charge detector is demonstrated by observing the charge stability diagram of a nearby and capacitively coupled semiconnected double quantum dot.

}, doi = {10.1103/PhysRevB.106.125423}, url = {https://link.aps.org/doi/10.1103/PhysRevB.106.125423}, author = {Lasek, A. A. and Barnes, C. H. W. and Ferrus, T.} } @article {2814, title = {Kramers{\textquoteright} degeneracy for open systems in thermal equilibrium}, journal = {Phys. Rev. B}, volume = {105}, year = {2022}, month = {3/10/2022}, pages = {L121104}, doi = {https://doi.org/10.1103/PhysRevB.105.L121104}, url = {https://arxiv.org/abs/2105.02888}, author = {Simon Lieu and Max McGinley and Oles Shtanko and Nigel R. Cooper and Alexey V. Gorshkov} } @article {3154, title = {Lattice-Based Quantum Advantage from Rotated Measurements}, year = {2022}, month = {10/18/2022}, abstract = {

Trapdoor claw-free functions (TCFs) are immensely valuable in cryptographic interactions between a classical client and a quantum server. Typically, a protocol has the quantum server prepare a superposition of two-bit strings of a claw and then measure it using Pauli-X or Z measurements. In this paper, we demonstrate a new technique that uses the entire range of qubit measurements from the XY-plane. We show the advantage of this approach in two applications. First, building on (Brakerski et al. 2018, Kalai et al. 2022), we show an optimized two-round proof of quantumness whose security can be expressed directly in terms of the hardness of the LWE (learning with errors) problem. Second, we construct a one-round protocol for blind remote preparation of an arbitrary state on the XY-plane up to a Pauli-Z correction.

}, keywords = {Cryptography and Security (cs.CR), Emerging Technologies (cs.ET), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.10143}, url = {https://arxiv.org/abs/2210.10143}, author = {Yusuf Alnawakhtha and Mantri, Atul and Carl Miller and Wang, Daochen} } @article {3027, title = {Linear growth of quantum circuit complexity}, journal = {Nat. Phys.}, year = {2022}, month = {3/28/2022}, abstract = {

The complexity of quantum states has become a key quantity of interest across various subfields of physics, from quantum computing to the theory of black holes. The evolution of generic quantum systems can be modelled by considering a collection of qubits subjected to sequences of random unitary gates. Here we investigate how the complexity of these random quantum circuits increases by considering how to construct a unitary operation from Haar-random two-qubit quantum gates. Implementing the unitary operation exactly requires a minimal number of gates\—this is the operation\’s exact circuit complexity. We prove a conjecture that this complexity grows linearly, before saturating when the number of applied gates reaches a threshold that grows exponentially with the number of qubits. Our proof overcomes difficulties in establishing lower bounds for the exact circuit complexity by combining differential topology and elementary algebraic geometry with an inductive construction of Clifford circuits.

}, doi = {https://doi.org/10.1038/s41567-022-01539-6}, author = {Jonas Haferkamp and Philippe Faist and Naga B. T. Kothakonda and Jens Eisert and Nicole Yunger Halpern} } @article {3014, title = {Machine-assisted discovery of integrable symplectic mappings}, year = {2022}, month = {3/22/2022}, abstract = {

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the algorithm is based on the knowledge that the evolution of an integrable system in the phase space is restricted to a lower-dimensional submanifold. Limiting ourselves to polygon invariants of motion, we analyze the shape of individual trajectories thus successfully distinguishing integrable motion from chaotic cases. For example, our method rediscovers some of the famous McMillan-Suris integrable mappings and discrete Painlev{\'e} equations. In total, over 100 new integrable families are presented and analyzed; some of them are isolated in the space of parameters, and some of them are families with one parameter (or the ratio of parameters) being continuous or discrete. At the end of the paper, we suggest how newly discovered maps are related to a general 2D symplectic map via an introduction of discrete perturbation theory and propose a method on how to construct smooth near-integrable dynamical systems based on mappings with polygon invariants.

}, keywords = {Accelerator Physics (physics.acc-ph), Adaptation and Self-Organizing Systems (nlin.AO), Exactly Solvable and Integrable Systems (nlin.SI), FOS: Physical sciences}, doi = {10.48550/ARXIV.2201.13133}, url = {https://arxiv.org/abs/2201.13133}, author = {Zolkin, Timofey and Kharkov, Yaroslav and Nagaitsev, Sergei} } @article {3148, title = {Mana and thermalization: Probing the feasibility of near-Clifford Hamiltonian simulation}, journal = {Physical Review B}, volume = {106}, year = {2022}, month = {9/28/2022}, abstract = {

Quantum hydrodynamics is the emergent classical dynamics governing transport of conserved quantities in generic strongly-interacting quantum systems. Recent matrix product operator methods have made simulations of quantum hydrodynamics in 1+1d tractable, but they do not naturally generalize to 2+1d or higher, and they offer limited guidance as to the difficulty of simulations on quantum computers. Near-Clifford simulation algorithms are not limited to one dimension, and future error-corrected quantum computers will likely be bottlenecked by non-Clifford operations. We therefore investigate the non-Clifford resource requirements for simulation of quantum hydrodynamics using {\textquoteleft}{\textquoteleft}mana\&$\#$39;\&$\#$39;, a resource theory of non-Clifford operations. For infinite-temperature starting states we find that the mana of subsystems quickly approaches zero, while for starting states with energy above some threshold the mana approaches a nonzero value. Surprisingly, in each case the finite-time mana is governed by the subsystem entropy, not the thermal state mana; we argue that this is because mana is a sensitive diagnostic of finite-time deviations from canonical typicality.

}, doi = {10.1103/physrevb.106.125130}, url = {https://arxiv.org/abs/2201.12367}, author = {Troy J. Sewell and Christopher David White} } @article {3142, title = {Many-Body Quantum Teleportation via Operator Spreading in the Traversable Wormhole Protocol}, journal = {Physical Review X}, volume = {12}, year = {2022}, month = {8/5/2022}, abstract = {

By leveraging shared entanglement between a pair of qubits, one can teleport a quantum state from one particle to another. Recent advances have uncovered an intrinsically many-body generalization of quantum teleportation, with an elegant and surprising connection to gravity. In particular, the teleportation of quantum information relies on many-body dynamics, which originate from strongly-interacting systems that are holographically dual to gravity; from the gravitational perspective, such quantum teleportation can be understood as the transmission of information through a traversable wormhole. Here, we propose and analyze a new mechanism for many-body quantum teleportation -- dubbed peaked-size teleportation. Intriguingly, peaked-size teleportation utilizes precisely the same type of quantum circuit as traversable wormhole teleportation, yet has a completely distinct microscopic origin: it relies upon the spreading of local operators under generic thermalizing dynamics and not gravitational physics. We demonstrate the ubiquity of peaked-size teleportation, both analytically and numerically, across a diverse landscape of physical systems, including random unitary circuits, the Sachdev-Ye-Kitaev model (at high temperatures), one-dimensional spin chains and a bulk theory of gravity with stringy corrections. Our results pave the way towards using many-body quantum teleportation as a powerful experimental tool for: (i) characterizing the size distributions of operators in strongly-correlated systems and (ii) distinguishing between generic and intrinsically gravitational scrambling dynamics. To this end, we provide a detailed experimental blueprint for realizing many-body quantum teleportation in both trapped ions and Rydberg atom arrays; effects of decoherence and experimental imperfections are analyzed.

}, doi = {10.1103/physrevx.12.031013}, url = {https://arxiv.org/abs/2102.00010}, author = {Thomas Schuster and Bryce Kobrin and Ping Gao and Iris Cong and Emil T. Khabiboulline and Norbert M. Linke and Mikhail D. Lukin and Christopher Monroe and Beni Yoshida and Norman Y. Yao} } @article {3202, title = {The Mathematics of Quantum Coin-Flipping}, journal = {Notices of the American Mathematical Society}, volume = {69}, year = {2022}, month = {12/2022}, pages = {1908-1917}, issn = {0002-9920}, doi = {https://doi.org/10.1090/noti2575}, url = {https://www.ams.org/notices/202211/rnoti-p1908.pdf}, author = {Carl Miller} } @article {3132, title = {Modular commutator in gapped quantum many-body systems}, journal = {Physical Review B}, volume = {106}, year = {2022}, month = {8/26/2022}, abstract = {

In arXiv:2110.06932, we argued that the chiral central charge -- a topologically protected quantity characterizing the edge theory of a gapped (2+1)-dimensional system -- can be extracted from the bulk by using an order parameter called the modular commutator. In this paper, we reveal general properties of the modular commutator and strengthen its relationship with the chiral central charge. First, we identify connections between the modular commutator and conditional mutual information, time reversal, and modular flow. Second, we prove, within the framework of the entanglement bootstrap program, that two topologically ordered media connected by a gapped domain wall must have the same modular commutator in their respective bulk. Third, we numerically calculate the value of the modular commutator for a bosonic lattice Laughlin state for finite sizes and extrapolate to the infinite-volume limit. The result of this extrapolation is consistent with the proposed formula up to an error of about 0.7\%.

}, doi = {10.1103/physrevb.106.075147}, url = {https://arxiv.org/abs/2110.10400}, author = {Isaac H. Kim and Bowen Shi and Kohtaro Kato and Victor V. Albert} } @article {3024, title = {Monitoring-induced Entanglement Entropy and Sampling Complexity}, year = {2022}, month = {1/29/2022}, abstract = {

The dynamics of open quantum systems is generally described by a master equation, which describes the loss of information into the environment. By using a simple model of uncoupled emitters, we illustrate how the recovery of this information depends on the monitoring scheme applied to register the decay clicks. The dissipative dynamics, in this case, is described by pure-state stochastic trajectories and we examine different unravelings of the same master equation. More precisely, we demonstrate how registering the sequence of clicks from spontaneously emitted photons through a linear optical interferometer induces entanglement in the trajectory states. Since this model consists of an array of single-photon emitters, we show a direct equivalence with Fock-state boson sampling and link the hardness of sampling the outcomes of the quantum jumps with the scaling of trajectory entanglement.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2201.12672}, url = {https://arxiv.org/abs/2201.12672}, author = {Van Regemortel, Mathias and Shtanko, Oles and Garc{\'\i}a-Pintos, Luis Pedro and Deshpande, Abhinav and Dehghani, Hossein and Alexey V. Gorshkov and Hafezi, Mohammad} } @article {3147, title = {Multi-Angle QAOA Does Not Always Need All Its Angles}, year = {2022}, month = {9/23/2022}, abstract = {

Introducing additional tunable parameters to quantum circuits is a powerful way of improving performance without increasing hardware requirements. A recently introduced multi-angle extension of the quantum approximate optimization algorithm (ma-QAOA) significantly improves the solution from QAOA by allowing the parameters for each term in the Hamiltonian to vary independently. However, prior results suggest that there is considerable redundancy in parameters, the removal of which would reduce the cost of parameter optimization. In this work, we show numerically that problem symmetries can be used to reduce the number of parameters used by ma-QAOA without decreasing the solution quality. We study MaxCut on all 7,565 connected, non-isomorphic 8-node graphs with a non-trivial symmetry group and show numerically that in 67.4\% of these graphs, symmetry can be used to reduce the number of parameters with no decrease in the objective, with the average ratio of parameters reduced by 28.1\%. Moreover, we show that in 35.9\% of the graphs this can be achieved by simply using the largest symmetry. For the graphs where reducing the number of parameters leads to a decrease in the objective, the largest symmetry can be used to reduce the parameter count by 37.1\% at the cost of only a 6.1\% decrease in the objective.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.11839}, url = {https://arxiv.org/abs/2209.11839}, author = {Shi, Kaiyan and Herrman, Rebekah and Shaydulin, Ruslan and Chakrabarti, Shouvanik and Pistoia, Marco and Larson, Jeffrey} } @article {3141, title = {N-body interactions between trapped ion qubits via spin-dependent squeezing}, journal = {Physical Review Letters}, volume = {129}, year = {2022}, month = {8/5/2022}, abstract = {

We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the M{\o}lmer-S{\o}rensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.

}, doi = {10.1103/physrevlett.129.063603}, url = {https://arxiv.org/abs/2202.04230}, author = {Or Katz and Marko Cetina and Christopher Monroe} } @article {3054, title = {Negative Quasiprobabilities Enhance Phase Estimation in Quantum-Optics Experiment}, journal = {Phys. Rev. Lett.}, volume = {128}, year = {2022}, month = {6/2/2022}, pages = {220504}, abstract = {

Operator noncommutation, a hallmark of quantum theory, limits measurement precision, according to uncertainty principles. Wielded correctly, though, noncommutation can boost precision. A recent foundational result relates a metrological advantage with negative quasiprobabilities\—quantum extensions of probabilities\—engendered by noncommuting operators. We crystallize the relationship in an equation that we prove theoretically and observe experimentally. Our proof-of-principle optical experiment features a filtering technique that we term partially postselected amplification (PPA). Using PPA, we measure a wave plate\’s birefringent phase. PPA amplifies, by over two orders of magnitude, the information obtained about the phase per detected photon. In principle, PPA can boost the information obtained from the average filtered photon by an arbitrarily large factor. The filter\’s amplification of systematic errors, we find, bounds the theoretically unlimited advantage in practice. PPA can facilitate any phase measurement and mitigates challenges that scale with trial number, such as proportional noise and detector saturation. By quantifying PPA\’s metrological advantage with quasiprobabilities, we reveal deep connections between quantum foundations and precision measurement.

}, doi = {10.1103/PhysRevLett.128.220504}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.128.220504}, author = {Lupu-Gladstein, Noah and Yilmaz, Y. Batuhan and Arvidsson-Shukur, David R. M. and Brodutch, Aharon and Pang, Arthur O. T. and Steinberg, Aephraim M. and Nicole Yunger Halpern} } @article {3076, title = {NISQ algorithm for the matrix elements of a generic observable}, year = {2022}, month = {5/20/2022}, abstract = {

The calculation of off-diagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and off-diagonal matrix elements of a generic observable in the energy eigenbasis of a given Hamiltonian. Several numerical simulations indicate that this approach can find many of the matrix elements even when the trial functions are randomly initialized across a wide range of parameter values without, at the same time, the need to prepare the energy eigenstates.\ 

}, url = {https://arxiv.org/abs/2205.10058}, author = {Rebecca Erbanni and Kishor Bharti and Leong-Chuan Kwek and Dario Poletti} } @article {3006, title = {Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions}, journal = {Physical Review Letters}, volume = {128}, year = {2022}, month = {2/11/2022}, abstract = {

Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar values of the critical exponents, making it unclear if there is only one underlying universality class. Here, we directly probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large onsite Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

}, doi = {10.1103/physrevlett.128.050602}, url = {https://arxiv.org/abs/2107.03393}, author = {Aidan Zabalo and Michael Gullans and Justin H. Wilson and Romain Vasseur and Andreas W. W. Ludwig and Sarang Gopalakrishnan and David A. Huse and J. H. Pixley} } @article {3203, title = {Opportunities and Challenges in Fault-Tolerant Quantum Computation}, year = {2022}, month = {10/28/2022}, abstract = {

I will give an overview of what I see as some of the most important future directions in the theory of fault-tolerant quantum computation. In particular, I will give a brief summary of the major problems that need to be solved in fault tolerance based on low-density parity check codes and in hardware-specific fault tolerance. I will then conclude with a discussion of a possible new paradigm for designing fault-tolerant protocols based on a space-time picture of quantum circuits.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.15844}, url = {https://arxiv.org/abs/2210.15844}, author = {Daniel Gottesman} } @article {3129, title = {Optical conductivity and orbital magnetization of Floquet vortex states}, year = {2022}, month = {4/20/2022}, abstract = {

Motivated by recent experimental demonstrations of Floquet topological insulators, there have been several theoretical proposals for using structured light, either spatial or spectral, to create other properties such as flat band and vortex states. In particular, the generation of vortex states in a massive Dirac fermion insulator irradiated by light carrying nonzero orbital angular momentum (OAM) has been proposed [Kim et al. Phys. Rev. B 105, L081301(2022)]. Here, we evaluate the orbital magnetization and optical conductivity as physical observables for such a system. We show that the OAM of light induces nonzero orbital magnetization and current density. The orbital magnetization density increases linearly as a function of OAM degree. In certain regimes, we find that orbital magnetization density is independent of the system size, width, and Rabi frequency of light. It is shown that the orbital magnetization arising from our Floquet theory is large and can be probed by magnetometry measurements. Furthermore, we study the optical conductivity for various types of electron transitions between different states such as vortex, edge, and bulk that are present in the system. Based on conductance frequency peaks, a scheme for the detection of vortex states is proposed.

}, keywords = {FOS: Physical sciences, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), Other Condensed Matter (cond-mat.other)}, doi = {10.48550/ARXIV.2204.09488}, url = {https://arxiv.org/abs/2204.09488}, author = {Ahmadabadi, Iman and Dehghani, Hossein and Hafezi, Mohammad} } @article {3196, title = {Optimal scaling quantum linear systems solver via discrete adiabatic theorem}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {10/7/2022}, pages = {040303}, abstract = {

Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition number κ of the linear system, without requiring a complicated variable-time amplitude amplification procedure. However, the most efficient of those procedures is still asymptotically sub-optimal by a factor of log(κ). Here, we prove a rigorous form of the adiabatic theorem that bounds the error in terms of the spectral gap for intrinsically discrete time evolutions. We use this discrete adiabatic theorem to develop a quantum algorithm for solving linear systems that is asymptotically optimal, in the sense that the complexity is strictly linear in κ, matching a known lower bound on the complexity. Our O(κlog(1/ϵ)) complexity is also optimal in terms of the combined scaling in κ and the precision ϵ. Compared to existing suboptimal methods, our algorithm is simpler and easier to implement. Moreover, we determine the constant factors in the algorithm, which would be suitable for determining the complexity in terms of gate counts for specific applications.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.3.040303}, url = {https://arxiv.org/abs/2111.08152}, author = {Costa, Pedro C. S. and Dong An and Sanders, Yuval R. and Su, Yuan and Babbush, Ryan and Berry, Dominic W.} } @article {3015, title = {Pauli Stabilizer Models of Twisted Quantum Doubles}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {3/30/2022}, abstract = {

We construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z4 toric code, where the condensation is implemented by making certain two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes - in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type I and type II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain 1-form symmetries of the TQD stabilizer models.

}, doi = {https://doi.org/10.1103\%2Fprxquantum.3.010353}, url = {https://arxiv.org/abs/2112.11394}, author = {Tyler D. Ellison and Yu-An Chen and Arpit Dua and Wilbur Shirley and Nathanan Tantivasadakarn and Dominic J. Williamson} } @article {3193, title = {Pauli topological subsystem codes from Abelian anyon theories}, year = {2022}, month = {11/7/2022}, abstract = {

We construct Pauli topological subsystem codes characterized by arbitrary two-dimensional Abelian anyon theories--this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum. Our work both extends the classification of two-dimensional Pauli topological subsystem codes to systems of composite-dimensional qudits and establishes that the classification is at least as rich as that of Abelian anyon theories. We exemplify the construction with topological subsystem codes defined on four-dimensional qudits based on the Z(1)4 anyon theory with degenerate braiding relations and the chiral semion theory--both of which cannot be captured by topological stabilizer codes. The construction proceeds by \"gauging out\" certain anyon types of a topological stabilizer code. This amounts to defining a gauge group generated by the stabilizer group of the topological stabilizer code and a set of anyonic string operators for the anyon types that are gauged out. The resulting topological subsystem code is characterized by an anyon theory containing a proper subset of the anyons of the topological stabilizer code. We thereby show that every Abelian anyon theory is a subtheory of a stack of toric codes and a certain family of twisted quantum doubles that generalize the double semion anyon theory. We further prove a number of general statements about the logical operators of translation invariant topological subsystem codes and define their associated anyon theories in terms of higher-form symmetries.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2211.03798}, url = {https://arxiv.org/abs/2211.03798}, author = {Ellison, Tyler D. and Chen, Yu-An and Dua, Arpit and Shirley, Wilbur and Tantivasadakarn, Nathanan and Williamson, Dominic J.} } @article {2931, title = {Post-Quantum Security of the Even-Mansour Cipher}, journal = {Eurocrypt}, year = {2022}, month = {12/14/2021}, abstract = {

The Even-Mansour cipher is a simple method for constructing a (keyed) pseudorandom permutation E from a public random permutation~P:{0,1}n\→{0,1}n. It is secure against classical attacks, with optimal attacks requiring qE queries to E and qP queries to P such that qE\⋅qP\≈2n. If the attacker is given \emph{quantum} access to both E and P, however, the cipher is completely insecure, with attacks using qE,qP=O(n) queries known. In any plausible real-world setting, however, a quantum attacker would have only \emph{classical} access to the keyed permutation~E implemented by honest parties, even while retaining quantum access to~P. Attacks in this setting with qE\⋅q2P\≈2n are known, showing that security degrades as compared to the purely classical case, but leaving open the question as to whether the Even-Mansour cipher can still be proven secure in this natural, \"post-quantum\" setting. We resolve this question, showing that any attack in that setting requires qE\⋅q2P+qP\⋅q2E\≈2n. Our results apply to both the two-key and single-key variants of Even-Mansour. Along the way, we establish several generalizations of results from prior work on quantum-query lower bounds that may be of independent interest.\ 

}, doi = {https://doi.org/10.48550/arXiv.2112.07530}, url = {https://arxiv.org/abs/2112.07530}, author = {Gorjan Alagic and Chen Bai and Jonathan Katz and Christian Majenz} } @article {3201, title = {Post-Quantum Security of the (Tweakable) FX Construction, and Applications}, year = {2022}, month = {8/29/2022}, abstract = {

The FX construction provides a way to increase the effective key length of a block cipher E. We prove security of a tweakable version of the FX construction in the post-quantum setting, i.e., against a quantum attacker given only classical access to the secretly keyed construction while retaining quantum access to E, a setting that seems to be the most relevant one for real-world applications. We then use our results to prove post-quantum security\—in the same model\—of the (plain) FX construction, Elephant (a finalist of NIST\&$\#$39;s lightweight cryptography standardization effort), and Chaskey (an ISO-standardized lightweight MAC

}, url = {https://eprint.iacr.org/2022/1097}, author = {Gorjan Alagic and Chen Bai and Jonathan Katz and Christian Majenz and Patrick Struck} } @article {3130, title = {Provably accurate simulation of gauge theories and bosonic systems}, journal = {Quantum}, volume = {6}, year = {2022}, month = {9/20/2022}, pages = {816}, abstract = {

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most ϵ can be achieved by choosing Λ to scale polylogarithmically with ϵ\−1, an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on Λ that achieves accuracy ϵ, obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy ϵ by truncating local quantum numbers at Λ=polylog(ϵ\−1).

}, doi = {https://doi.org/10.22331\%2Fq-2022-09-22-816}, url = {https://arxiv.org/abs/2110.06942}, author = {Yu Tong and Victor V. Albert and Jarrod R. McClean and John Preskill and Yuan Su} } @article {3131, title = {Provably efficient machine learning for quantum many-body problems}, journal = {Science}, volume = {377}, year = {2022}, month = {9/26/2022}, abstract = {

Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

}, doi = {10.1126/science.abk3333}, url = {https://arxiv.org/abs/2106.12627}, author = {Hsin-Yuan Huang and Richard Kueng and Giacomo Torlai and Victor V. Albert and John Preskill} } @article {3150, title = {Quantum Algorithms for Sampling Log-Concave Distributions and Estimating Normalizing Constants}, journal = {Advances in Neural Information Processing Systems (NeurIPS 2022)}, volume = {35}, year = {2022}, month = {10/12/2022}, keywords = {FOS: Computer and information sciences, FOS: Mathematics, FOS: Physical sciences, Machine Learning (cs.LG), Optimization and Control (math.OC), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.06539}, url = {https://arxiv.org/abs/2210.06539}, author = {Andrew M. Childs and Li, Tongyang and Liu, Jin-Peng and Wang, Chunhao and Zhang, Ruizhe} } @article {2983, title = {Quantum computational advantage via high-dimensional Gaussian boson sampling}, journal = {Science Advances}, volume = {8}, year = {2022}, month = {1/5/2022}, pages = {eabi7894}, abstract = {

A programmable quantum computer based on fiber optics outperforms classical computers with a high level of confidence. Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We provide evidence for the hardness of GBS, comparable to the strongest theoretical proposals for QCA. We also propose a QCA architecture we call high-dimensional GBS, which is programmable and can be implemented with low loss using few optical components. We show that particular algorithms for simulating GBS are outperformed by high-dimensional GBS experiments at modest system sizes. This work thus opens the path to demonstrating QCA with programmable photonic processors.

}, doi = {10.1126/sciadv.abi7894}, url = {https://www.science.org/doi/abs/10.1126/sciadv.abi7894}, author = {Abhinav Deshpande and Arthur Mehta and Trevor Vincent and Nicolas Quesada and Marcel Hinsche and Marios Ioannou and Lars Madsen and Jonathan Lavoie and Haoyu Qi and Jens Eisert and Dominik Hangleiter and Bill Fefferman and Ish Dhand} } @article {3137, title = {Quantum Depth in the Random Oracle Model}, year = {2022}, month = {10/12/2022}, abstract = {

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a random oracle:
(a) BPPQNCBPP\≠BQP. This refutes Jozsa\&$\#$39;s conjecture [QIP 05] in the random oracle model. As a result, this gives the first instantiatable separation between the classes by replacing the oracle with a cryptographic hash function, yielding a resolution to one of Aaronson\&$\#$39;s ten semi-grand challenges in quantum computing.
(b) BPPQNC⊈QNCBPP and QNCBPP⊈BPPQNC. This shows that there is a subtle interplay between classical computation and shallow quantum computation. In fact, for the second separation, we establish that, for some problems, the ability to perform adaptive measurements in a single shallow quantum circuit, is more useful than the ability to perform polynomially many shallow quantum circuits without adaptive measurements.
(c) There exists a 2-message proof of quantum depth protocol. Such a protocol allows a classical verifier to efficiently certify that a prover must be performing a computation of some minimum quantum depth. Our proof of quantum depth can be instantiated using the recent proof of quantumness construction by Yamakawa and Zhandry [STOC 22].

}, keywords = {Computational Complexity (cs.CC), Cryptography and Security (cs.CR), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.06454}, url = {https://arxiv.org/abs/2210.06454}, author = {Arora, Atul Singh and Coladangelo, Andrea and Coudron, Matthew and Gheorghiu, Alexandru and Singh, Uttam and Waldner, Hendrik} } @article {3138, title = {Quantum divide and conquer}, year = {2022}, month = {10/12/2022}, abstract = {

The divide-and-conquer framework, used extensively in classical algorithm design, recursively breaks a problem of size n into smaller subproblems (say, a copies of size n/b each), along with some auxiliary work of cost Caux(n), to give a recurrence relation
C(n)\≤aC(n/b)+Caux(n)
for the classical complexity C(n). We describe a quantum divide-and-conquer framework that, in certain cases, yields an analogous recurrence relation
CQ(n)\≤a\−\−\√CQ(n/b)+O(CauxQ(n))
that characterizes the quantum query complexity. We apply this framework to obtain near-optimal quantum query complexities for various string problems, such as (i) recognizing regular languages; (ii) decision versions of String Rotation and String Suffix; and natural parameterized versions of (iii) Longest Increasing Subsequence and (iv) Longest Common Subsequence.

}, keywords = {Data Structures and Algorithms (cs.DS), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.06419}, url = {https://arxiv.org/abs/2210.06419}, author = {Andrew M. Childs and Kothari, Robin and Kovacs-Deak, Matt and Sundaram, Aarthi and Wang, Daochen} } @article {2873, title = {Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks}, journal = {PRX Quantum}, volume = {3}, year = {2022}, month = {05/11/2022}, pages = {020332}, abstract = {

We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal non-Clifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes as well as non-stabilizer codes over qubits and qudits. For a contractible tensor network, the sequence of contractions also constructs a decoding/encoding circuit. To highlight the framework\&$\#$39;s range of capabilities and to provide a tutorial, we lay out some examples where we glue together simple stabilizer codes to construct non-trivial codes. These examples include the toric code and its variants, a holographic code with transversal non-Clifford operators, a 3d stabilizer code, and other stabilizer codes with interesting properties. Surprisingly, we find that the surface code is equivalent to the 2d Bacon-Shor code after \"dualizing\" its tensor network encoding map.

}, doi = {https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.3.020332}, url = {https://arxiv.org/abs/2109.08158}, author = {ChunJun Cao and Brad Lackey} } @article {3124, title = {Quantum Many-Body Scars from Einstein-Podolsky-Rosen States in Bilayer Systems}, year = {2022}, month = {9/12/2022}, abstract = {

Quantum many-body scar states are special eigenstates of nonintegrable models with distinctive entanglement features that give rise to infinitely long-lived coherent dynamics under quantum quenches from certain initial states. We elaborate on a construction of quantum many-body scar states in which they emerge from Einstein-Podolsky-Rosen (EPR) states in systems with two layers, wherein the two layers are maximally entangled. We apply this construction to spin systems as well as systems of itinerant fermions and bosons and demonstrate how symmetries can be harnessed to enhance its versatility. We show that several well-known examples of quantum many-body scars, including the tower of states in the spin-1 XY model and the η-pairing states in the Fermi-Hubbard model, can be understood within this formalism. We also demonstrate how an {\it infinite} tower of many-body scar states can emerge in bilayer Bose-Hubbard models with charge conservation.

}, keywords = {FOS: Physical sciences, Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2209.05527}, url = {https://arxiv.org/abs/2209.05527}, author = {Wildeboer, Julia and Langlett, Christopher M. and Yang, Zhi-Cheng and Alexey V. Gorshkov and Iadecola, Thomas and Xu, Shenglong} } @article {3191, title = {Quantum Natural Proof: A New Perspective of Hybrid Quantum-Classical Program Verification}, year = {2022}, month = {11/11/2022}, abstract = {

Many quantum programs are assured by formal verification, but such verification is usually laborious and time-consuming. This paper proposes quantum natural proof (QNP), an automated proof system for verifying hybrid quantum-classical algorithms. Natural proofs are a subclass of proofs that are amenable to completely automated reasoning, provide sound but incomplete procedures, and capture common reasoning tactics in program verification. The core of QNP is a type-guided quantum proof system, named Qafny, which views quantum operations as some classical array operations that can be modeled as proof rules in a classical separation logic framework, suitable for automated reasoning. We proved the soundness and completeness of the Qafny proof system as well as the soundness of the proof system compilation from Qafny to Dafny. By using the QNP implementation in Dafny, automated verification can be efficiently perform for many hybrid quantum-classical algorithms, including GHZ, Shor\&$\#$39;s, Grover\&$\#$39;s, and quantum walk algorithms, which saves a great amount of human efforts. In addition, quantum programs written in Qafny can be compiled to quantum circuits so that every verified quantum program can be run on a quantum machine.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Programming Languages (cs.PL), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.06411}, url = {https://arxiv.org/abs/2211.06411}, author = {Li, Liyi and Zhu, Mingwei and Lee, Yi and Chang, Le and Wu, Xiaodi} } @article {2996, title = {Quantum Routing with Teleportation}, year = {2022}, month = {4/8/2022}, abstract = {

We study the problem of implementing arbitrary permutations of qubits under interaction constraints in quantum systems that allow for arbitrarily fast local operations and classical communication (LOCC). In particular, we show examples of speedups over swap-based and more general unitary routing methods by distributing entanglement and using LOCC to perform quantum teleportation. We further describe an example of an interaction graph for which teleportation gives a logarithmic speedup in the worst-case routing time over swap-based routing. We also study limits on the speedup afforded by quantum teleportation - showing an O(NlogN\−\−\−\−\−\−\−\√) upper bound on the separation in routing time for any interaction graph - and give tighter bounds for some common classes of graphs.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2204.04185}, url = {https://arxiv.org/abs/2204.04185}, author = {Devulapalli, Dhruv and Schoute, Eddie and Bapat, Aniruddha and Andrew M. Childs and Alexey V. Gorshkov} } @article {2997, title = {Quantum Simulation for High Energy Physics}, year = {2022}, month = {4/7/2022}, abstract = {

It is for the first time that Quantum Simulation for High Energy Physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in Quantum Information Sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This community whitepaper is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

}, keywords = {FOS: Physical sciences, High Energy Physics - Lattice (hep-lat), High Energy Physics - Phenomenology (hep-ph), High Energy Physics - Theory (hep-th), Nuclear Theory (nucl-th), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2204.03381}, url = {https://arxiv.org/abs/2204.03381}, author = {Bauer, Christian W. and Zohreh Davoudi and Balantekin, A. Baha and Bhattacharya, Tanmoy and Carena, Marcela and de Jong, Wibe A. and Draper, Patrick and El-Khadra, Aida and Gemelke, Nate and Hanada, Masanori and Kharzeev, Dmitri and Lamm, Henry and Li, Ying-Ying and Liu, Junyu and Lukin, Mikhail and Meurice, Yannick and Monroe, Christopher and Nachman, Benjamin and Pagano, Guido and Preskill, John and Rinaldi, Enrico and Roggero, Alessandro and Santiago, David I. and Savage, Martin J. and Siddiqi, Irfan and Siopsis, George and Van Zanten, David and Wiebe, Nathan and Yamauchi, Yukari and Yeter-Aydeniz, K{\"u}bra and Zorzetti, Silvia} } @article {3187, title = {Quantum simulation of real-space dynamics}, journal = {Quantum}, volume = {6}, year = {2022}, month = {11/8/2022}, pages = {860}, abstract = {

Quantum simulation is a prominent application of quantum computers. While there is extensive previous work on simulating finite-dimensional systems, less is known about quantum algorithms for real-space dynamics. We conduct a systematic study of such algorithms. In particular, we show that the dynamics of a d-dimensional Schr{\"o}dinger equation with η particles can be simulated with gate complexity O~(ηdFpoly(log(g\′/ϵ))), where ϵ is the discretization error, g\′ controls the higher-order derivatives of the wave function, and F measures the time-integrated strength of the potential. Compared to the best previous results, this exponentially improves the dependence on ϵ and g\′ from poly(g\′/ϵ) to poly(log(g\′/ϵ)) and polynomially improves the dependence on T and d, while maintaining best known performance with respect to η. For the case of Coulomb interactions, we give an algorithm using η3(d+η)Tpoly(log(ηdTg\′/(Δϵ)))/Δ one- and two-qubit gates, and another using η3(4d)d/2Tpoly(log(ηdTg\′/(Δϵ)))/Δ one- and two-qubit gates and QRAM operations, where T is the evolution time and the parameter Δ regulates the unbounded Coulomb interaction. We give applications to several computational problems, including faster real-space simulation of quantum chemistry, rigorous analysis of discretization error for simulation of a uniform electron gas, and a quadratic improvement to a quantum algorithm for escaping saddle points in nonconvex optimization.

}, doi = {https://doi.org/10.22331/q-2022-11-17-860}, url = {https://doi.org/10.22331\%2Fq-2022-11-17-860}, author = {Andrew M. Childs and Jiaqi Leng and Tongyang Li and Jin-Peng Liu and Chenyi Zhang} } @article {3146, title = {Quantum state tomography via non-convex Riemannian gradient descent}, year = {2022}, month = {10/10/2022}, abstract = {

The recovery of an unknown density matrix of large size requires huge computational resources. The recent Factored Gradient Descent (FGD) algorithm and its variants achieved state-of-the-art performance since they could mitigate the dimensionality barrier by utilizing some of the underlying structures of the density matrix. Despite their theoretical guarantee of a linear convergence rate, the convergence in practical scenarios is still slow because the contracting factor of the FGD algorithms depends on the condition number κ of the ground truth state. Consequently, the total number of iterations can be as large as O(κ\−\−\√ln(1ε)) to achieve the estimation error ε. In this work, we derive a quantum state tomography scheme that improves the dependence on κ to the logarithmic scale; namely, our algorithm could achieve the approximation error ε in O(ln(1κε)) steps. The improvement comes from the application of the non-convex Riemannian gradient descent (RGD). The contracting factor in our approach is thus a universal constant that is independent of the given state. Our theoretical results of extremely fast convergence and nearly optimal error bounds are corroborated by numerical results.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2210.04717}, url = {https://arxiv.org/abs/2210.04717}, author = {Hsu, Ming-Chien and Kuo, En-Jui and Yu, Wei-Hsuan and Cai, Jian-Feng and Hsieh, Min-Hsiu} } @article {3186, title = {Qunity: A Unified Language for Quantum and Classical Computing (Extended Version)}, year = {2022}, month = {4/26/2022}, abstract = {

We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and classical effects. For example, one can use sum types to implement the direct sum of linear operators, exception-handling syntax to implement projective measurements, and aliasing to induce entanglement. Further, Qunity takes advantage of the overlooked BQP subroutine theorem, allowing one to construct reversible subroutines from irreversible quantum algorithms through the uncomputation of \"garbage\" outputs. Unlike existing languages that enable quantum aspects with separate add-ons (like a classical language with quantum gates bolted on), Qunity provides a unified syntax and a novel denotational semantics that guarantees that programs are quantum mechanically valid. We present Qunity\&$\#$39;s syntax, type system, and denotational semantics, showing how it can cleanly express several quantum algorithms. We also detail how Qunity can be compiled into a low-level qubit circuit language like OpenQASM, proving the realizability of our design.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Logic in Computer Science (cs.LO), Programming Languages (cs.PL), Quantum Physics (quant-ph)}, doi = {https://doi.org/10.48550/arXiv.2204.12384}, url = {https://arxiv.org/abs/2204.12384}, author = {Voichick, Finn and Li, Liyi and Rand, Robert and Hicks, Michael} } @article {3200, title = {Resource theory of quantum uncomplexity}, journal = {Physical Review A}, volume = {106}, year = {2022}, month = {12/19/2022}, abstract = {

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state\&$\#$39;s complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state\&$\#$39;s distance from maximal complexity, or \"uncomplexity,\" the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind\&$\#$39;s conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.

}, doi = {10.1103/physreva.106.062417}, url = {https://arxiv.org/abs/2110.11371}, author = {Nicole Yunger Halpern and Naga B. T. Kothakonda and Jonas Haferkamp and Anthony Munson and Jens Eisert and Philippe Faist} } @article {3189, title = {Sample-optimal classical shadows for pure states}, year = {2022}, month = {11/21/2022}, abstract = {

We consider the classical shadows task for pure states in the setting of both joint and independent measurements. The task is to measure few copies of an unknown pure state ρ in order to learn a classical description which suffices to later estimate expectation values of observables. Specifically, the goal is to approximate Tr(Oρ) for any Hermitian observable O to within additive error ϵ provided Tr(O2)\≤B and ||O||=1. Our main result applies to the joint measurement setting, where we show Θ~(B\−\−\√ϵ\−1+ϵ\−2) samples of ρ are necessary and sufficient to succeed with high probability. The upper bound is a quadratic improvement on the previous best sample complexity known for this problem. For the lower bound, we see that the bottleneck is not how fast we can learn the state but rather how much any classical description of ρ can be compressed for observable estimation. In the independent measurement setting, we show that O(Bd\−\−\−\√ϵ\−1+ϵ\−2) samples suffice. Notably, this implies that the random Clifford measurements algorithm of Huang, Kueng, and Preskill, which is sample-optimal for mixed states, is not optimal for pure states. Interestingly, our result also uses the same random Clifford measurements but employs a different estimator.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Information Theory (cs.IT), Machine Learning (cs.LG), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.11810}, url = {https://arxiv.org/abs/2211.11810}, author = {Grier, Daniel and Pashayan, Hakop and Luke Schaeffer} } @article {3136, title = {Scalably learning quantum many-body Hamiltonians from dynamical data}, year = {2022}, month = {9/28/2022}, abstract = {

The physics of a closed quantum mechanical system is governed by its Hamiltonian. However, in most practical situations, this Hamiltonian is not precisely known, and ultimately all there is are data obtained from measurements on the system. In this work, we introduce a highly scalable, data-driven approach to learning families of interacting many-body Hamiltonians from dynamical data, by bringing together techniques from gradient-based optimization from machine learning with efficient quantum state representations in terms of tensor networks. Our approach is highly practical, experimentally friendly, and intrinsically scalable to allow for system sizes of above 100 spins. In particular, we demonstrate on synthetic data that the algorithm works even if one is restricted to one simple initial state, a small number of single-qubit observables, and time evolution up to relatively short times. For the concrete example of the one-dimensional Heisenberg model our algorithm exhibits an error constant in the system size and scaling as the inverse square root of the size of the data set.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Machine Learning (cs.LG), Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2209.14328}, url = {https://arxiv.org/abs/2209.14328}, author = {Wilde, Frederik and Kshetrimayum, Augustine and Roth, Ingo and Dominik Hangleiter and Sweke, Ryan and Eisert, Jens} } @article {3204, title = {A scheme to create and verify scalable entanglement in optical lattice}, journal = {npj Quantum Information}, volume = {8}, year = {2022}, month = {9/4/2022}, abstract = {

To achieve scalable quantum information processing, great efforts have been devoted to the creation of large-scale entangled states in various physical systems. Ultracold atom in optical lattice is considered as one of the promising platforms due to its feasible initialization and parallel manipulation. In this work, we propose an efficient scheme to generate and characterize global entanglement in the optical lattice. With only two-layer quantum circuits, the generation utilizes two-qubit entangling gates based on the superexchange interaction in double wells. The parallelism of these operations enables the generation to be fast and scalable. To verify the entanglement of this non-stabilizer state, we mainly design three complementary detection protocols which are less resource-consuming compared to the full tomography. In particular, one just needs two homogenous local measurement settings to identify the entanglement property. Our entanglement generation and verification protocols provide the foundation for the further quantum information processing in optical lattice.

}, doi = {10.1038/s41534-022-00609-0}, url = {https://arxiv.org/abs/2209.01531}, author = {You Zhou and Bo Xiao and Meng-Da Li and Qi Zhao and Zhen-Sheng Yuan and Xiongfeng Ma and Jian-Wei Pan} } @article {3009, title = {Self-Testing of a Single Quantum System: Theory and Experiment}, year = {2022}, month = {3/17/2022}, abstract = {

Certifying individual quantum devices with minimal assumptions is crucial for the development of quantum technologies. Here, we investigate how to leverage single-system contextuality to realize self-testing. We develop a robust self-testing protocol based on the simplest contextuality witness for the simplest contextual quantum system, the Klyachko-Can-Binicio{\u g}lu-Shumovsky (KCBS) inequality for the qutrit. We establish a lower bound on the fidelity of the state and the measurements (to an ideal configuration) as a function of the value of the witness under a pragmatic assumption on the measurements we call the KCBS orthogonality condition. We apply the method in an experiment with randomly chosen measurements on a single trapped 40Ca+ and near-perfect detection efficiency. The observed statistics allow us to self-test the system and provide the first experimental demonstration of quantum self-testing of a single system. Further, we quantify and report that deviations from our assumptions are minimal, an aspect previously overlooked by contextuality experiments.

}, keywords = {Atomic Physics (physics.atom-ph), FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.48550/arXiv.2203.09003}, url = {https://arxiv.org/abs/2203.09003}, author = {Hu, Xiao-Min and Xie, Yi and Arora, Atul Singh and Ai, Ming-Zhong and Bharti, Kishor and Zhang, Jie and Wu, Wei and Chen, Ping-Xing and Cui, Jin-Ming and Liu, Bi-Heng and Huang, Yun-Feng and Li, Chuan-Feng and Guo, Guang-Can and Roland, J{\'e}r{\'e}mie and Cabello, Ad{\'a}n and Kwek, Leong-Chuan} } @article {3017, title = {Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors}, year = {2022}, month = {3/14/2022}, abstract = {

Mitigating errors in quantum information processing devices is especially important in the absence of fault tolerance. An effective method in suppressing state-preparation errors is using multiple copies to distill the ideal component from a noisy quantum state. Here, we use classical shadows and randomized measurements to circumvent the need for coherent access to multiple copies at an exponential cost. We study the scaling of resources using numerical simulations and find that the overhead is still favorable compared to full state tomography. We optimize measurement resources under realistic experimental constraints and apply our method to an experiment preparing Greenberger-Horne-Zeilinger (GHZ) state with trapped ions. In addition to improving stabilizer measurements, the analysis of the improved results reveals the nature of errors affecting the experiment. Hence, our results provide a directly applicable method for mitigating errors in near-term quantum computers.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2203.07309}, url = {https://arxiv.org/abs/2203.07309}, author = {Seif, Alireza and Cian, Ze-Pei and Zhou, Sisi and Chen, Senrui and Jiang, Liang} } @article {3178, title = {Sharp complexity phase transitions generated by entanglement}, year = {2022}, month = {12/20/2022}, abstract = {

Entanglement is one of the physical properties of quantum systems responsible for the computational hardness of simulating quantum systems. But while the runtime of specific algorithms, notably tensor network algorithms, explicitly depends on the amount of entanglement in the system, it is unknown whether this connection runs deeper and entanglement can also cause inherent, algorithm-independent complexity. In this work, we quantitatively connect the entanglement present in certain quantum systems to the computational complexity of simulating those systems. Moreover, we completely characterize the entanglement and complexity as a function of a system parameter. Specifically, we consider the task of simulating single-qubit measurements of k--regular graph states on n qubits. We show that, as the regularity parameter is increased from 1 to n\−1, there is a sharp transition from an easy regime with low entanglement to a hard regime with high entanglement at k=3, and a transition back to easy and low entanglement at k=n\−3. As a key technical result, we prove a duality for the simulation complexity of regular graph states between low and high regularity.

}, keywords = {Computational Complexity (cs.CC), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2212.10582}, url = {https://arxiv.org/abs/2212.10582}, author = {Ghosh, Soumik and Deshpande, Abhinav and Dominik Hangleiter and Alexey V. Gorshkov and Fefferman, Bill} } @article {3071, title = {Simulation Complexity of Many-Body Localized Systems}, year = {2022}, month = {5/25/2022}, abstract = {

We use complexity theory to rigorously investigate the difficulty of classically simulating evolution under many-body localized (MBL) Hamiltonians. Using the defining feature that MBL systems have a complete set of quasilocal integrals of motion (LIOMs), we demonstrate a transition in the classical complexity of simulating such systems as a function of evolution time. On one side, we construct a quasipolynomial-time tensor-network-inspired algorithm for strong simulation of 1D MBL systems (i.e., calculating the expectation value of arbitrary products of local observables) evolved for any time polynomial in the system size. On the other side, we prove that even weak simulation, i.e. sampling, becomes formally hard after an exponentially long evolution time, assuming widely believed conjectures in complexity theory. Finally, using the consequences of our classical simulation results, we also show that the quantum circuit complexity for MBL systems is sublinear in evolution time. This result is a counterpart to a recent proof that the complexity of random quantum circuits grows linearly in time.\ 

}, url = {https://arxiv.org/abs/2205.12967}, author = {Adam Ehrenberg and Abhinav Deshpande and Christopher L. Baldwin and Dmitry A. Abanin and Alexey V. Gorshkov} } @article {3018, title = {Simultaneous Stoquasticity}, journal = {Phys. Rev. A}, volume = {105}, year = {2022}, month = {06/09/2022}, abstract = {

Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1103/PhysRevA.105.062601}, url = {https://arxiv.org/abs/2202.08863}, author = {Jacob Bringewatt and Brady, Lucas T.} } @article {3065, title = {A single T-gate makes distribution learning hard}, year = {2022}, month = {7/7/2022}, abstract = {

The task of learning a probability distribution from samples is ubiquitous across the natural sciences. The output distributions of local quantum circuits form a particularly interesting class of distributions, of key importance both to quantum advantage proposals and a variety of quantum machine learning algorithms. In this work, we provide an extensive characterization of the learnability of the output distributions of local quantum circuits. Our first result yields insight into the relationship between the efficient learnability and the efficient simulatability of these distributions. Specifically, we prove that the density modelling problem associated with Clifford circuits can be efficiently solved, while for depth d=nΩ(1) circuits the injection of a single T-gate into the circuit renders this problem hard. This result shows that efficient simulatability does not imply efficient learnability. Our second set of results provides insight into the potential and limitations of quantum generative modelling algorithms. We first show that the generative modelling problem associated with depth d=nΩ(1) local quantum circuits is hard for any learning algorithm, classical or quantum. As a consequence, one cannot use a quantum algorithm to gain a practical advantage for this task. We then show that, for a wide variety of the most practically relevant learning algorithms -- including hybrid-quantum classical algorithms -- even the generative modelling problem associated with depth d=ω(log(n)) Clifford circuits is hard. This result places limitations on the applicability of near-term hybrid quantum-classical generative modelling algorithms.

}, url = {https://arxiv.org/abs/2207.03140}, author = {Marcel Hinsche and Marios Ioannou and Alexander Nietner and Jonas Haferkamp and Yihui Quek and Dominik Hangleiter and Jean-Pierre Seifert and Jens Eisert and Ryan Sweke} } @article {2999, title = {Snowmass 2021 White Paper: Tabletop experiments for infrared quantum gravity}, year = {2022}, month = {3/22/2022}, abstract = {

Progress in the quantum readout and control of mechanical devices from single atoms to large masses may enable a first generation of experiments probing the gravitational interaction in the quantum regime, conceivably within the next decade. In this Snowmass whitepaper, we briefly outline the possibilities and challenges facing the realization of these experiments. In particular, we emphasize the need for detailed theories of modifications to the usual effective QFT of gravitons in the infrared regime E/L3<}, keywords = {FOS: Physical sciences, General Relativity and Quantum Cosmology (gr-qc), High Energy Physics - Phenomenology (hep-ph), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2203.11846}, url = {https://arxiv.org/abs/2203.11846}, author = {Carney, Daniel and Chen, Yanbei and Geraci, Andrew and M{\"u}ller, Holger and Panda, Cristian D. and Stamp, Philip C. E. and Taylor, Jacob M.} } @article {3000, title = {Snowmass 2021 White Paper: The Windchime Project}, year = {2022}, month = {3/14/2022}, abstract = {

The absence of clear signals from particle dark matter in direct detection experiments motivates new approaches in disparate regions of viable parameter space. In this Snowmass white paper, we outline the Windchime project, a program to build a large array of quantum-enhanced mechanical sensors. The ultimate aim is to build a detector capable of searching for Planck mass-scale dark matter purely through its gravitational coupling to ordinary matter. In the shorter term, we aim to search for a number of other physics targets, especially some ultralight dark matter candidates. Here, we discuss the basic design, open R\&D challenges and opportunities, current experimental efforts, and both short- and long-term physics targets of the Windchime project.

}, keywords = {Cosmology and Nongalactic Astrophysics (astro-ph.CO), FOS: Physical sciences, High Energy Physics - Experiment (hep-ex), High Energy Physics - Phenomenology (hep-ph)}, doi = {10.48550/ARXIV.2203.07242}, url = {https://arxiv.org/abs/2203.07242}, author = {The Windchime Collaboration and Attanasio, Alaina and Bhave, Sunil A. and Blanco, Carlos and Carney, Daniel and Demarteau, Marcel and Elshimy, Bahaa and Febbraro, Michael and Feldman, Matthew A. and Ghosh, Sohitri and Hickin, Abby and Hong, Seongjin and Lang, Rafael F. and Lawrie, Benjamin and Li, Shengchao and Liu, Zhen and Maldonado, Juan P. A. and Marvinney, Claire and Oo, Hein Zay Yar and Pai, Yun-Yi and Pooser, Raphael and Qin, Juehang and Sparmann, Tobias J. and Taylor, Jacob M. and Tian, Hao and Tunnell, Christopher} } @article {3008, title = {Spectral Form Factor of a Quantum Spin Glass}, year = {2022}, month = {4/4/2022}, abstract = {

It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum p-spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations -- the exponential of the spin glass \"complexity\" as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.

}, keywords = {Disordered Systems and Neural Networks (cond-mat.dis-nn), FOS: Physical sciences, High Energy Physics - Theory (hep-th), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {https://doi.org/10.48550/arXiv.2203.12753}, url = {https://arxiv.org/abs/2203.12753}, author = {Winer, Michael and Barney, Richard and Christopher L. Baldwin and Galitski, Victor and Swingle, Brian} } @article {3063, title = {Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process}, journal = {NIST}, year = {2022}, month = {7/2022}, abstract = {

The National Institute of Standards and Technology is in the process of selecting publickey cryptographic algorithms through a public, competition-like process. The new publickey cryptography standards will specify additional digital signature, public-key encryption, and key-establishment algorithms to augment Federal Information Processing Standard (FIPS) 186-4, Digital Signature Standard (DSS), as well as NIST Special Publication (SP) 800-56A Revision 3, Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B Revision 2, Recommendation for Pair-Wise Key Establishment Using Integer Factorization Cryptography. It is intended that these algorithms will be capable of protecting sensitive information well into the foreseeable future, including after the advent of quantum computers.

This report describes the evaluation and selection process of the NIST Post-Quantum Cryptography Standardization process third-round candidates based on public feedback and internal review. The report summarizes each of the 15 third-round candidate algorithms and identifies those selected for standardization, as well as those that will continue to be evaluated in a fourth round of analysis. The public-key encryption and key-establishment algorithm that will be standardized is CRYSTALS\–KYBER. The digital signatures that will be standardized are CRYSTALS\–Dilithium, FALCON, and SPHINCS+. While there are multiple signature algorithms selected, NIST recommends CRYSTALS\–Dilithium as the primary algorithm to be implemented. In addition, four of the alternate key-establishment candidate algorithms will advance to a fourth round of evaluation: BIKE, Classic McEliece, HQC, and SIKE. These candidates are still being considered for future standardization. NIST will also issue a new Call for Proposals for public-key digital signature algorithms to augment and diversify its signature portfolio.

}, doi = {https://doi.org/10.6028/NIST.IR.8413-upd1}, author = {Gorjan Alagic and Daniel Apon and David Cooper and Quynh Dang and Thinh Dang and John Kelsey and Jacob Lichtinger and Carl Miller and Dustin Moody and Rene Peralta and Ray Perlner and Angela Robinson} } @article {3199, title = {Tailoring three-dimensional topological codes for biased noise}, year = {2022}, month = {11/3/2022}, abstract = {

Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for several advantages including a transversal implementation of non-Clifford logical gates, single-shot decoding strategies, parallelized decoding in the case of fracton codes as well as construction of fractal lattice codes. Motivated by this, we tailor 3D topological codes for enhanced storage performance under biased Pauli noise. We present Clifford deformations of various 3D topological codes, such that they exhibit a threshold error rate of 50\% under infinitely biased Pauli noise. Our examples include the 3D surface code on the cubic lattice, the 3D surface code on a checkerboard lattice that lends itself to a subsystem code with a single-shot decoder, the 3D color code, as well as fracton models such as the X-cube model, the Sierpinski model and the Haah code. We use the belief propagation with ordered statistics decoder (BP-OSD) to study threshold error rates at finite bias. We also present a rotated layout for the 3D surface code, which uses roughly half the number of physical qubits for the same code distance under appropriate boundary conditions. Imposing coprime periodic dimensions on this rotated layout leads to logical operators of weight O(n) at infinite bias and a corresponding exp[\−O(n)] subthreshold scaling of the logical failure rate, where n is the number of physical qubits in the code. Even though this scaling is unstable due to the existence of logical representations with O(1) low-rate Pauli errors, the number of such representations scales only polynomially for the Clifford-deformed code, leading to an enhanced effective distance.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.02116}, url = {https://arxiv.org/abs/2211.02116}, author = {Huang, Eric and Pesah, Arthur and Chubb, Christopher T. and Vasmer, Michael and Dua, Arpit} } @article {2765, title = {Theoretical bounds on data requirements for the ray-based classification}, journal = {SN Comput. Sci.}, volume = {3}, year = {2022}, month = {02/26/2022}, abstract = {

The problem of classifying high-dimensional shapes in real-world data grows in complexity as the dimension of the space increases. For the case of identifying convex shapes of different geometries, a new classification framework has recently been proposed in which the intersections of a set of one-dimensional representations, called rays, with the boundaries of the shape are used to identify the specific geometry. This ray-based classification (RBC) has been empirically verified using a synthetic dataset of two- and three-dimensional shapes [1] and, more recently, has also been validated experimentally [2]. Here, we establish a bound on the number of rays necessary for shape classification, defined by key angular metrics, for arbitrary convex shapes. For two dimensions, we derive a lower bound on the number of rays in terms of the shape\&$\#$39;s length, diameter, and exterior angles. For convex polytopes in R^N, we generalize this result to a similar bound given as a function of the dihedral angle and the geometrical parameters of polygonal faces. This result enables a different approach for estimating high-dimensional shapes using substantially fewer data elements than volumetric or surface-based approaches.

}, doi = {https://doi.org/10.1007/s42979-021-00921-0}, url = {https://arxiv.org/abs/2103.09577}, author = {Brian J. Weber and Sandesh S. Kalantre and Thomas McJunkin and J. M. Taylor and Justyna P. Zwolak} } @article {3192, title = {A theory of quantum differential equation solvers: limitations and fast-forwarding}, year = {2022}, month = {11/9/2022}, abstract = {

We study the limitations and fast-forwarding of quantum algorithms for solving linear ordinary differential equation (ODE) systems with particular focus on non-quantum dynamics, where the coefficient matrix in the ODE is not anti-Hermitian or the ODE is inhomogeneous. On the one hand, for generic homogeneous linear ODEs, by proving worst-case lower bounds, we show that quantum algorithms suffer from computational overheads due to two types of {\textquoteleft}{\textquoteleft}non-quantumness\&$\#$39;\&$\#$39;: real part gap and non-normality of the coefficient matrix. We then show that ODEs in the absence of both types of {\textquoteleft}{\textquoteleft}non-quantumness\&$\#$39;\&$\#$39; are equivalent to quantum dynamics, and reach the conclusion that quantum algorithms for quantum dynamics work best. We generalize our results to the inhomogeneous case and find that existing generic quantum ODE solvers cannot be substantially improved. To obtain these lower bounds, we propose a general framework for proving lower bounds on quantum algorithms that are amplifiers, meaning that they amplify the difference between a pair of input quantum states. On the other hand, we show how to fast-forward quantum algorithms for solving special classes of ODEs which leads to improved efficiency. More specifically, we obtain quadratic to exponential improvements in terms of the evolution time T and the spectral norm of the coefficient matrix for the following classes of ODEs: inhomogeneous ODEs with a negative definite coefficient matrix, inhomogeneous ODEs with a coefficient matrix having an eigenbasis that can be efficiently prepared on a quantum computer and eigenvalues that can be efficiently computed classically, and the spatially discretized inhomogeneous heat equation and advection-diffusion equation. We give fast-forwarding algorithms that are conceptually different from existing ones in the sense that they neither require time discretization nor solving high-dimensional linear systems.

}, keywords = {FOS: Mathematics, FOS: Physical sciences, Numerical Analysis (math.NA), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2211.05246}, url = {https://arxiv.org/abs/2211.05246}, author = {Dong An and Liu, Jin-Peng and Wang, Daochen and Zhao, Qi} } @article {3012, title = {Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond}, year = {2022}, month = {2/10/2022}, abstract = {

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by U(1)2 Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on 2n-dimensional qudits that feature surface anyons described by U(1)2n Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.

}, keywords = {FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2202.05442}, url = {https://arxiv.org/abs/2202.05442}, author = {Shirley, Wilbur and Chen, Yu-An and Dua, Arpit and Ellison, Tyler D. and Tantivasadakarn, Nathanan and Williamson, Dominic J.} } @article {3197, title = {Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schr{\"o}dinger Equation}, journal = {Quantum}, volume = {6}, year = {2022}, month = {apr}, pages = {690}, abstract = {

We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm that is both insensitive to the rapid changes of the time-dependent Hamiltonian and exhibits commutator scaling. Our method can be used for efficient Hamiltonian simulation in the interaction picture. In particular, we demonstrate that for the simulation of the Schr{\"o}dinger equation, our method exhibits superconvergence and achieves a surprising second order convergence rate, of which the proof rests on a careful application of pseudo-differential calculus. Numerical results verify the effectiveness and the superconvergence property of our method.

}, doi = {10.22331/q-2022-04-15-690}, url = {https://arxiv.org/abs/2111.03103v2}, author = {Dong An and Di Fang and Lin Lin} } @article {3069, title = {Topological Edge Mode Tapering}, year = {2022}, month = {6/14/2022}, abstract = {

Mode tapering, or the gradual manipulation of the size of some mode, is a requirement for any system that aims to efficiently interface two or more subsystems of different mode sizes. While high efficiency tapers have been demonstrated, they often come at the cost of a large device footprint or challenging fabrication. Topological photonics, offering robustness to certain types of disorder as well as chirality, has proved to be a well-suited design principle for numerous applications in recent years. Here we present a new kind of mode taper realized through topological bandgap engineering. We numerically demonstrate a sixfold change in mode width over an extremely compact 8μm distance with near unity efficiency in the optical domain. With suppressed backscattering and no excitation of higher-order modes, such a taper could enable new progress in the development of scalable, multi-component systems in classical and quantum optics.

}, url = {https://arxiv.org/abs/2206.07056}, author = {Christopher J. Flower and Sabyasachi Barik and Sunil Mittal and Mohammad Hafezi} } @article {3005, title = {Toward Robust Autotuning of Noisy Quantum dot Devices}, journal = {Physical Review Applied}, volume = {17}, year = {2022}, month = {02/26/2022}, abstract = {

The current autotuning approaches for quantum dot (QD) devices, while showing some success, lack an assessment of data reliability. This leads to unexpected failures when noisy or otherwise low-quality data is processed by an autonomous system. In this work, we propose a framework for robust autotuning of QD devices that combines a machine learning (ML) state classifier with a data quality control module. The data quality control module acts as a \"gatekeeper\" system, ensuring that only reliable data are processed by the state classifier. Lower data quality results in either device recalibration or termination. To train both ML systems, we enhance the QD simulation by incorporating synthetic noise typical of QD experiments. We confirm that the inclusion of synthetic noise in the training of the state classifier significantly improves the performance, resulting in an accuracy of 95.0(9) \% when tested on experimental data. We then validate the functionality of the data quality control module by showing that the state classifier performance deteriorates with decreasing data quality, as expected. Our results establish a robust and flexible ML framework for autonomous tuning of noisy QD devices.

}, doi = {https://doi.org/10.1103/PhysRevApplied.17.024069}, url = {https://arxiv.org/abs/2108.00043}, author = {Joshua Ziegler and Thomas McJunkin and E.S. Joseph and Sandesh S. Kalantre and Benjamin Harpt and D.E. Savage and M.G. Lagally and M.A. Eriksson and Jacob M. Taylor and Justyna P. Zwolak} } @article {3004, title = {Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice}, journal = {Science}, volume = {377}, year = {2022}, month = {8/18/2022}, pages = {885-889}, abstract = {

Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a walker traverses while maintaining coherence. Here, we do this by combining the fast, programmable control provided by optical tweezer arrays with the scalable, homogeneous environment of an optical lattice. Using this new combination of tools we study continuous-time quantum walks of single atoms on a 2D square lattice, and perform proof-of-principle demonstrations of spatial search using these walks. When scaled to more particles, the capabilities demonstrated here can be extended to study a variety of problems in quantum information science and quantum simulation, including the deterministic assembly of ground and excited states in Hubbard models with tunable interactions, and performing versions of spatial search in a larger graph with increased connectivity, where search by quantum walk can be more effective.

}, keywords = {Atomic Physics (physics.atom-ph), FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1126/science.abo0608}, url = {https://arxiv.org/abs/2202.01204}, author = {Young, Aaron W. and Eckner, William J. and Schine, Nathan and Andrew M. Childs and Kaufman, Adam M.} } @article {3120, title = {Ultrastrong light-matter interaction in a photonic crystal}, year = {2022}, month = {9/29/2022}, abstract = {

Harnessing the interaction between light and matter at the quantum level has been a central theme in the fields of atomic physics and quantum optics, with applications from quantum computation to quantum metrology. Combining complex interactions with photonic synthetic materials provides an opportunity to investigate novel quantum phases and phenomena, establishing interesting connections to condensed matter physics. Here we explore many-body phenomena with a single artificial atom coupled to the many discrete modes of a photonic crystal. This experiment reaches the ultrastrong light-matter coupling regime using the circuit QED paradigm, by galvanically coupling a highly nonlinear fluxonium qubit to a tight-binding lattice of microwave resonators. In this regime, the transport of a single photon is strongly modified by the presence of multi-photon bound states, owing to interactions that break particle number conservation. Exploiting the effective photon-photon interactions mediated by the qubit, the driven system can be configured as a continuous reservoir of strongly-correlated photons, a resource of interest for quantum networks. This work opens exciting prospects for exploring nonlinear quantum optics at the single-photon level and stabilizing entangled many-body phases of light.

}, keywords = {FOS: Physical sciences, Quantum Gases (cond-mat.quant-gas), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2209.14972}, url = {https://arxiv.org/abs/2209.14972}, author = {Vrajitoarea, Andrei and Belyansky, Ron and Lundgren, Rex and Whitsitt, Seth and Alexey V. Gorshkov and Houck, Andrew A.} } @article {3030, title = {Universal scattering with general dispersion relations}, journal = {Phys. Rev. Research}, volume = {4}, year = {2022}, month = {4/6/2022}, chapter = {023014}, abstract = {

Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension D\≥1 when the density of states diverges at a specific energy. To illustrate the underlying principles in an experimentally relevant setting, we focus on waveguide quantum electrodynamics (QED) problems (i.e. D=1) with dispersion relation ϵ(k)=\±|d|km, where m\≥2 is an integer. For a large class of these problems for any positive integer m, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E\→0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson\&$\#$39;s theorem -- which relates the scattering phases to the number of bound states -- to waveguide QED scattering for these more general dispersion relations. We then extend these results to general integer dimensions D\≥1, dispersion relations ϵ(k)=|k|a for a D-dimensional momentum vector k with any real positive a, and separable potential scattering.

}, keywords = {FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph)}, doi = {https://doi.org/10.1103/PhysRevResearch.4.023014}, url = {https://arxiv.org/abs/2103.09830}, author = {Wang, Yidan and Michael Gullans and Na, Xuesen and Whitsitt, Seth and Alexey V. Gorshkov} } @article {2760, title = {Universality in one-dimensional scattering with general dispersion relations}, journal = {Phys. Rev. Res.}, volume = {4}, year = {2022}, month = {3/17/2021}, chapter = {023014}, abstract = {

Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in one dimension when the dispersion relation is ϵ(k)=\±|d|km, where m\≥2 is an integer. We study impurity scattering problems in which a single-particle in a one-dimensional waveguide scatters off of an inhomogeneous, discrete set of sites locally coupled to the waveguide. For a large class of these problems, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E\→0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson\&$\#$39;s theorem -- which relates the scattering phases to the number of bound states -- to impurity scattering for these more general dispersion relations.

}, doi = {https://doi.org/10.48550/arXiv.2103.09830}, url = {https://arxiv.org/abs/2103.09830}, author = {Yidan Wang and Michael Gullans and Xuesen Na and Alexey V. Gorshkov} } @article {3020, title = {Unlimited non-causal correlations and their relation to non-locality}, journal = {Quantum}, volume = {6}, year = {2022}, month = {3/22/2022}, pages = {673}, abstract = {

Non-causal correlations certify the lack of a definite causal order among localized space-time regions. In stark contrast to scenarios where a single region influences its own causal past, some processes that distribute non-causal correlations satisfy a series of natural desiderata: logical consistency, linear and reversible dynamics, and computational tameness. Here, we present such processes among arbitrary many regions where each region influences every other but itself, and show that the above desiderata are altogether insufficient to limit the amount of \"acausality\" of non-causal correlations. This leaves open the identification of a principle that forbids non-causal correlations. Our results exhibit qualitative and quantitative parallels with the non-local correlations due to Ardehali and Svetlichny.

}, doi = {https://doi.org/10.22331\%2Fq-2022-03-29-673}, url = {https://arxiv.org/abs/2104.06234}, author = {{\"A}min Baumeler and Amin Shiraz Gilani and Jibran Rashid} } @article {3043, title = {Where we are with quantum}, journal = {Nature Physics}, year = {2022}, month = {4/28/2022}, abstract = {

A theoretical analysis shows how a person\’s location in space could be verified by the transmission of single photons. A vital application of quantum networks may be within reach.

}, issn = {1745-2473}, doi = {https://doi.org/10.1038/s41567-022-01597-w}, author = {Yusuf Alnawakhtha and Carl Miller} } @article {2858, title = {Algebraic Reasoning of Quantum Programs via Non-Idempotent Kleene Algebra}, year = {2021}, month = {10/13/2021}, abstract = {

We investigate the algebraic reasoning of quantum programs inspired by the success of classical program analysis based on Kleene algebra. One prominent example of such is the famous Kleene Algebra with Tests (KAT), which has furnished both theoretical insights and practical tools. The succinctness of algebraic reasoning would be especially desirable for scalable analysis of quantum programs, given the involvement of exponential-size matrices in most of the existing methods. A few key features of KAT including the idempotent law and the nice properties of classical tests, however, fail to hold in the context of quantum programs due to their unique quantum features, especially in branching. We propose the Non-idempotent Kleena Algebra (NKA) as a natural alternative and identify complete and sound semantic models for NKA as well as their appropriate quantum interpretations. In light of applications of KAT, we are able to demonstrate algebraic proofs in NKA of quantum compiler optimization and the normal form of quantum while-programs. Moreover, we extend NKA with Tests (i.e., NKAT), where tests model quantum predicates following the rules of effect algebra, and illustrate how to encode propositional quantum Hoare logic as NKAT theorems.

}, doi = {https://doi.org/10.1145/3519939.3523713}, url = {https://arxiv.org/abs/2110.07018}, author = {Yuxiang Peng and Mingsheng Ying and Xiaodi Wu} } @article {2691, title = {Approximate Bacon-Shor Code and Holography}, journal = {Journal of High Energy Physics}, volume = {2021}, year = {2021}, month = {5/14/2021}, abstract = {

We construct an explicit and solvable toy model for the AdS/CFT correspondence in the form of an approximate quantum error correction code with a non-trivial center in the code subalgebra. Specifically, we use the Bacon-Shor codes and perfect tensors to construct a gauge code (or a stabilizer code with gauge-fixing), which we call the holographic hybrid code. This code admits a local log-depth encoding/decoding circuit, and can be represented as a holographic tensor network which satisfies an analog of the Ryu-Takayanagi formula and reproduces features of the sub-region duality. We then construct approximate versions of the holographic hybrid codes by \"skewing\" the code subspace, where the size of skewing is analogous to the size of the gravitational constant in holography. These approximate hybrid codes are not necessarily stabilizer codes, but they can be expressed as the superposition of holographic tensor networks that are stabilizer codes. For such constructions, different logical states, representing different bulk matter content, can \"back-react\" on the emergent geometry, resembling a key feature of gravity. The locality of the bulk degrees of freedom becomes subspace-dependent and approximate. Such subspace-dependence is manifest in the form of bulk operator reconstruction from the boundary. Exact complementary error correction breaks down for certain bipartition of the boundary degrees of freedom; however, a limited, state-dependent form is preserved for particular subspaces. We also construct an example where the connected two-point correlation functions can have a power-law decay. Coupled with known constraints from holography, a weakly back-reacting bulk also forces these skewed tensor network models to the \"large N limit\" where they are built by concatenating a large N number of copies.

}, doi = {https://doi.org/10.1007/JHEP05(2021)127}, url = {https://arxiv.org/abs/2010.05960}, author = {ChunJun Cao and Brad Lackey} } @article {2809, title = {Behavior of Analog Quantum Algorithms}, year = {2021}, month = {7/2/2021}, abstract = {

Analog quantum algorithms are formulated in terms of Hamiltonians rather than unitary gates and include quantum adiabatic computing, quantum annealing, and the quantum approximate optimization algorithm (QAOA). These algorithms are promising candidates for near-term quantum applications, but they often require fine tuning via the annealing schedule or variational parameters. In this work, we explore connections between these analog algorithms, as well as limits in which they become approximations of the optimal procedure.Notably, we explore how the optimal procedure approaches a smooth adiabatic procedure but with a superposed oscillatory pattern that can be explained in terms of the interactions between the ground state and first excited state that effect the coherent error cancellation of diabatic transitions. Furthermore, we provide numeric and analytic evidence that QAOA emulates this optimal procedure with the length of each QAOA layer equal to the period of the oscillatory pattern. Additionally, the ratios of the QAOA bangs are determined by the smooth, non-oscillatory part of the optimal procedure. We provide arguments for these phenomena in terms of the product formula expansion of the optimal procedure. With these arguments, we conclude that different analog algorithms can emulate the optimal protocol under different limits and approximations. Finally, we present a new algorithm for better approximating the optimal protocol using the analytic and numeric insights from the rest of the paper. In practice, numerically, we find that this algorithm outperforms standard QAOA and naive quantum annealing procedures.\ 

}, url = {https://arxiv.org/abs/2107.01218}, author = {Lucas T. Brady and Lucas Kocia and Przemyslaw Bienias and Aniruddha Bapat and Yaroslav Kharkov and Alexey V. Gorshkov} } @article {2307, title = {Can you sign a quantum state?}, journal = {v4: version for publication in Quantum, v5: CC license}, year = {2021}, month = {12/6/2021}, abstract = {

Cryptography with quantum states exhibits a number of surprising and counterintuitive features. In a 2002 work, Barnum et al. argued informally that these strange features should imply that digital signatures for quantum states are impossible (Barnum et al., FOCS 2002). In this work, we perform the first rigorous study of the problem of signing quantum states. We first show that the intuition of Barnum et al. was correct, by proving an impossibility result which rules out even very weak forms of signing quantum states. Essentially, we show that any non-trivial combination of correctness and security requirements results in negligible security. This rules out all quantum signature schemes except those which simply measure the state and then sign the outcome using a classical scheme. In other words, only classical signature schemes exist. We then show a positive result: it is possible to sign quantum states, provided that they are also encrypted with the public key of the intended recipient. Following classical nomenclature, we call this notion quantum signcryption. Classically, signcryption is only interesting if it provides superior efficiency to simultaneous encryption and signing. Our results imply that, quantumly, it is far more interesting: by the laws of quantum mechanics, it is the only signing method available. We develop security definitions for quantum signcryption, ranging from a simple one-time two-user setting, to a chosen-ciphertext-secure many-time multi-user setting. We also give secure constructions based on post-quantum public-key primitives. Along the way, we show that a natural hybrid method of combining classical and quantum schemes can be used to \"upgrade\" a secure classical scheme to the fully-quantum setting, in a wide range of cryptographic settings including signcryption, authenticated encryption, and chosen-ciphertext security.

}, url = {https://arxiv.org/abs/1811.11858}, author = {Gorjan Alagic and Tommaso Gagliardoni and Christian Majenz} } @article {2857, title = {Chiral transport of hot carriers in graphene in the quantum Hall regime}, year = {2021}, month = {10/3/2021}, abstract = {

Photocurrent (PC) measurements can reveal the relaxation dynamics of photo-excited hot carriers beyond the linear response of conventional transport experiments, a regime important for carrier multiplication. In graphene subject to a magnetic field, PC measurements are able to probe the existence of Landau levels with different edge chiralities which is exclusive to relativistic electron systems. Here, we report the accurate measurement of PC in graphene in the quantum Hall regime. Prominent PC oscillations as a function of gate voltage on samples\&$\#$39; edges are observed. These oscillation amplitudes form an envelope which depends on the strength of the magnetic field, as does the PCs\&$\#$39; power dependence and their saturation behavior. We explain these experimental observations through a model using optical Bloch equations, incorporating relaxations through acoustic-, optical- phonons and Coulomb interactions. The simulated PC agrees with our experimental results, leading to a unified understanding of the chiral PC in graphene at various magnetic field strengths, and providing hints for the occurrence of a sizable carrier multiplication.\ 

}, url = {https://arxiv.org/abs/2110.01079}, author = {Bin Cao and Tobias Grass and Olivier Gazzano and Kishan Ashokbhai Patel and Jiuning Hu and Markus M{\"u}ller and Tobias Huber and Luca Anzi and Kenji Watanabe and Takashi Taniguchi and David Newell and Michael Gullans and Roman Sordan and Mohammad Hafezi and Glenn Solomon} } @article {2813, title = {Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models}, year = {2021}, month = {5/13/2021}, abstract = {

Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincar{\'e} disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically-frustrated hyperbolic quantum spin models with finite-range or exponentially-decaying interaction.

}, url = {https://arxiv.org/abs/2105.06490}, author = {Przemyslaw Bienias and Igor Boettcher and Ron Belyansky and Alicia J. Koll{\'a}r and Alexey V. Gorshkov} } @article {2684, title = {Circulation by microwave-induced vortex transport for signal isolation}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {6/14/2021}, pages = {030309}, abstract = {

Magnetic fields break time-reversal symmetry, which is leveraged in many settings to enable the nonreciprocal behavior of light. This is the core physics of circulators and other elements used in a variety of microwave and optical settings. Commercial circulators in the microwave domain typically use ferromagnetic materials and wave interference, requiring large devices and large fields. However, quantum information devices for sensing and computation require small sizes, lower fields, and better on-chip integration. Equivalences to ferromagnetic order---such as the XY model---can be realized at much lower magnetic fields by using arrays of superconducting islands connected by Josephson junctions. Here we show that the quantum-coherent motion of a single vortex in such an array suffices to induce nonreciprocal behavior, enabling a small-scale, moderate-bandwidth, and low insertion loss circulator at very low magnetic fields and at microwave frequencies relevant for experiments with qubits.

}, doi = {https://doi.org/10.1103/PRXQuantum.2.030309}, url = {https://arxiv.org/abs/2010.04118}, author = {Brittany Richman and J. M. Taylor} } @article {2920, title = {Clustering of steady-state correlations in open systems with long-range interactions}, year = {2021}, month = {10/28/2021}, abstract = {

Lieb-Robinson bounds are powerful analytical tools for constraining the dynamic and static properties of non-relativistic quantum systems. Recently, a complete picture for closed systems that evolve unitarily in time has been achieved. In experimental systems, however, interactions with the environment cannot generally be ignored, and the extension of Lieb-Robinson bounds to dissipative systems which evolve non-unitarily in time remains an open challenge. In this work, we prove two Lieb-Robinson bounds that constrain the dynamics of open quantum systems with long-range interactions that decay as a power-law in the distance between particles. Using a combination of these Lieb-Robinson bounds and mixing bounds which arise from \"reversibility\" -- naturally satisfied for thermal environments -- we prove the clustering of correlations in the steady states of open quantum systems with long-range interactions. Our work provides an initial step towards constraining the steady-state entanglement structure for a broad class of experimental platforms, and we highlight several open directions regarding the application of Lieb-Robinson bounds to dissipative systems.

}, url = {https://arxiv.org/abs/2110.15368}, author = {Andrew Y. Guo and Simon Lieu and Minh C. Tran and Alexey V. Gorshkov} } @article {2914, title = {Comment on "Using an atom interferometer to infer gravitational entanglement generation{\textquoteright}{\textquoteright}}, year = {2021}, month = {11/8/2021}, abstract = {

Our paper arXiv:2101.11629 contains a technical error which changes some of the conclusions. We thank Streltsov, Pedernales, and Plenio for bringing the essence of this error to our attention. Here we explain the error, examine its consequences, and suggest methods to overcome the resulting weakness in the proposed experiment.

}, url = {https://arxiv.org/abs/2111.04667}, author = {Daniel Carney and Holger M{\"u}ller and Jacob M. Taylor} } @article {2867, title = {Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {9/17/2021}, abstract = {

Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered as being inimical to quantum many-body correlations, ultimately leading the system to a classically tractable state. This work shows that noise represented by two-body processes, such as pair loss, plays the same role as many-body interactions and makes otherwise classically simulable systems universal for quantum computing. We analyze such processes in detail and establish a complexity transition between simulable and nonsimulable systems as a function of a tuning parameter. We determine important classes of simulable and nonsimulable two-body dissipation. Finally, we show how using resonant dissipation in cold atoms can enhance the performance of two-qubit gates.\ 

}, issn = {2691-3399}, doi = {10.1103/prxquantum.2.030350}, url = {http://dx.doi.org/10.1103/PRXQuantum.2.030350}, author = {Shtanko, Oles and Deshpande, Abhinav and Julienne, Paul S. and Alexey V. Gorshkov} } @article {2807, title = {Compressed Sensing Measurement of Long-Range Correlated Noise}, year = {2021}, month = {5/26/2021}, abstract = {

Long-range correlated errors can severely impact the performance of NISQ (noisy intermediate-scale quantum) devices, and fault-tolerant quantum computation. Characterizing these errors is important for improving the performance of these devices, via calibration and error correction, and to ensure correct interpretation of the results. We propose a compressed sensing method for detecting two-qubit correlated dephasing errors, assuming only that the correlations are sparse (i.e., at most s pairs of qubits have correlated errors, where s \<\< n(n-1)/2, and n is the total number of qubits). In particular, our method can detect long-range correlations between any two qubits in the system (i.e., the correlations are not restricted to be geometrically local).
Our method is highly scalable: it requires as few as m = O(s log n) measurement settings, and efficient classical postprocessing based on convex optimization. In addition, when m = O(s log^4(n)), our method is highly robust to noise, and has sample complexity O(max(n,s)^2 log^4(n)), which can be compared to conventional methods that have sample complexity O(n^3). Thus, our method is advantageous when the correlations are sufficiently sparse, that is, when s \< O(n^(3/2) / log^2(n)). Our method also performs well in numerical simulations on small system sizes, and has some resistance to state-preparation-and-measurement (SPAM) errors. The key ingredient in our method is a new type of compressed sensing measurement, which works by preparing entangled Greenberger-Horne-Zeilinger states (GHZ states) on random subsets of qubits, and measuring their decay rates with high precision.

}, url = {https://arxiv.org/abs/2105.12589}, author = {Alireza Seif and Mohammad Hafezi and Yi-Kai Liu} } @article {2638, title = {Conformal field theories are magical}, journal = {Physical Review B}, volume = {103}, year = {2021}, month = {2/25/2021}, pages = {075145}, abstract = {

\"Magic\" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large mana at the model\&$\#$39;s critical point, and that this mana resides in the system\&$\#$39;s correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.

}, doi = {https://journals.aps.org/prb/pdf/10.1103/PhysRevB.103.075145}, url = {https://arxiv.org/abs/2007.01303}, author = {Christopher David White and ChunJun Cao and Brian Swingle} } @article {2939, title = {Constructing quantum many-body scar Hamiltonians from Floquet automata}, year = {2021}, month = {12/22/2021}, abstract = {

We provide a systematic approach for constructing approximate quantum many-body scars(QMBS) starting from two-layer Floquet automaton circuits that exhibit trivial many-body revivals. We do so by applying successively more restrictions that force local gates of the automaton circuit to commute concomitantly more accurately when acting on select scar states. With these rules in place, an effective local, Floquet Hamiltonian is seen to capture dynamics of the automata over a long prethermal window, and neglected terms can be used to estimate the relaxation of revivals. We provide numerical evidence for such a picture and use our construction to derive several QMBS models, including the celebrated PXP model.

}, url = {https://arxiv.org/abs/2112.12153}, author = {Pierre-Gabriel Rozon and Michael Gullans and Kartiek Agarwal} } @article {2919, title = {Cross-Platform Comparison of Arbitrary Quantum Computations}, year = {2021}, month = {7/27/2021}, abstract = {

As we approach the era of quantum advantage, when quantum computers (QCs) can outperform any classical computer on particular tasks, there remains the difficult challenge of how to validate their performance. While algorithmic success can be easily verified in some instances such as number factoring or oracular algorithms, these approaches only provide pass/fail information for a single QC. On the other hand, a comparison between different QCs on the same arbitrary circuit provides a lower-bound for generic validation: a quantum computation is only as valid as the agreement between the results produced on different QCs. Such an approach is also at the heart of evaluating metrological standards such as disparate atomic clocks. In this paper, we report a cross-platform QC comparison using randomized and correlated measurements that results in a wealth of information on the QC systems. We execute several quantum circuits on widely different physical QC platforms and analyze the cross-platform fidelities.

}, url = {https://arxiv.org/abs/2107.11387}, author = {Daiwei Zhu and Ze-Pei Cian and Crystal Noel and Andrew Risinger and Debopriyo Biswas and Laird Egan and Yingyue Zhu and Alaina M. Green and Cinthia Huerta Alderete and Nhung H. Nguyen and Qingfeng Wang and Andrii Maksymov and Yunseong Nam and Marko Cetina and Norbert M. Linke and Mohammad Hafezi and Christopher Monroe} } @article {2815, title = {Crystallography of Hyperbolic Lattices}, year = {2021}, month = {5/3/2021}, abstract = {

Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch\&$\#$39;s theorem precludes a simple understanding of their band structure. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive, for the first time, a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. Our results find application for both finite and infinite hyperbolic lattices. We describe a method to efficiently generate finite hyperbolic lattices of arbitrary size and explain why the present crystallography is the first step towards a complete band theory of hyperbolic lattices and apply it to construct Bloch wave Hamiltonians. This work lays the foundation for generalizing some of the most powerful concepts of solid state physics, such as crystal momentum and Brillouin zone, to the emerging field of hyperbolic lattices and tabletop simulations of gravitational theories, and reveals the connections to concepts from topology and algebraic geometry.

}, url = {https://arxiv.org/abs/2105.01087}, author = {Igor Boettcher and Alexey V. Gorshkov and Alicia J. Koll{\'a}r and Joseph Maciejko and Steven Rayan and Ronny Thomale} } @article {2817, title = {Decoding conformal field theories: from supervised to unsupervised learning}, year = {2021}, month = {7/10/2021}, abstract = {

We use machine learning to classify rational two-dimensional conformal field theories. We first use the energy spectra of these minimal models to train a supervised learning algorithm. We find that the machine is able to correctly predict the nature and the value of critical points of several strongly correlated spin models using only their energy spectra. This is in contrast to previous works that use machine learning to classify different phases of matter, but do not reveal the nature of the critical point between phases. Given that the ground-state entanglement Hamiltonian of certain topological phases of matter is also described by conformal field theories, we use supervised learning on R{\'e}yni entropies and find that the machine is able to identify which conformal field theory describes the entanglement Hamiltonian with only the lowest few R{\'e}yni entropies to a high degree of accuracy. Finally, using autoencoders, an unsupervised learning algorithm, we find a hidden variable that has a direct correlation with the central charge and discuss prospects for using machine learning to investigate other conformal field theories, including higher-dimensional ones. Our results highlight that machine learning can be used to find and characterize critical points and also hint at the intriguing possibility to use machine learning to learn about more complex conformal field theories.

}, url = {https://arxiv.org/abs/2106.13485}, author = {En-Jui Kuo and Alireza Seif and Rex Lundgren and Seth Whitsitt and Mohammad Hafezi} } @article {2631, title = {Device-independent Randomness Expansion with Entangled Photons}, journal = {Nat. Phys. }, year = {2021}, month = {01/28/2021}, abstract = {

With the growing availability of experimental loophole-free Bell tests, it has become possible to implement a new class of device-independent random number generators whose output can be certified to be uniformly random without requiring a detailed model of the quantum devices used. However, all of these experiments require many input bits in order to certify a small number of output bits, and it is an outstanding challenge to develop a system that generates more randomness than is used. Here, we devise a device-independent spot-checking protocol which uses only uniform bits as input. Implemented with a photonic loophole-free Bell test, we can produce 24\% more certified output bits (1,181,264,237) than consumed input bits (953,301,640), which is 5 orders of magnitude more efficient than our previous work [arXiv:1812.07786]. The experiment ran for 91.0 hours, creating randomness at an average rate of 3606 bits/s with a soundness error bounded by 5.7\×10\−7 in the presence of classical side information. Our system will allow for greater trust in public sources of randomness, such as randomness beacons, and the protocols may one day enable high-quality sources of private randomness as the device footprint shrinks.

}, doi = {https://doi.org/10.1038/s41567-020-01153-4}, url = {https://arxiv.org/abs/1912.11158}, author = {Lynden K. Shalm and Yanbao Zhang and Joshua C. Bienfang and Collin Schlager and Martin J. Stevens and Michael D. Mazurek and Carlos Abell{\'a}n and Waldimar Amaya and Morgan W. Mitchell and Mohammad A. Alhejji and Honghao Fu and Joel Ornstein and Richard P. Mirin and Sae Woo Nam and Emanuel Knill} } @article {2916, title = {Discovering hydrodynamic equations of many-body quantum systems}, year = {2021}, month = {11/3/2021}, abstract = {

Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum systems often admit a simplified description, which involves a small set of physical observables and requires only a few parameters such as sound velocity or viscosity. Unveiling the relationship between these hydrodynamic equations and the underlying microscopic theory usually requires a great effort by condensed matter theorists. In the present paper, we develop a new machine-learning framework for automated discovery of effective equations from a limited set of available data, thus bypassing complicated analytical derivations. The data can be generated from numerical simulations or come from experimental quantum simulator platforms. Using integrable models, where direct comparisons can be made, we reproduce previously known hydrodynamic equations, strikingly discover novel equations and provide their derivation whenever possible. We discover new hydrodynamic equations describing dynamics of interacting systems, for which the derivation remains an outstanding challenge. Our approach provides a new interpretable method to study properties of quantum materials and quantum simulators in non-perturbative regimes.

}, url = {https://arxiv.org/abs/2111.02385}, author = {Yaroslav Kharkov and Oles Shtanko and Alireza Seif and Przemyslaw Bienias and Mathias Van Regemortel and Mohammad Hafezi and Alexey V. Gorshkov} } @article {2881, title = {EasyPQC: Verifying Post-Quantum Cryptography}, journal = {ACM CCS 2021}, year = {2021}, month = {9/20/2021}, abstract = {

EasyCrypt is a formal verification tool used extensively for formalizing concrete security proofs of cryptographic constructions. However, the EasyCrypt formal logics consider only classical attackers, which means that post-quantum security proofs cannot be formalized and machine-checked with this tool. In this paper we prove that a natural extension of the EasyCrypt core logics permits capturing a wide class of post-quantum cryptography proofs, settling a question raised by (Unruh, POPL 2019). Leveraging our positive result, we implement EasyPQC, an extension of EasyCrypt for post-quantum security proofs, and use EasyPQC to verify post-quantum security of three classic constructions: PRF-based MAC, Full Domain Hash and GPV08 identity-based encryption.

}, doi = {https://dx.doi.org/10.1145/3460120.3484567}, author = {Manuel Barbosa and Gilles Barthe and Xiong Fan and Benjamin Gr{\'e}goire and Shih-Han Hung and Jonathan Katz and Pierre-Yves Strub and Xiaodi Wu and Li Zhou} } @article {2700, title = {Efficient quantum algorithm for dissipative nonlinear differential equations}, journal = {Proceedings of the National Academy of Sciences}, volume = {118}, year = {2021}, month = {3/1/2021}, chapter = {e2026805118}, abstract = {

While there has been extensive previous work on efficient quantum algorithms for linear differential equations, analogous progress for nonlinear differential equations has been severely limited due to the linearity of quantum mechanics. Despite this obstacle, we develop a quantum algorithm for initial value problems described by dissipative quadratic n-dimensional ordinary differential equations. Assuming R\<1, where R is a parameter characterizing the ratio of the nonlinearity to the linear dissipation, this algorithm has complexity T2poly(logT,logn)/ϵ, where T is the evolution time and ϵ is the allowed error in the output quantum state. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in T. We achieve this improvement using the method of Carleman linearization, for which we give an improved convergence theorem. This method maps a system of nonlinear differential equations to an infinite-dimensional system of linear differential equations, which we discretize, truncate, and solve using the forward Euler method and the quantum linear system algorithm. We also provide a lower bound on the worst-case complexity of quantum algorithms for general quadratic differential equations, showing that the problem is intractable for R\≥2\–\√. Finally, we discuss potential applications of this approach to problems arising in biology as well as in fluid and plasma dynamics.

}, doi = {https://doi.org/10.1073/pnas.2026805118}, url = {https://arxiv.org/abs/2011.03185}, author = {Jin-Peng Liu and Herman {\O}ie Kolden and Hari K. Krovi and Nuno F. Loureiro and Konstantina Trivisa and Andrew M. Childs} } @article {2426, title = {Efficient quantum measurement of Pauli operators}, journal = {Quantum}, volume = {5}, year = {2021}, month = {01/19/2021}, chapter = {385}, abstract = {

Estimating the expectation value of an observable is a fundamental task in quantum computation. Unfortunately, it is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed computational basis. One common solution splits the observable into a weighted sum of Pauli operators and measures each separately, at the cost of many measurements. An improved version first groups mutually commuting Pauli operators together and then measures all operators within each group simultaneously. The effectiveness of this depends on two factors. First, to enable simultaneous measurement, circuits are required to rotate each group to the computational basis. In our work, we present two efficient circuit constructions that suitably rotate any group of k commuting n-qubit Pauli operators using at most kn\−k(k+1)/2 and O(kn/logk) two-qubit gates respectively. Second, metrics that justifiably measure the effectiveness of a grouping are required. In our work, we propose two natural metrics that operate under the assumption that measurements are distributed optimally among groups. Motivated by our new metrics, we introduce SORTED INSERTION, a grouping strategy that is explicitly aware of the weighting of each Pauli operator in the observable. Our methods are numerically illustrated in the context of the Variational Quantum Eigensolver, where the observables in question are molecular Hamiltonians. As measured by our metrics, SORTED INSERTION outperforms four conventional greedy colouring algorithms that seek the minimum number of groups.

}, doi = {https://doi.org/10.22331/q-2021-01-20-385}, url = {https://arxiv.org/abs/1908.06942}, author = {Ophelia Crawford and Barnaby van Straaten and Daochen Wang and Thomas Parks and Earl Campbell and Stephen Brierley} } @article {2821, title = {Efficient quantum programming using EASE gates on a trapped-ion quantum computer}, year = {2021}, month = {7/15/2021}, abstract = {

Parallel operations in conventional computing have proven to be an essential tool for efficient and practical computation, and the story is not different for quantum computing. Indeed, there exists a large body of works that study advantages of parallel implementations of quantum gates for efficient quantum circuit implementations. Here, we focus on the recently invented efficient, arbitrary, simultaneously entangling (EASE) gates, available on a trapped-ion quantum computer. Leveraging its flexibility in selecting arbitrary pairs of qubits to be coupled with any degrees of entanglement, all in parallel, we show a n-qubit Clifford circuit can be implemented using 6log(n) EASE gates, a n-qubit multiply-controlled NOT gate can be implemented using 3n/2 EASE gates, and a n-qubit permutation can be implemented using six EASE gates. We discuss their implications to near-term quantum chemistry simulations and the state of the art pattern matching algorithm. Given Clifford + multiply-controlled NOT gates form a universal gate set for quantum computing, our results imply efficient quantum computation by EASE gates, in general.

}, url = {https://arxiv.org/abs/2107.07591}, author = {Nikodem Grzesiak and Andrii Maksymov and Pradeep Niroula and Yunseong Nam} } @article {2725, title = {Energy storage and coherence in closed and open quantum batteries}, journal = {Quantum}, volume = {5}, year = {2021}, month = {7/15/2021}, pages = {505}, abstract = {

We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy storage can be bounded by the Hilbert-Schmidt coherence of the density matrix in the spectral basis of the unitary operator that encodes the evolution of the battery. We also show that an analogous bound can be obtained in terms of the battery\&$\#$39;s Hamiltonian coherence in the basis of the unitary operator by evaluating their commutator. We apply these bounds to a 4-state quantum system and the anisotropic XY Ising model in the closed system case, and the Spin-Boson model in the open case.\ 

}, doi = {https://doi.org/10.22331/q-2021-07-15-505}, url = {https://arxiv.org/abs/2012.15026}, author = {Francesco Caravelli and Bin Yan and Luis Pedro Garc{\'\i}a-Pintos and Alioscia Hamma} } @article {2932, title = {Entangled quantum cellular automata, physical complexity, and Goldilocks rules}, journal = {Quantum Science and Technology}, volume = {6}, year = {2021}, month = {9/29/2021}, pages = {045017}, abstract = {

Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under \"Goldilocks rules\" that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms -- Rydberg arrays, trapped ions, and superconducting qubits -- can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA.

}, issn = {2058-9565}, doi = {10.1088/2058-9565/ac1c41}, url = {http://dx.doi.org/10.1088/2058-9565/ac1c41}, author = {Hillberry, Logan E and Jones, Matthew T and Vargas, David L and Rall, Patrick and Nicole Yunger Halpern and Bao, Ning and Notarnicola, Simone and Montangero, Simone and Carr, Lincoln D} } @article {2724, title = {Entanglement and purification transitions in non-Hermitian quantum mechanics}, journal = {Phys. Rev. Lett., in press}, year = {2021}, month = {12/2/2020}, abstract = {

A quantum system subject to continuous measurement and post-selection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the rate of post-selection, this non-Hermitian Hamiltonian undergoes a spectral phase transition. On one side of this phase transition (for weak post-selection) an initially mixed density matrix remains mixed at all times, and an initially unentangled state develops volume-law entanglement; on the other side, an arbitrary initial state approaches a unique pure state with low entanglement. We identify this transition with an exceptional point in the spectrum of the non-Hermitian Hamiltonian, at which PT symmetry is spontaneously broken. We characterize the transition as well as the nontrivial steady state that emerges at late times in the mixed phase using exact diagonalization and an approximate, analytically tractable mean-field theory; these methods yield consistent conclusions.

}, url = {https://arxiv.org/abs/2012.01435}, author = {Sarang Gopalakrishnan and Michael Gullans} } @article {2776, title = {Entanglement Phase Transitions in Measurement-Only Dynamics}, journal = {Physical Review X}, volume = {11}, year = {2021}, month = {1/2/2021}, abstract = {

Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate. This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements. We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone. This motivates us to introduce \emph{measurement-only models}, in which the \"scrambling\" and \"un-scrambling\" effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes. This represents a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits. We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models. We find that the principle driving the EPTs in these models is \emph{frustration}, or mutual incompatibility, of the measurements. Suprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local (≳3-body) operators. We identify a class of exceptions to this behavior (\"bipartite ensembles\") which cannot sustain an entangling phase, but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points. Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light-cone, despite the non-locality inherent to quantum measurements.

}, doi = {10.1103/PhysRevX.11.011030}, url = {https://arxiv.org/abs/2004.09560}, author = {Ippoliti, Matteo and Michael Gullans and Gopalakrishnan, Sarang and Huse, David A. and Khemani, Vedika} } @article {2872, title = {Estimating distinguishability measures on quantum computers}, year = {2021}, month = {8/18/2021}, abstract = {

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent distinguishability measures are those based on the fidelity and trace distance, due to their physical interpretations. In this paper, we propose and review several algorithms for estimating distinguishability measures based on trace distance and fidelity, and we evaluate their performance using simulators of quantum computers. The algorithms can be used for distinguishing quantum states, channels, and strategies (the last also known in the literature as \"quantum combs\"). The fidelity-based algorithms offer novel physical interpretations of these distinguishability measures in terms of the maximum probability with which a single prover (or competing provers) can convince a verifier to accept the outcome of an associated computation. We simulate these algorithms by using a variational approach with parameterized quantum circuits and find that they converge well for the examples that we consider.\ 

}, url = {https://arxiv.org/abs/2108.08406}, author = {Rochisha Agarwal and Soorya Rethinasamy and Kunal Sharma and Mark M. Wilde} } @article {2928, title = {Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies}, year = {2021}, month = {10/27/2021}, abstract = {

We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary Z2 topological order with fermionic particle and fermionic loop excitations that have mutual π statistics. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary Z2 symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.

}, url = {https://arxiv.org/abs/2110.14644}, author = {Yu-An Chen and Po-Shen Hsin} } @conference {2941, title = {Expanding the VOQC Toolkit}, booktitle = {The Second International Workshop on Programming Languages for Quantum Computing (PLanQC 2021)}, year = {2021}, month = {06/2021}, abstract = {

voqc [Hietala et al. 2021b] (pronounced \“vox\”) is a compiler for quantum circuits, in the style of
tools like Qiskit [Aleksandrowicz et al. 2019], tket [Cambridge Quantum Computing Ltd 2019],
Quilc [Rigetti Computing 2019], and Cirq [Developers 2021]. What makes voqc different from these
tools is that it has been formally verified in the Coq proof assistant [Coq Development Team 2019].
voqc source programs are expressed in sqir, a simple quantum intermediate representation, which
has a precise mathematical semantics. We use Gallina, Coq\’s programming language, to implement
voqc transformations over sqir programs, and use Coq to prove the source program\’s semantics
are preserved. We then extract these Gallina definitions to OCaml, and compile the OCaml code to
a library that can operate on standard-formatted circuits.
voqc, and sqir, were built to be general-purpose. For example, while we originally designed sqir
for use in verified optimizations, we subsequently found sqir could also be suitable for writing, and
proving correct, source programs [Hietala et al. 2021a]. We have continued to develop the voqc
codebase to expand its reach and utility.
In this abstract, we present new extensions to voqc as an illustration of its flexibility. These
include support for calling voqc transformations from Python, added support for new gate sets
and optimizations, and the extension of our notion of correctness to include mapping-preservation,
which allows us to apply optimizations after mapping, reducing the cost introduced by making a
program conform to hardware constraints.

}, url = {http://rand.cs.uchicago.edu/files/planqc_2021c.pdf}, author = {Kesha Hietala and Liyi Li and Akshaj Gaur and Aaron Green and Robert Rand and Xiaodi Wu and Michael Hicks} } @article {2877, title = {An explicit vector algorithm for high-girth MaxCut}, year = {2021}, month = {8/27/2021}, abstract = {

We give an approximation algorithm for MaxCut and provide guarantees on the average fraction of edges cut on d-regular graphs of girth \≥2k. For every d\≥3 and k\≥4, our approximation guarantees are better than those of all other classical and quantum algorithms known to the authors. Our algorithm constructs an explicit vector solution to the standard semidefinite relaxation of MaxCut and applies hyperplane rounding. It may be viewed as a simplification of the previously best known technique, which approximates Gaussian wave processes on the infinite d-regular tree.

}, url = {https://arxiv.org/abs/2108.12477}, author = {Jessica K. Thompson and Ojas Parekh and Kunal Marwaha} } @article {2756, title = {Exploiting anticommutation in Hamiltonian simulation}, year = {2021}, month = {3/14/2021}, abstract = {

Quantum computing can efficiently simulate Hamiltonian dynamics of many-body quantum physics, a task that is generally intractable with classical computers. The hardness lies at the ubiquitous anti-commutative relations of quantum operators, in corresponding with the notorious negative sign problem in classical simulation. Intuitively, Hamiltonians with more commutative terms are also easier to simulate on a quantum computer, and anti-commutative relations generally cause more errors, such as in the product formula method. Here, we theoretically explore the role of anti-commutative relation in Hamiltonian simulation. We find that, contrary to our intuition, anti-commutative relations could also reduce the hardness of Hamiltonian simulation. Specifically, Hamiltonians with mutually anti-commutative terms are easy to simulate, as what happens with ones consisting of mutually commutative terms. Such a property is further utilized to reduce the algorithmic error or the gate complexity in the truncated Taylor series quantum algorithm for general problems. Moreover, we propose two modified linear combinations of unitaries methods tailored for Hamiltonians with different degrees of anti-commutation. We numerically verify that the proposed methods exploiting anti-commutative relations could significantly improve the simulation accuracy of electronic Hamiltonians. Our work sheds light on the roles of commutative and anti-commutative relations in simulating quantum systems.

}, url = {https://arxiv.org/abs/2103.07988}, author = {Qi Zhao and Xiao Yuan} } @article {2860, title = {Exponentially Many Local Minima in Quantum Neural Networks}, journal = {Proceedings of the 38th International Conference on Machine Learning, PMLR}, volume = {139}, year = {2021}, month = {10/5/2021}, pages = {12144-12155}, abstract = {

Quantum Neural Networks (QNNs), or the so-called variational quantum circuits, are important quantum applications both because of their similar promises as classical neural networks and because of the feasibility of their implementation on near-term intermediate-size noisy quantum machines (NISQ). However, the training task of QNNs is challenging and much less understood. We conduct a quantitative investigation on the landscape of loss functions of QNNs and identify a class of simple yet extremely hard QNN instances for training. Specifically, we show for typical under-parameterized QNNs, there exists a dataset that induces a loss function with the number of spurious local minima depending exponentially on the number of parameters. Moreover, we show the optimality of our construction by providing an almost matching upper bound on such dependence. While local minima in classical neural networks are due to non-linear activations, in quantum neural networks local minima appear as a result of the quantum interference phenomenon. Finally, we empirically confirm that our constructions can indeed be hard instances in practice with typical gradient-based optimizers, which demonstrates the practical value of our findings.\ 

}, url = {https://arxiv.org/pdf/2110.02479.pdf}, author = {Xuchen You and Xiaodi Wu} } @article {2605, title = {Faster Digital Quantum Simulation by Symmetry Protection}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {2/14/2021}, type = {Report number: FERMILAB-PUB-20-240-QIS-T}, abstract = {

Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply our technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, our algorithm can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that our technique can also protect simulation against other types of coherent, temporally correlated errors, such as the 1/f noise commonly found in solid-state experiments.

}, issn = {2691-3399}, doi = {http://dx.doi.org/10.1103/PRXQuantum.2.010323}, url = {https://arxiv.org/abs/2006.16248}, author = {Minh C. Tran and Yuan Su and Daniel Carney and J. M. Taylor} } @article {2811, title = {Feedback-stabilized dynamical steady states in the Bose-Hubbard model}, journal = {Phys. Rev. Research}, volume = {3}, year = {2021}, month = {12/15/2021}, pages = {043075 }, abstract = {

The implementation of a combination of continuous weak measurement and classical feedback provides a powerful tool for controlling the evolution of quantum systems. In this work, we investigate the potential of this approach from three perspectives. First, we consider a double-well system in the classical large-atom-number limit, deriving the exact equations of motion in the presence of feedback. Second, we consider the same system in the limit of small atom number, revealing the effect that quantum fluctuations have on the feedback scheme. Finally, we explore the behavior of modest sized Hubbard chains using exact numerics, demonstrating the near-deterministic preparation of number states, a tradeoff between local and non-local feedback for state preparation, and evidence of a feedback-driven symmetry-breaking phase transition.

}, doi = {https://doi.org/10.1103/PhysRevResearch.3.043075}, url = {https://arxiv.org/abs/2106.09744}, author = {Jeremy T. Young and Alexey V. Gorshkov and I. B. Spielman} } @article {2925, title = {From Quantum Codes to Gravity: A Journey of Gravitizing Quantum Mechanics}, year = {2021}, month = {11/30/2021}, abstract = {

In this note, I review a recent approach to quantum gravity that \"gravitizes\" quantum mechanics by emerging geometry and gravity from complex quantum states. Drawing further insights from tensor network toy models in AdS/CFT, I propose that approximate quantum error correction codes, when re-adapted into the aforementioned framework, also has promise in emerging gravity in near-flat geometries.

}, url = {https://arxiv.org/abs/2112.00199}, author = {ChunJun Cao} } @article {2762, title = {Frustration-induced anomalous transport and strong photon decay in waveguide QED}, journal = {Phys. Rev. Research}, volume = {3}, year = {2021}, month = {9/16/2021}, abstract = {

We study the propagation of photons in a one-dimensional environment consisting of two non-interacting species of photons frustratingly coupled to a single spin-1/2. The ultrastrong frustrated coupling leads to an extreme mixing of the light and matter degrees of freedom, resulting in the disintegration of the spin and a breakdown of the \"dressed-spin\", or polaron, description. Using a combination of numerical and analytical methods, we show that the elastic response becomes increasingly weak at the effective spin frequency, showing instead an increasingly strong and broadband response at higher energies. We also show that the photons can decay into multiple photons of smaller energies. The total probability of these inelastic processes can be as large as the total elastic scattering rate, or half of the total scattering rate, which is as large as it can be. The frustrated spin induces strong anisotropic photon-photon interactions that are dominated by inter-species interactions. Our results are relevant to state-of-the-art circuit and cavity quantum electrodynamics experiments.

}, doi = {https://doi.org/10.1103/PhysRevResearch.3.L032058}, url = {https://arxiv.org/abs/2007.03690}, author = {Ron Belyansky and Seth Whitsitt and Rex Lundgren and Yidan Wang and Andrei Vrajitoarea and Andrew A. Houck and Alexey V. Gorshkov} } @article {3019, title = {Fully device-independent quantum key distribution using synchronous correlations}, year = {2021}, month = {10/27/2021}, abstract = {

We derive a device-independent quantum key distribution protocol based on synchronous correlations and their Bell inequalities. This protocol offers several advantages over other device-independent schemes including symmetry between the two users and no need for preshared randomness. We close a \"synchronicity\" loophole by showing that an almost synchronous correlation inherits the self-testing property of the associated synchronous correlation. We also pose a new security assumption that closes the \"locality\" (or \"causality\") loophole: an unbounded adversary with even a small uncertainty about the users\&$\#$39; choice of measurement bases cannot produce any almost synchronous correlation that approximately maximally violates a synchronous Bell inequality.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2110.14530}, url = {https://arxiv.org/abs/2110.14530}, author = {Rodrigues, Nishant and Lackey, Brad} } @article {2819, title = {Garc{\'\i}a-Pintos, Hamma, and del Campo Reply}, journal = {Phys. Rev. Lett.}, volume = {127}, year = {2021}, month = {7/9/2021}, pages = {028902}, abstract = {

We acknowledge that a derivation reported in Phys. Rev. Lett. 125, 040601 (2020) is incorrect as pointed out by Cusumano and Rudnicki. We respond by giving a correct proof of the claim \“fluctuations in the free energy operator upper bound the charging power of a quantum battery\” that we made in the Letter.

}, doi = {10.1103/PhysRevLett.127.028902}, author = {Luis Pedro Garc{\'\i}a-Pintos and Alioscia Hamma and Adolfo del Campo} } @article {2936, title = {Generalization in quantum machine learning from few training data}, year = {2021}, month = {11/9/2021}, abstract = {

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as T/N\−\−\−\−\√. When only K<}, url = {https://arxiv.org/abs/2111.05292}, author = {Matthias C. Caro and Hsin-Yuan Huang and M. Cerezo and Kunal Sharma and Andrew Sornborger and Lukasz Cincio and Patrick J. Coles} } @article {2812, title = {Higher cup products on hypercubic lattices: application to lattice models of topological phases}, year = {2021}, month = {6/9/2021}, abstract = {

In this paper, we derive the explicit formula for higher cup products on hypercubic lattices, based on the recently developed geometrical interpretation in the simplicial case. We illustrate how this formalism can elucidate lattice constructions on hypercubic lattices for various models and deriving them from spacetime actions. In particular, we demonstrate explicitly that the (3+1)D SPT S=12\∫w22+w41 (where w1 and w2 are the first and second Stiefel-Whitney classes) is dual to the 3-fermion Walker-Wang model constructed on the cubic lattice by Burnell-Chen-Fidkowski-Vishwanath. Other examples include the double-semion model, and also the {\textquoteleft}fermionic\&$\#$39; toric code in arbitrary dimensions on hypercubic lattices. In addition, we extend previous constructions of exact boson-fermion dualities and the Gu-Wen Grassmann Integral to arbitrary dimensions. Another result which may be of independent interest is a derivation of a cochain-level action for the generalized double-semion model, reproducing a recently derived action on the cohomology level.

}, url = {https://arxiv.org/abs/2106.05274}, author = {Yu-An Chen and Sri Tata} } @article {2543, title = {High-precision quantum algorithms for partial differential equations}, journal = {Quantum 5, 574}, volume = {5}, year = {2021}, month = {11/4/2021}, abstract = {

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity poly(1/ε), where ε is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be poly(d,log(1/ε)), where d is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations.\ 

}, doi = {https://doi.org/10.22331/q-2021-11-10-574}, url = {https://arxiv.org/abs/2002.07868}, author = {Andrew M. Childs and Jin-Peng Liu and Aaron Ostrander} } @article {2924, title = {How to engineer a quantum wavefunction}, year = {2021}, month = {12/2/2021}, abstract = {

In a conventional experiment, inductive inferences between source and target systems are typically justified with reference to a uniformity principle between systems of the same material type. In an analogue quantum simulation, by contrast, scientists aim to learn about target quantum systems of one material type via an experiment on a source quantum system of a different material type. In this paper, we argue that such an inference can be justified by reference to the two quantum systems being of the same empirical type. We illustrate this novel experimental practice of wavefunction engineering with reference to the example of Bose-Hubbard systems.\ 

}, url = {https://arxiv.org/abs/2112.01105}, author = {Peter W. Evans and Dominik Hangleiter and Karim P. Y. Th{\'e}bault} } @article {2771, title = {Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations}, year = {2021}, month = {3/15/2021}, abstract = {

We consider a class of holographic tensor networks that are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility for an efficient variational ansatz, we provide guidelines for constructing networks consisting of multiple types of tensors that can support power-law correlation. We also provide an explicit construction of one such network, which approximates the holographic HaPPY pentagon code in the limit where variational parameters are taken to be small.

}, url = {https://arxiv.org/abs/2103.08631}, author = {ChunJun Cao and Jason Pollack and Yixu Wang} } @article {2772, title = {On the Impossibility of Post-Quantum Black-Box Zero-Knowledge in Constant Rounds}, year = {2021}, month = {3/20/2021}, abstract = {

We investigate the existence of constant-round post-quantum black-box zero-knowledge protocols for NP. As a main result, we show that there is no constant-round post-quantum black-box zero-knowledge argument for NP unless NP\⊆BQP. As constant-round black-box zero-knowledge arguments for NP exist in the classical setting, our main result points out a fundamental difference between post-quantum and classical zero-knowledge protocols. Combining previous results, we conclude that unless NP\⊆BQP, constant-round post-quantum zero-knowledge protocols for NP exist if and only if we use non-black-box techniques or relax certain security requirements such as relaxing standard zero-knowledge to ϵ-zero-knowledge. Additionally, we also prove that three-round and public-coin constant-round post-quantum black-box ϵ-zero-knowledge arguments for NP do not exist unless NP\⊆BQP.

}, url = {https://arxiv.org/abs/2103.11244}, author = {Nai-Hui Chia and Kai-Min Chung and Qipeng Liu and Takashi Yamakawa} } @article {2908, title = {Interactive Protocols for Classically-Verifiable Quantum Advantage}, year = {2021}, month = {12/9/2021}, abstract = {

Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output is itself classically intractable. On the other hand, certain quantum algorithms (e.g. prime factorization via Shor\&$\#$39;s algorithm) are efficiently verifiable, but require more resources than what is available on near-term devices. One way to bridge the gap between verifiability and implementation is to use \"interactions\" between a prover and a verifier. By leveraging cryptographic functions, such protocols enable the classical verifier to enforce consistency in a quantum prover\&$\#$39;s responses across multiple rounds of interaction. In this work, we demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer. We execute two complementary protocols -- one based upon the learning with errors problem and another where the cryptographic construction implements a computational Bell test. To perform multiple rounds of interaction, we implement mid-circuit measurements on a subset of trapped ion qubits, with subsequent coherent evolution. For both protocols, the performance exceeds the asymptotic bound for classical behavior; maintaining this fidelity at scale would conclusively demonstrate verifiable quantum advantage.

}, url = {https://arxiv.org/abs/2112.05156}, author = {Daiwei Zhu and Gregory D. Kahanamoku-Meyer and Laura Lewis and Crystal Noel and Or Katz and Bahaa Harraz and Qingfeng Wang and Andrew Risinger and Lei Feng and Debopriyo Biswas and Laird Egan and Alexandru Gheorghiu and Yunseong Nam and Thomas Vidick and Umesh Vazirani and Norman Y. Yao and Marko Cetina and Christopher Monroe} } @article {2869, title = {Learnability of the output distributions of local quantum circuits}, year = {2021}, month = {10/11/2021}, abstract = {

There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC) learnability of quantum circuit Born machines, i.e., the output distributions of local quantum circuits. We first show a negative result, namely, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable in the statistical query model, i.e., when given query access to empirical expectation values of bounded functions over the sample space. This immediately implies the hardness, for both quantum and classical algorithms, of learning from statistical queries the output distributions of local quantum circuits using any gate set which includes the Clifford group. As many practical generative modelling algorithms use statistical queries -- including those for training quantum circuit Born machines -- our result is broadly applicable and strongly limits the possibility of a meaningful quantum advantage for learning the output distributions of local quantum circuits. As a positive result, we show that in a more powerful oracle model, namely when directly given access to samples, the output distributions of local Clifford circuits are computationally efficiently PAC learnable by a classical learner. Our results are equally applicable to the problems of learning an algorithm for generating samples from the target distribution (generative modelling) and learning an algorithm for evaluating its probabilities (density modelling). They provide the first rigorous insights into the learnability of output distributions of local quantum circuits from the probabilistic modelling perspective.\ 

}, url = {https://arxiv.org/abs/2110.05517}, author = {Marcel Hinsche and Marios Ioannou and Alexander Nietner and Jonas Haferkamp and Yihui Quek and Dominik Hangleiter and Jean-Pierre Seifert and Jens Eisert and Ryan Sweke} } @article {2929, title = {Lefschetz Thimble Quantum Monte Carlo for Spin Systems}, year = {2021}, month = {10/20/2021}, abstract = {

Monte Carlo simulations are often useful tools for modeling quantum systems, but in some cases they suffer from a sign problem, which manifests as an oscillating phase attached to the probabilities being sampled. This sign problem generally leads to an exponential slow down in the time taken by a Monte Carlo algorithm to reach any given level of accuracy, and it has been shown that completely solving the sign problem for an arbitrary quantum system is NP-hard. However, a variety of techniques exist for mitigating the sign problem in specific cases; in particular, the technique of deforming the Monte Carlo simulation\&$\#$39;s plane of integration onto Lefschetz thimbles (that is, complex hypersurfaces of stationary phase) has seen success for many problems of interest in the context of quantum field theories. We extend this methodology to discrete spin systems by utilizing spin coherent state path integrals to re-express the spin system\&$\#$39;s partition function in terms of continuous variables. This translation to continuous variables introduces additional challenges into the Lefschetz thimble method, which we address. We show that these techniques do indeed work to lessen the sign problem on some simple spin systems.

}, url = {https://arxiv.org/abs/2110.10699}, author = {T. C. Mooney and Jacob Bringewatt and Lucas T. Brady} } @article {2759, title = {The Lieb-Robinson light cone for power-law interactions}, year = {2021}, month = {3/29/2021}, abstract = {

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as 1/rα at distance r? Here, we present a definitive answer to this question for all exponents α\>2d and all spatial dimensions d. Schematically, information takes time at least rmin{1,α\−2d} to propagate a distance~r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

}, url = {https://arxiv.org/abs/2103.15828}, author = {Minh C. Tran and Andrew Y. Guo and Christopher L. Baldwin and Adam Ehrenberg and Alexey V. Gorshkov and Andrew Lucas} } @article {2934, title = {Limits to Perception by Quantum Monitoring with Finite Efficiency}, journal = {Entropy}, volume = {23}, year = {2021}, month = {11/17/2021}, pages = {1527}, abstract = {

We formulate limits to perception under continuous quantum measurements by comparing the quantum states assigned by agents that have partial access to measurement outcomes. To this end, we provide bounds on the trace distance and the relative entropy between the assigned state and the actual state of the system. These bounds are expressed solely in terms of the purity and von Neumann entropy of the state assigned by the agent, and are shown to characterize how an agent\’s perception of the system is altered by access to additional information. We apply our results to Gaussian states and to the dynamics of a system embedded in an environment illustrated on a quantum Ising chain.

}, issn = {1099-4300}, doi = {10.3390/e23111527}, url = {https://www.mdpi.com/1099-4300/23/11/1527}, author = {Garc{\'\i}a-Pintos, Luis Pedro and del Campo, Adolfo} } @article {2865, title = {Linear and continuous variable spin-wave processing using a cavity-coupled atomic ensemble}, year = {2021}, month = {9/30/2021}, abstract = {

Spin-wave excitations in ensembles of atoms are gaining attention as a quantum information resource. However, current techniques with atomic spin waves do not achieve universal quantum information processing. We conduct a theoretical analysis of methods to create a high-capacity universal quantum processor and network node using an ensemble of laser-cooled atoms, trapped in a one-dimensional periodic potential and coupled to a ring cavity. We describe how to establish linear quantum processing using a lambda-scheme in a rubidium-atom system, calculate the expected experimental operational fidelities. Second, we derive an efficient method to achieve linear controllability with a single ensemble of atoms, rather than two-ensembles as proposed in [K. C. Cox et al. Spin-Wave Quantum Computing with Atoms in a Single-Mode Cavity, preprint 2021]. Finally, we propose to use the spin-wave processor for continuous-variable quantum information processing and present a scheme to generate large dual-rail cluster states useful for deterministic computing.\ 

}, url = {https://arxiv.org/abs/2109.15246}, author = {Kevin C. Cox and Przemyslaw Bienias and David H. Meyer and Donald P. Fahey and Paul D. Kunz and Alexey V. Gorshkov} } @article {2871, title = {Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain}, year = {2021}, month = {9/22/2021}, abstract = {

We consider the random-field Heisenberg model, a paradigmatic model for many-body localization (MBL), and add a Markovian dephasing bath coupled to the Anderson orbitals of the model\&$\#$39;s non-interacting limit. We map this system to a classical facilitated hopping model that is computationally tractable for large system sizes, and investigate its dynamics. The classical model exhibits a robust crossover between an ergodic (thermal) phase and a frozen (localized) phase. The frozen phase is destabilized by thermal subregions (bubbles), which thermalize surrounding sites by providing a fluctuating interaction energy and so enable off-resonance particle transport. Investigating steady state transport, we observe that the interplay between thermal and frozen bubbles leads to a clear transition between diffusive and subdiffusive regimes. This phenomenology both describes the MBL system coupled to a bath, and provides a classical analogue for the many-body localization transition in the corresponding quantum model, in that the classical model displays long local memory times. It also highlights the importance of the details of the bath coupling in studies of MBL systems coupled to thermal environments.

}, url = {https://arxiv.org/abs/2109.10926}, author = {Kai Klocke and Christopher David White and Michael Buchhold} } @article {2923, title = {Machine learning outperforms thermodynamics in measuring how well a many-body system learns a drive}, journal = {Scientific Reports}, volume = {11}, year = {2021}, month = {10/22/2021}, abstract = {

Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now, many-body learning has been detected with thermodynamic properties, such as work absorption and strain. We progress beyond these macroscopic properties first defined for equilibrium contexts: We quantify statistical mechanical learning using representation learning, a machine-learning model in which information squeezes through a bottleneck. By calculating properties of the bottleneck, we measure four facets of many-body systems\&$\#$39; learning: classification ability, memory capacity, discrimination ability, and novelty detection. Numerical simulations of a classical spin glass illustrate our technique. This toolkit exposes self-organization that eludes detection by thermodynamic measures: Our toolkit more reliably and more precisely detects and quantifies learning by matter while providing a unifying framework for many-body learning.\ 

}, issn = {2045-2322}, doi = {https://doi.org/10.1038/s41598-021-88311-7}, url = {https://arxiv.org/abs/2004.03604}, author = {Zhong, Weishun and Gold, Jacob M. and Marzen, Sarah and England, Jeremy L. and Nicole Yunger Halpern} } @article {2730, title = {Machine-learning enhanced dark soliton detection in Bose-Einstein condensates}, journal = {Mach. Learn.: Sci. Technol. }, volume = {2}, year = {2021}, month = {6/17/2021}, pages = {035020}, abstract = {

Most data in cold-atom experiments comes from images, the analysis of which is limited by our preconceptions of the patterns that could be present in the data. We focus on the well-defined case of detecting dark solitons -- appearing as local density depletions in a BEC -- using a methodology that is extensible to the general task of pattern recognition in images of cold atoms. Studying soliton dynamics over a wide range of parameters requires the analysis of large datasets, making the existing human-inspection-based methodology a significant bottleneck. Here we describe an automated classification and positioning system for identifying localized excitations in atomic Bose-Einstein condensates (BECs) utilizing deep convolutional neural networks to eliminate the need for human image examination. Furthermore, we openly publish our labeled dataset of dark solitons, the first of its kind, for further machine learning research.

}, doi = {https://doi.org/10.1088/2632-2153/abed1e}, url = {https://arxiv.org/abs/2101.05404}, author = {Shangjie Guo and Amilson R. Fritsch and Craig Greenberg and I. B. Spielman and Justyna P. Zwolak} } @article {2810, title = {Magic State Distillation from Entangled States}, year = {2021}, month = {6/23/2021}, abstract = {

Magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can improve the distillation outcome. We analyze a few explicit examples and show that spin squeezing can be used to convert non-distillable states into distillable ones.
Our analysis also suggests that the conventional product input states assumed by magic distillation protocols are extremely atypical among general states with distillable magic. It further justifies the need for studying a diverse range of entangled inputs that yield magic states with high probability.

}, url = {https://arxiv.org/abs/2106.12591}, author = {Ning Bao and ChunJun Cao and Vincent Paul Su} } @article {2777, title = {Maximum Refractive Index of an Atomic Medium}, journal = {Physical Review X}, volume = {11}, year = {2021}, month = {2/18/2021}, abstract = {

It is interesting to observe that all optical materials with a positive refractive index have a value of index that is of order unity. Surprisingly, though, a deep understanding of the mechanisms that lead to this universal behavior seems to be lacking. Moreover, this observation is difficult to reconcile with the fact that a single, isolated atom is known to have a giant optical response, as characterized by a resonant scattering cross section that far exceeds its physical size. Here, we theoretically and numerically investigate the evolution of the optical properties of an ensemble of ideal atoms as a function of density, starting from the dilute gas limit, including the effects of multiple scattering and near-field interactions. Interestingly, despite the giant response of an isolated atom, we find that the maximum index does not indefinitely grow with increasing density, but rather reaches a limiting value n\≈1.7. We propose an explanation based upon strong-disorder renormalization group theory, in which the near-field interaction combined with random atomic positions results in an inhomogeneous broadening of atomic resonance frequencies. This mechanism ensures that regardless of the physical atomic density, light at any given frequency only interacts with at most a few near-resonant atoms per cubic wavelength, thus limiting the maximum index attainable. Our work is a promising first step to understand the limits of refractive index from a bottom-up, atomic physics perspective, and also introduces renormalization group as a powerful tool to understand the generally complex problem of multiple scattering of light overall.

}, doi = {10.1103/PhysRevX.11.011026}, url = {https://arxiv.org/abs/2006.01680}, author = {Andreoli, Francesco and Michael Gullans and High, Alexander A. and Browaeys, Antoine and Chang, Darrick E.} } @article {2780, title = {The membership problem for constant-sized quantum correlations is undecidable}, year = {2021}, month = {1/26/2021}, abstract = {

When two spatially separated parties make measurements on an unknown entangled quantum state, what correlations can they achieve? How difficult is it to determine whether a given correlation is a quantum correlation? These questions are central to problems in quantum communication and computation. Previous work has shown that the general membership problem for quantum correlations is computationally undecidable. In the current work we show something stronger: there is a family of constant-sized correlations -- that is, correlations for which the number of measurements and number of measurement outcomes are fixed -- such that solving the quantum membership problem for this family is computationally impossible. Thus, the undecidability that arises in understanding Bell experiments is not dependent on varying the number of measurements in the experiment. This places strong constraints on the types of descriptions that can be given for quantum correlation sets. Our proof is based on a combination of techniques from quantum self-testing and from undecidability results of the third author for linear system nonlocal games.

}, url = {https://arxiv.org/abs/2101.11087}, author = {Honghao Fu and Carl Miller and William Slofstra} } @article {2770, title = {Meta Hamiltonian Learning}, year = {2021}, month = {4/9/2021}, abstract = {

Efficient characterization of quantum devices is a significant challenge critical for the development of large scale quantum computers. We consider an experimentally motivated situation, in which we have a decent estimate of the Hamiltonian, and its parameters need to be characterized and fine-tuned frequently to combat drifting experimental variables. We use a machine learning technique known as meta-learning to learn a more efficient optimizer for this task. We consider training with the nearest-neighbor Ising model and study the trained model\&$\#$39;s generalizability to other Hamiltonian models and larger system sizes. We observe that the meta-optimizer outperforms other optimization methods in average loss over test samples. This advantage follows from the meta-optimizer being less likely to get stuck in local minima, which highly skews the distribution of the final loss of the other optimizers. In general, meta-learning decreases the number of calls to the experiment and reduces the needed classical computational resources.

}, url = {https://arxiv.org/abs/2104.04453}, author = {Przemyslaw Bienias and Alireza Seif and Mohammad Hafezi} } @article {2935, title = {Noise-induced barren plateaus in variational quantum algorithms}, journal = {Nature Communications}, volume = {12}, year = {2021}, month = {11/29/2021}, pages = {6961}, abstract = {

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

}, doi = {https://doi.org/10.1038/s41467-021-27045-6}, author = {Samson Wang and Enrico Fontana and M. Cerezo and Kunal Sharma and Akira Sone and Lukasz Cincio and Patrick J. Coles} } @article {2938, title = {On nonlinear transformations in quantum computation}, year = {2021}, month = {12/23/2021}, abstract = {

While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of quantum computing from solving nonlinear equations to data processing and quantum machine learning. Here we develop algorithms for implementing nonlinear transformations of input quantum states. Our algorithms are framed around the concept of a weighted state, a mathematical entity describing the output of an operational procedure involving both quantum circuits and classical post-processing.

}, url = {https://arxiv.org/abs/2112.12307}, author = {Zo{\"e} Holmes and Nolan Coble and Andrew T. Sornborger and Yi{\u g}it Suba{\c s}{\i}} } @article {2880, title = {Nonlocal Games, Compression Theorems, and the Arithmetical Hierarchy}, year = {2021}, month = {10/9/2021}, abstract = {

We investigate the connection between the complexity of nonlocal games and the arithmetical hierarchy, a classification of languages according to the complexity of arithmetical formulas defining them. It was recently shown by Ji, Natarajan, Vidick, Wright and Yuen that deciding whether the (finite-dimensional) quantum value of a nonlocal game is 1 or at most 12 is complete for the class Σ1 (i.e., RE). A result of Slofstra implies that deciding whether the commuting operator value of a nonlocal game is equal to 1 is complete for the class Π1 (i.e., coRE). We prove that deciding whether the quantum value of a two-player nonlocal game is exactly equal to 1 is complete for Π2; this class is in the second level of the arithmetical hierarchy and corresponds to formulas of the form \"\∀x\∃yϕ(x,y)\". This shows that exactly computing the quantum value is strictly harder than approximating it, and also strictly harder than computing the commuting operator value (either exactly or approximately). We explain how results about the complexity of nonlocal games all follow in a unified manner from a technique known as compression. At the core of our Π2-completeness result is a new \"gapless\" compression theorem that holds for both quantum and commuting operator strategies. Our compression theorem yields as a byproduct an alternative proof of Slofstra\&$\#$39;s result that the set of quantum correlations is not closed. We also show how a \"gap-preserving\" compression theorem for commuting operator strategies would imply that approximating the commuting operator value is complete for Π1.

}, url = {https://arxiv.org/abs/2110.04651}, author = {Hamoon Mousavi and Seyed Sajjad Nezhadi and Henry Yuen} } @article {2768, title = {Observation of a prethermal discrete time crystal}, year = {2021}, month = {2/2/2021}, abstract = {

The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the discovery of novel phases of matter, often catalyzed by driving the system periodically. The inherent heating from such Floquet drives can be tempered by including strong disorder in the system, but this can also mask the generality of non-equilibrium phases. In this work, we utilize a trapped-ion quantum simulator to observe signatures of a non-equilibrium driven phase without disorder: the prethermal discrete time crystal (PDTC). Here, many-body heating is suppressed not by disorder-induced many-body localization, but instead via high-frequency driving, leading to an expansive time window where non-equilibrium phases can emerge. We observe a number of key features that distinguish the PDTC from its many-body-localized disordered counterpart, such as the drive-frequency control of its lifetime and the dependence of time-crystalline order on the energy density of the initial state. Floquet prethermalization is thus presented as a general strategy for creating, stabilizing and studying intrinsically out-of-equilibrium phases of matter.

}, url = {https://arxiv.org/abs/2102.01695}, author = {Antonis Kyprianidis and Francisco Machado and William Morong and Patrick Becker and Kate S. Collins and Dominic V. Else and Lei Feng and Paul W. Hess and Chetan Nayak and Guido Pagano and Norman Y. Yao and Christopher Monroe} } @article {2805, title = {Observation of measurement-induced quantum phases in a trapped-ion quantum computer}, year = {2021}, month = {6/10/2021}, abstract = {

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the \"pure\" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the \"mixed\" or \"coding\" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.

}, url = {https://arxiv.org/abs/2106.05881}, author = {Crystal Noel and Pradeep Niroula and Daiwei Zhu and Andrew Risinger and Laird Egan and Debopriyo Biswas and Marko Cetina and Alexey V. Gorshkov and Michael Gullans and David A. Huse and Christopher Monroe} } @article {2763, title = {Observation of Stark many-body localization without disorder}, year = {2021}, month = {2/14/2021}, abstract = {

Thermalization is a ubiquitous process of statistical physics, in which details of few-body observables are washed out in favor of a featureless steady state. Even in isolated quantum many-body systems, limited to reversible dynamics, thermalization typically prevails. However, in these systems, there is another possibility: many-body localization (MBL) can result in preservation of a non-thermal state. While disorder has long been considered an essential ingredient for this phenomenon, recent theoretical work has suggested that a quantum many-body system with a uniformly increasing field -- but no disorder -- can also exhibit MBL, resulting in {\textquoteleft}Stark MBL.\&$\#$39; Here we realize Stark MBL in a trapped-ion quantum simulator and demonstrate its key properties: halting of thermalization and slow propagation of correlations. Tailoring the interactions between ionic spins in an effective field gradient, we directly observe their microscopic equilibration for a variety of initial states, and we apply single-site control to measure correlations between separate regions of the spin chain. Further, by engineering a varying gradient, we create a disorder-free system with coexisting long-lived thermalized and nonthermal regions. The results demonstrate the unexpected generality of MBL, with implications about the fundamental requirements for thermalization and with potential uses in engineering long-lived non-equilibrium quantum matter.

}, url = {https://arxiv.org/abs/2102.07250}, author = {W. Morong and F. Liu and P. Becker and K. S. Collins and L. Feng and A. Kyprianidis and G. Pagano and T. You and Alexey V. Gorshkov and C. Monroe} } @article {2926, title = {Optimal scaling quantum linear systems solver via discrete adiabatic theorem}, year = {2021}, month = {11/15/2021}, abstract = {

Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition number κ of the linear system, without requiring a complicated variable-time amplitude amplification procedure. However, the most efficient of those procedures is still asymptotically sub-optimal by a factor of log(κ). Here, we prove a rigorous form of the adiabatic theorem that bounds the error in terms of the spectral gap for intrinsically discrete time evolutions. We use this discrete adiabatic theorem to develop a quantum algorithm for solving linear systems that is asymptotically optimal, in the sense that the complexity is strictly linear in κ, matching a known lower bound on the complexity. Our O(κlog(1/ε)) complexity is also optimal in terms of the combined scaling in κ and the precision ε. Compared to existing suboptimal methods, our algorithm is simpler and easier to implement. Moreover, we determine the constant factors in the algorithm, which would be suitable for determining the complexity in terms of gate counts for specific applications.\ 

}, url = {https://arxiv.org/abs/2111.08152}, author = {Pedro C. S. Costa and Dong An and Yuval R. Sanders and Yuan Su and Ryan Babbush and Dominic W. Berry} } @article {2806, title = {Phase-engineered bosonic quantum codes}, journal = {Physical Review A}, volume = {103}, year = {2021}, month = {6/29/2021}, pages = {062427}, abstract = {

Continuous-variable systems protected by bosonic quantum codes have emerged as a promising platform for quantum information. To date, the design of code words has centered on optimizing the state occupation in the relevant basis to generate the distance needed for error correction. Here, we show tuning the phase degree of freedom in the design of code words can affect, and potentially enhance, the protection against Markovian errors that involve excitation exchange with the environment. As illustrations, we first consider phase engineering bosonic codes with uniform spacing in the Fock basis that correct excitation loss with a Kerr unitary and show that these modified codes feature destructive interference between error code words and, with an adapted \“two-level\” recovery, the error protection is significantly enhanced. We then study protection against energy decay with the presence of mode nonlinearities \…

}, url = {https://authors.library.caltech.edu/109764/2/1901.05358.pdf}, author = {Linshu Li and Dylan J Young and Victor V. Albert and Kyungjoo Noh and Chang-Ling Zou and Liang Jiang} } @article {2827, title = {Precise Hamiltonian identification of a superconducting quantum processor}, year = {2021}, month = {8/18/2021}, abstract = {

The required precision to perform quantum simulations beyond the capabilities of classical computers imposes major experimental and theoretical challenges. Here, we develop a characterization technique to benchmark the implementation precision of a specific quantum simulation task. We infer all parameters of the bosonic Hamiltonian that governs the dynamics of excitations in a two-dimensional grid of nearest-neighbour coupled superconducting qubits. We devise a robust algorithm for identification of Hamiltonian parameters from measured times series of the expectation values of single-mode canonical coordinates. Using super-resolution and denoising methods, we first extract eigenfrequencies of the governing Hamiltonian from the complex time domain measurement; next, we recover the eigenvectors of the Hamiltonian via constrained manifold optimization over the orthogonal group. For five and six coupled qubits, we identify Hamiltonian parameters with sub-MHz precision and construct a spatial implementation error map for a grid of 27 qubits. Our approach enables us to distinguish and quantify the effects of state preparation and measurement errors and show that they are the dominant sources of errors in the implementation. Our results quantify the implementation accuracy of analog dynamics and introduce a diagnostic toolkit for understanding, calibrating, and improving analog quantum processors.

}, url = {https://arxiv.org/abs/2108.08319}, author = {Dominik Hangleiter and Ingo Roth and Jens Eisert and Pedram Roushan} } @article {2876, title = {Preparing Renormalization Group Fixed Points on NISQ Hardware}, year = {2021}, month = {9/20/2021}, abstract = {

Noisy intermediate-scale quantum (NISQ) hardware is typically limited to low-depth quantum circuits to limit the number of opportunities for introduction of error by unreliable quantum gates. A less-explored alternative approach is to repeatedly apply a quantum channel with a desired quantum state as a stable fixed point. Increased circuit depth can in this case be beneficial rather than harmful due to dissipative self-correction. The quantum channels constructed from MERA circuits can be interpreted in terms of the renormalization group(RG), and their fixed points are RG fixed points, i.e. scale-invariant systems such as conformal field theories. Here, building upon the theoretical proposal of Kim and Swingle, we numerically and experimentally study the robust preparation of the ground state of the critical Ising model using circuits adapted from the work of Evenbly and White. The experimental implementation exhibits self-correction through renormalization seen in the convergence and stability of local observables, and makes essential use of the ability to measure and reset individual qubits afforded by the \"quantum CCD\" architecture of the Honeywell ion-trap. We also numerically test error mitigation by zero-noise extrapolation schemes specially adapted for renormalization circuits, which are able to outperform typical extrapolation schemes using lower gate overhead.\ 

}, url = {https://arxiv.org/abs/2109.09787}, author = {Troy J. Sewell and Stephen P. Jordan} } @article {2863, title = {Proposal for gravitational direct detection of dark matter}, journal = {Physical Review D}, volume = {102}, year = {2021}, month = {8/23/2021}, abstract = {

The only coupling dark matter is guaranteed to have with the standard model is through gravity. Here we propose a concept for direct dark matter detection using only this gravitational coupling. We suggest that an array of quantum-limited mechanical impulse sensors may be capable of detecting the correlated gravitational force created by a passing dark matter particle. We consider the effects of irreducible noise from couplings of the sensors to the environment and noise due to the quantum measurement process. We show that the signal from Planck-scale dark matter is in principle detectable using a large number of gram-scale sensors in a meter-scale array with sufficiently low quantum noise, and discuss some experimental challenges en route to achieving this target.

}, issn = {2470-0029}, doi = {https://doi.org/10.1103/PhysRevD.102.072003}, url = {https://arxiv.org/abs/1903.00492}, author = {Carney, Daniel and Ghosh, Sohitri and Krnjaic, Gordan and Taylor, Jacob M.} } @article {2816, title = {Protocols for estimating multiple functions with quantum sensor networks: Geometry and performance}, journal = {Physical Review Research}, volume = {3}, year = {2021}, month = {5/3/2021}, abstract = {

We consider the problem of estimating multiple analytic functions of a set of local parameters via qubit sensors in a quantum sensor network. To address this problem, we highlight a generalization of the sensor symmetric performance bounds of Rubio et. al. [J. Phys. A: Math. Theor. 53 344001 (2020)] and develop a new optimized sequential protocol for measuring such functions. We compare the performance of both approaches to one another and to local protocols that do not utilize quantum entanglement, emphasizing the geometric significance of the coefficient vectors of the measured functions in determining the best choice of measurement protocol. We show that, in many cases, especially for a large number of sensors, the optimized sequential protocol results in more accurate measurements than the other strategies. In addition, in contrast to the the sensor symmetric approach, the sequential protocol is known to always be explicitly implementable. The sequential protocol is very general and has a wide range of metrological applications.

}, issn = {2643-1564}, doi = {10.1103/physrevresearch.3.033011}, url = {https://arxiv.org/abs/2104.09540}, author = {Jacob Bringewatt and Boettcher, Igor and Niroula, Pradeep and Bienias, Przemyslaw and Alexey V. Gorshkov} } @article {2729, title = {Proving Quantum Programs Correct}, journal = {Schloss Dagstuhl}, year = {2021}, month = {7/13/2021}, abstract = {

As quantum computing steadily progresses from theory to practice, programmers are faced with a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of mechanized proof to the domain of quantum programming in the context of the SQIR development. It verifies the correctness of a range of a quantum algorithms including Simon\&$\#$39;s algorithm, Grover\&$\#$39;s algorithm, and quantum phase estimation, a key component of Shor\&$\#$39;s algorithm. In doing so, it aims to highlight both the successes and challenges of formal verification in the quantum context and motivate the theorem proving community to target quantum computing as an application domain.

}, doi = {https://doi.org/10.4230/LIPIcs.ITP.2021.21}, url = {https://arxiv.org/abs/2010.01240}, author = {Kesha Hietala and Robert Rand and Shih-Han Hung and Liyi Li and Michael Hicks} } @article {2942, title = {Proving Quantum Programs Correct}, journal = {12th International Conference on Interactive Theorem Proving (ITP 2021)}, volume = {193}, year = {2021}, month = {06/2021}, pages = {21:1{\textendash}21:19}, abstract = {

As quantum computing progresses steadily from theory into practice, programmers will face
a common problem: How can they be sure that their code does what they intend it to do? This
paper presents encouraging results in the application of mechanized proof to the domain of quantum
programming in the context of the sqir development. It verifies the correctness of a range of a
quantum algorithms including Grover\’s algorithm and quantum phase estimation, a key component
of Shor\’s algorithm. In doing so, it aims to highlight both the successes and challenges of formal
verification in the quantum context and motivate the theorem proving community to target quantum
computing as an application domain.

}, isbn = {978-3-95977-188-7}, issn = {1868-8969}, doi = {10.4230/LIPIcs.ITP.2021.21}, url = {https://drops.dagstuhl.de/opus/volltexte/2021/13916}, author = {Hietala, Kesha and Rand, Robert and Hung, Shih-Han and Li, Liyi and Hicks, Michael}, editor = {Cohen, Liron and Kaliszyk, Cezary} } @article {2645, title = {Quantum Algorithms for Escaping from Saddle Points}, journal = {Quantum}, volume = {5}, year = {2021}, month = {8/19/2021}, abstract = {

We initiate the study of quantum algorithms for escaping from saddle points with provable guarantee. Given a function f:Rn\→R, our quantum algorithm outputs an ϵ-approximate second-order stationary point using O~(log2n/ϵ1.75) queries to the quantum evaluation oracle (i.e., the zeroth-order oracle). Compared to the classical state-of-the-art algorithm by Jin et al. with O~(log6n/ϵ1.75) queries to the gradient oracle (i.e., the first-order oracle), our quantum algorithm is polynomially better in terms of n and matches its complexity in terms of 1/ϵ. Our quantum algorithm is built upon two techniques: First, we replace the classical perturbations in gradient descent methods by simulating quantum wave equations, which constitutes the polynomial speedup in n for escaping from saddle points. Second, we show how to use a quantum gradient computation algorithm due to Jordan to replace the classical gradient queries by quantum evaluation queries with the same complexity. Finally, we also perform numerical experiments that support our quantum speedup.

}, doi = {https://doi.org/10.22331/q-2021-08-20-529}, url = {https://arxiv.org/abs/2007.10253}, author = {Chenyi Zhang and Jiaqi Leng and Tongyang Li} } @article {3022, title = {Quantum Algorithms for Reinforcement Learning with a Generative Model}, journal = {Proceedings of the 38th International Conference on Machine Learning, PMLR}, volume = {139}, year = {2021}, month = {12/15/2021}, chapter = {10916-10926}, abstract = {

Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an optimal policy for a γ-discounted Markov decision process (MDP). For such an MDP, we design quantum algorithms that approximate an optimal policy (π\∗), the optimal value function (v\∗), and the optimal Q-function (q\∗), assuming the algorithms can access samples from the environment in quantum superposition. This assumption is justified whenever there exists a simulator for the environment; for example, if the environment is a video game or some other program. Our quantum algorithms, inspired by value iteration, achieve quadratic speedups over the best-possible classical sample complexities in the approximation accuracy (ϵ) and two main parameters of the MDP: the effective time horizon (11\−γ) and the size of the action space (A). Moreover, we show that our quantum algorithm for computing q\∗ is optimal by proving a matching quantum lower bound.

}, keywords = {FOS: Computer and information sciences, FOS: Physical sciences, Machine Learning (cs.LG), Quantum Physics (quant-ph)}, doi = {10.48550/ARXIV.2112.08451}, url = {https://arxiv.org/abs/2112.08451}, author = {Daochen Wang and Sundaram, Aarthi and Kothari, Robin and Kapoor, Ashish and Roetteler, Martin} } @article {2917, title = {Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware}, journal = {Physical Review A}, volume = {104}, year = {2021}, month = {12/8/2021}, abstract = {

Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks (DTQWs) and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves to the multiqubit states of a quantum processor, we present different configurations of quantum circuits for the implementation of DTQWs in one-dimensional position space. We provide example circuits for a five-qubit processor and address scalability to higher dimensions as well as larger quantum processors.

}, issn = {2469-9934}, doi = {https://doi.org/10.1103/PhysRevA.104.062401}, url = {https://arxiv.org/abs/2001.11197}, author = {Singh, Shivani and Alderete, C. Huerta and Balu, Radhakrishnan and Monroe, Christopher and Linke, Norbert M. and Chandrashekar, C. M.} } @article {2773, title = {Quantum Computational Supremacy via High-Dimensional Gaussian Boson Sampling}, year = {2021}, month = {2/24/2021}, abstract = {

Photonics is a promising platform for demonstrating quantum computational supremacy (QCS) by convincingly outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing photonics proposals and demonstrations face significant hurdles. Experimentally, current implementations of Gaussian boson sampling lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make significant progress in improving both the theoretical evidence and experimental prospects. On the theory side, we provide strong evidence for the hardness of Gaussian boson sampling, placing it on par with the strongest theoretical proposals for QCS. On the experimental side, we propose a new QCS architecture, high-dimensional Gaussian boson sampling, which is programmable and can be implemented with low loss rates using few optical components. We show that particular classical algorithms for simulating GBS are vastly outperformed by high-dimensional Gaussian boson sampling experiments at modest system sizes. This work thus opens the path to demonstrating QCS with programmable photonic processors.

}, url = {https://arxiv.org/abs/2102.12474}, author = {Abhinav Deshpande and Arthur Mehta and Trevor Vincent and Nicolas Quesada and Marcel Hinsche and Marios Ioannou and Lars Madsen and Jonathan Lavoie and Haoyu Qi and Jens Eisert and Dominik Hangleiter and Bill Fefferman and Ish Dhand} } @article {2633, title = {Quantum exploration algorithms for multi-armed bandits}, journal = {Proceedings of the 35th Conference on Artificial Intelligence (AAAI 2021)}, volume = {35}, year = {2021}, month = {2021}, pages = {10102-10110}, abstract = {

\ Identifying the best arm of a multi-armed bandit is a central problem in bandit optimization. We study a quantum computational version of this problem with coherent oracle access to states encoding the reward probabilities of each arm as quantum amplitudes. Specifically, we show that we can find the best arm with fixed confidence using O~(\∑ni=2Δ\−2i\−\−\−\−\−\−\−\−\√) quantum queries, where Δi represents the difference between the mean reward of the best arm and the ith-best arm. This algorithm, based on variable-time amplitude amplification and estimation, gives a quadratic speedup compared to the best possible classical result. We also prove a matching quantum lower bound (up to poly-logarithmic factors).

}, url = {https://ojs.aaai.org/index.php/AAAI/article/view/17212}, author = {Daochen Wang and Xuchen You and Tongyang Li and Andrew M. Childs} } @article {2885, title = {Quantum Lattice Sieving}, year = {2021}, month = {10/26/2021}, abstract = {

Lattices are very important objects in the effort to construct cryptographic primitives that are secure against quantum attacks. A central problem in the study of lattices is that of finding the shortest non-zero vector in the lattice. Asymptotically, sieving is the best known technique for solving the shortest vector problem, however, sieving requires memory exponential in the dimension of the lattice. As a consequence, enumeration algorithms are often used in place of sieving due to their linear memory complexity, despite their super-exponential runtime. In this work, we present a heuristic quantum sieving algorithm that has memory complexity polynomial in the size of the length of the sampled vectors at the initial step of the sieve. In other words, unlike most sieving algorithms, the memory complexity of our algorithm does not depend on the number of sampled vectors at the initial step of the sieve.

}, url = {https://arxiv.org/abs/2110.13352}, author = {Nishant Rodrigues and Brad Lackey} } @article {2875, title = {Quantum Machine Learning for Finance}, year = {2021}, month = {9/9/2021}, abstract = {

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade, and achieve disruptive impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from Quantum Computing not only in the medium and long terms, but even in the short term. This review paper presents the state of the art of quantum algorithms for financial applications, with particular focus to those use cases that can be solved via Machine Learning.

}, url = {https://arxiv.org/abs/2109.04298}, author = {Marco Pistoia and Syed Farhan Ahmad and Akshay Ajagekar and Alexander Buts and Shouvanik Chakrabarti and Dylan Herman and Shaohan Hu and Andrew Jena and Pierre Minssen and Pradeep Niroula and Arthur Rattew and Yue Sun and Romina Yalovetzky} } @article {2826, title = {Quantum Meets the Minimum Circuit Size Problem}, year = {2021}, month = {8/6/2021}, abstract = {

In this work, we initiate the study of the Minimum Circuit Size Problem (MCSP) in the quantum setting. MCSP is a problem to compute the circuit complexity of Boolean functions. It is a fascinating problem in complexity theory---its hardness is mysterious, and a better understanding of its hardness can have surprising implications to many fields in computer science.
We first define and investigate the basic complexity-theoretic properties of minimum quantum circuit size problems for three natural objects: Boolean functions, unitaries, and quantum states. We show that these problems are not trivially in NP but in QCMA (or have QCMA protocols). Next, we explore the relations between the three quantum MCSPs and their variants. We discover that some reductions that are not known for classical MCSP exist for quantum MCSPs for unitaries and states, e.g., search-to-decision reduction and self-reduction. Finally, we systematically generalize results known for classical MCSP to the quantum setting (including quantum cryptography, quantum learning theory, quantum circuit lower bounds, and quantum fine-grained complexity) and also find new connections to tomography and quantum gravity. Due to the fundamental differences between classical and quantum circuits, most of our results require extra care and reveal properties and phenomena unique to the quantum setting. Our findings could be of interest for future studies, and we post several open problems for further exploration along this direction.

}, url = {https://arxiv.org/abs/2108.03171}, author = {Nai-Hui Chia and Chi-Ning Chou and Jiayu Zhang and Ruizhe Zhang} } @article {2886, title = {Quantum query complexity with matrix-vector products}, journal = {Proceedings of the 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021), Leibniz International Proceedings in Informatics}, volume = {198}, year = {2021}, month = {3/14/2021}, pages = {55:1-55:19}, abstract = {

We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear system that it specifies, quantum computers do not provide an asymptotic speedup over classical computation. On the other hand, we show that for some problems, such as computing the parities of rows or columns or deciding if there are two identical rows or columns, quantum computers provide exponential speedup. We demonstrate this by showing equivalence between models that provide matrix-vector products, vector-matrix products, and vector-matrix-vector products, whereas the power of these models can vary significantly for classical computation.

}, doi = {https://arxiv.org/ct?url=https\%3A\%2F\%2Fdx.doi.org\%2F10.4230\%2FLIPIcs.ICALP.2021.55\&v=2de93347}, url = {https://arxiv.org/abs/2102.11349}, author = {Andrew M. Childs and Shih-Han Hung and Tongyang Li} } @article {2878, title = {Quantum Query Complexity with Matrix-Vector Products}, journal = {48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)}, year = {2021}, month = {2/7/2021}, publisher = {Schloss Dagstuhl {\textendash} Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, abstract = {

We study quantum algorithms that learn properties of a matrix using queries that return its action on an input vector. We show that for various problems, including computing the trace, determinant, or rank of a matrix or solving a linear system that it specifies, quantum computers do not provide an asymptotic speedup over classical computation. On the other hand, we show that for some problems, such as computing the parities of rows or columns or deciding if there are two identical rows or columns, quantum computers provide exponential speedup. We demonstrate this by showing equivalence between models that provide matrix-vector products, vector-matrix products, and vector-matrix-vector products, whereas the power of these models can vary significantly for classical computation.

}, isbn = {978-3-95977-195-5}, doi = {10.4230/LIPIcs.ICALP.2021.55}, url = {https://drops.dagstuhl.de/opus/volltexte/2021/14124}, author = {Andrew M. Childs and Hung, Shih-Han and Li, Tongyang} } @article {2751, title = {Quantum routing with fast reversals}, journal = {Quantum}, volume = {5}, year = {2021}, month = {8/24/2021}, chapter = {533}, abstract = {

We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length n, we show that there exists a constant ϵ\≈0.034 such that the quantum routing time is at most (1\−ϵ)n, whereas any swap-based protocol needs at least time n\−1. This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. Furthermore, we show that our algorithm approaches a quantum routing time of 2n/3 in expectation for uniformly random permutations, whereas swap-based protocols require time n asymptotically. Additionally, we consider sparse permutations that route k\≤n qubits and give algorithms with quantum routing time at most n/3+O(k2) on paths and at most 2r/3+O(k2) on general graphs with radius r.

}, doi = {https://doi.org/10.22331/q-2021-08-31-533}, url = {https://arxiv.org/abs/2103.03264}, author = {Aniruddha Bapat and Andrew M. Childs and Alexey V. Gorshkov and Samuel King and Eddie Schoute and Hrishee Shastri} } @article {2874, title = {Quantum Simulation with Hybrid Tensor Networks}, journal = {Physical Review Letters}, volume = {127}, year = {2021}, month = {8/31/2021}, abstract = {

Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors, inheriting both their distinct features in efficient representation of many-body wave functions. With the example of hybrid tree tensor networks, we demonstrate efficient quantum simulation using a quantum computer whose size is significantly smaller than the one of the target system. We numerically benchmark our method for finding the ground state of 1D and 2D spin systems of up to 8\×8 and 9\×8 qubits with operations only acting on 8+1 and 9+1 qubits,~respectively. Our approach sheds light on simulation of large practical problems with intermediate-scale quantum computers, with potential applications in chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.

}, issn = {1079-7114}, doi = {10.1103/physrevlett.127.040501}, url = {http://dx.doi.org/10.1103/PhysRevLett.127.040501}, author = {Yuan, Xiao and Sun, Jinzhao and Liu, Junyu and Zhao, Qi and Zhou, You} } @article {2710, title = {Quantum-accelerated multilevel Monte Carlo methods for stochastic differential equations in mathematical finance}, journal = {Quantum 5, 481 (2021)}, volume = {5}, year = {2021}, month = {6/22/2021}, pages = {481}, abstract = {

Inspired by recent progress in quantum algorithms for ordinary and partial differential equations, we study quantum algorithms for stochastic differential equations (SDEs). Firstly we provide a quantum algorithm that gives a quadratic speed-up for multilevel Monte Carlo methods in a general setting. As applications, we apply it to compute expection values determined by classical solutions of SDEs, with improved dependence on precision. We demonstrate the use of this algorithm in a variety of applications arising in mathematical finance, such as the Black-Scholes and Local Volatility models, and Greeks. We also provide a quantum algorithm based on sublinear binomial sampling for the binomial option pricing model with the same improvement.

}, doi = {https://doi.org/10.22331/q-2021-06-24-481}, url = {https://arxiv.org/abs/2012.06283}, author = {Dong An and Noah Linden and Jin-Peng Liu and Ashley Montanaro and Changpeng Shao and Jiasu Wang} } @article {2671, title = {Quench Dynamics of a Fermi Gas with Strong Long-Range Interactions}, journal = {Phys. Rev. X}, volume = {11}, year = {2021}, month = {5/24/2021}, abstract = {

We induce strong non-local interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing. The system is approximately described by a t\−V model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction. We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime. To probe the interplay of non-local interactions with tunneling, we investigate the short-time relaxation dynamics of charge density waves in the gas. We find that strong nearest-neighbor interactions slow down the relaxation. Our work opens the door for quantum simulations of systems with strong non-local interactions such as extended Fermi-Hubbard models.

}, doi = {https://doi.org/10.1103/PhysRevX.11.021036}, url = {https://arxiv.org/abs/2010.05871}, author = {Elmer Guardado-Sanchez and Benjamin M. Spar and Peter Schauss and Ron Belyansky and Jeremy T. Young and Przemyslaw Bienias and Alexey V. Gorshkov and Thomas Iadecola and Waseem S. Bakr} } @article {2808, title = {Rainbow Scars: From Area to Volume Law}, year = {2021}, month = {7/12/2021}, abstract = {

Quantum many-body scars (QMBS) constitute a new quantum dynamical regime in which rare \"scarred\" eigenstates mediate weak ergodicity breaking. One open question is to understand the most general setting in which these states arise. In this work, we develop a generic construction that embeds a new class of QMBS, rainbow scars, into the spectrum of an arbitrary Hamiltonian. Unlike other examples of QMBS, rainbow scars display extensive bipartite entanglement entropy while retaining a simple entanglement structure. Specifically, the entanglement scaling is volume-law for a random bipartition, while scaling for a fine-tuned bipartition is sub-extensive. When internal symmetries are present, the construction leads to multiple, and even towers of rainbow scars revealed through distinctive non-thermal dynamics. To this end, we provide an experimental road map for realizing rainbow scar states in a Rydberg-atom quantum simulator, leading to coherent oscillations distinct from the strictly sub-volume-law QMBS previously realized in the same system.\ 

}, url = {https://arxiv.org/abs/2107.03416}, author = {Christopher M. Langlett and Zhi-Cheng Yang and Julia Wildeboer and Alexey V. Gorshkov and Thomas Iadecola and Shenglong Xu} } @article {2766, title = {Ray-based framework for state identification in quantum dot devices}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {06/17/2021}, abstract = {

Quantum dots (QDs) defined with electrostatic gates are a leading platform for a scalable quantum computing implementation. However, with increasing numbers of qubits, the complexity of the control parameter space also grows. Traditional measurement techniques, relying on complete or near-complete exploration via two-parameter scans (images) of the device response, quickly become impractical with increasing numbers of gates. Here, we propose to circumvent this challenge by introducing a measurement technique relying on one-dimensional projections of the device response in the multi-dimensional parameter space. Dubbed as the ray-based classification (RBC) framework, we use this machine learning (ML) approach to implement a classifier for QD states, enabling automated recognition of qubit-relevant parameter regimes. We show that RBC surpasses the 82 \% accuracy benchmark from the experimental implementation of image-based classification techniques from prior work while cutting down the number of measurement points needed by up to 70 \%. The reduction in measurement cost is a significant gain for time-intensive QD measurements and is a step forward towards the scalability of these devices. We also discuss how the RBC-based optimizer, which tunes the device to a multi-qubit regime, performs when tuning in the two- and three-dimensional parameter spaces defined by plunger and barrier gates that control the dots. This work provides experimental validation of both efficient state identification and optimization with ML techniques for non-traditional measurements in quantum systems with high-dimensional parameter spaces and time-intensive measurements.

}, doi = {https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.020335}, url = {https://arxiv.org/abs/2102.11784}, author = {Justyna P. Zwolak and Thomas McJunkin and Sandesh S. Kalantre and Samuel F. Neyens and E. R. MacQuarrie and Mark A. Eriksson and J. M. Taylor} } @article {3025, title = {Relaxation of non-integrable systems and correlation functions}, year = {2021}, month = {12/17/2021}, abstract = {

We investigate early-time equilibration rates of observables in closed many-body quantum systems and compare them to those of two correlation functions, first introduced by Kubo and Srednicki. We explore whether these different rates coincide at a universal value that sets the timescales of processes at a finite energy density. We find evidence for this coincidence when the initial conditions are sufficiently generic, or typical. We quantify this with the effective dimension of the state and with a state-observable effective dimension, which estimate the number of energy levels that participate in the dynamics. Our findings are confirmed by proving that these different timescales coincide for dynamics generated by Haar-random Hamiltonians. This also allows to quantitatively understand the scope of previous theoretical results on equilibration timescales and on random matrix formalisms. We approach this problem with exact, full spectrum diagonalization. The numerics are carried out in a non-integrable Heisenberg-like Hamiltonian, and the dynamics are investigated for several pairs of observables and states.

}, keywords = {FOS: Physical sciences, Quantum Physics (quant-ph), Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el)}, doi = {10.48550/ARXIV.2112.09475}, url = {https://arxiv.org/abs/2112.09475}, author = {Riddell, Jonathon and Garc{\'\i}a-Pintos, Luis Pedro and Alhambra, {\'A}lvaro M.} } @article {2921, title = {Resource theory of quantum uncomplexity}, year = {2021}, month = {10/21/2021}, abstract = {

Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state\&$\#$39;s complexity quantifies the number of computational gates required to prepare the state from a simple tensor product. The greater a state\&$\#$39;s distance from maximal complexity, or {\textquoteleft}{\textquoteleft}uncomplexity,\&$\#$39;\&$\#$39; the more useful the state is as input to a quantum computation. Separately, resource theories -- simple models for agents subject to constraints -- are burgeoning in quantum information theory. We unite the two domains, confirming Brown and Susskind\&$\#$39;s conjecture that a resource theory of uncomplexity can be defined. The allowed operations, fuzzy operations, are slightly random implementations of two-qubit gates chosen by an agent. We formalize two operational tasks, uncomplexity extraction and expenditure. Their optimal efficiencies depend on an entropy that we engineer to reflect complexity. We also present two monotones, uncomplexity measures that decline monotonically under fuzzy operations, in certain regimes. This work unleashes on many-body complexity the resource-theory toolkit from quantum information theory.

}, url = {https://arxiv.org/abs/2110.11371}, author = {Nicole Yunger Halpern and Naga B. T. Kothakonda and Jonas Haferkamp and Anthony Munson and Jens Eisert and Philippe Faist} } @article {2569, title = {Resource-Optimized Fermionic Local-Hamiltonian Simulation on Quantum Computer for Quantum Chemistry}, journal = {Quantum}, volume = {5}, year = {2021}, month = {7/21/2021}, abstract = {

The ability to simulate a fermionic system on a quantum computer is expected to revolutionize chemical engineering, materials design, nuclear physics, to name a few. Thus, optimizing the simulation circuits is of significance in harnessing the power of quantum computers. Here, we address this problem in two aspects. In the fault-tolerant regime, we optimize the $\rzgate$ and $\tgate$ gate counts along with the ancilla qubit counts required, assuming the use of a product-formula algorithm for implementation. We obtain a savings ratio of two in the gate counts and a savings ratio of eleven in the number of ancilla qubits required over the state of the art. In the pre-fault tolerant regime, we optimize the two-qubit gate counts, assuming the use of the variational quantum eigensolver (VQE) approach. Specific to the latter, we present a framework that enables bootstrapping the VQE progression towards the convergence of the ground-state energy of the fermionic system. This framework, based on perturbation theory, is capable of improving the energy estimate at each cycle of the VQE progression, by about a factor of three closer to the known ground-state energy compared to the standard VQE approach in the test-bed, classically-accessible system of the water molecule. The improved energy estimate in turn results in a commensurate level of savings of quantum resources, such as the number of qubits and quantum gates, required to be within a pre-specified tolerance from the known ground-state energy. We also explore a suite of generalized transformations of fermion to qubit operators and show that resource-requirement savings of up to more than 20\% is possible.

}, doi = {https://doi.org/10.22331/q-2021-07-26-509}, url = {https://arxiv.org/abs/2004.04151}, author = {Qingfeng Wang and Ming Li and Christopher Monroe and Yunseong Nam} } @article {2818, title = {Robust Self-Testing of Multiparticle Entanglement}, journal = {Phys. Rev. Lett. }, volume = {127}, year = {2021}, month = {12/7/2021}, pages = {230503}, abstract = {

Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Due to the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multi-particle quantum entanglement. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger (GHZ) states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.

}, doi = {https://doi.org/10.1103/PhysRevLett.127.230503}, url = {https://arxiv.org/abs/2105.10298}, author = {Dian Wu and Qi Zhao and Xue-Mei Gu and Han-Sen Zhong and You Zhou and Li-Chao Peng and Jian Qin and Yi-Han Luo and Kai Chen and Li Li and Nai-Le Liu and Chao-Yang Lu and Jian-Wei Pan} } @article {2767, title = {RPPLNS: Pay-per-last-N-shares with a Randomised Twist}, year = {2021}, month = {2/15/2021}, abstract = {

\"Pay-per-last-N-shares\" (PPLNS) is one of the most common payout strategies used by mining pools in Proof-of-Work (PoW) cryptocurrencies. As with any payment scheme, it is imperative to study issues of incentive compatibility of miners within the pool. For PPLNS this question has only been partially answered; we know that reasonably-sized miners within a PPLNS pool prefer following the pool protocol over employing specific deviations. In this paper, we present a novel modification to PPLNS where we randomise the protocol in a natural way. We call our protocol \"Randomised pay-per-last-N-shares\" (RPPLNS), and note that the randomised structure of the protocol greatly simplifies the study of its incentive compatibility. We show that RPPLNS maintains the strengths of PPLNS (i.e., fairness, variance reduction, and resistance to pool hopping), while also being robust against a richer class of strategic mining than what has been shown for PPLNS.

}, url = {https://arxiv.org/abs/2102.07681}, author = {Philip Lazos and Francisco J. Marmolejo-Coss{\'\i}o and Xinyu Zhou and Jonathan Katz} } @article {2761, title = {Singularities in nearly-uniform 1D condensates due to quantum diffusion}, year = {2021}, month = {3/10/2021}, abstract = {

Dissipative systems can often exhibit wavelength-dependent loss rates. One prominent example is Rydberg polaritons formed by electromagnetically-induced transparency, which have long been a leading candidate for studying the physics of interacting photons and also hold promise as a platform for quantum information. In this system, dissipation is in the form of quantum diffusion, i.e., proportional to k2 (k being the wavevector) and vanishing at long wavelengths as k\→0. Here, we show that one-dimensional condensates subject to this type of loss are unstable to long-wavelength density fluctuations in an unusual manner: after a prolonged period in which the condensate appears to relax to a uniform state, local depleted regions quickly form and spread ballistically throughout the system. We connect this behavior to the leading-order equation for the nearly-uniform condensate -- a dispersive analogue to the Kardar-Parisi-Zhang (KPZ) equation -- which develops singularities in finite time. Furthermore, we show that the wavefronts of the depleted regions are described by purely dissipative solitons within a pair of hydrodynamic equations, with no counterpart in lossless condensates. We close by discussing conditions under which such singularities and the resulting solitons can be physically realized.

}, url = {https://arxiv.org/abs/2103.06293}, author = {Christopher L. Baldwin and P. Bienias and Alexey V. Gorshkov and Michael Gullans and M. Maghrebi} } @article {2911, title = {Spin chains, defects, and quantum wires for the quantum-double edge}, year = {2021}, month = {11/23/2021}, abstract = {

Non-Abelian defects that bind Majorana or parafermion zero modes are prominent in several topological quantum computation schemes. Underpinning their established understanding is the quantum Ising spin chain, which can be recast as a fermionic model or viewed as a standalone effective theory for the surface-code edge -- both of which harbor non-Abelian defects. We generalize these notions by deriving an effective Ising-like spin chain describing the edge of quantum-double topological order. Relating Majorana and parafermion modes to anyonic strings, we introduce quantum-double generalizations of non-Abelian defects. We develop a way to embed finite-group valued qunits into those valued in continuous groups. Using this embedding, we provide a continuum description of the spin chain and recast its non-interacting part as a quantum wire via addition of a Wess-Zumino-Novikov-Witten term and non-Abelian bosonization.

}, url = {https://arxiv.org/abs/2111.12096}, author = {Victor V. Albert and David Aasen and Wenqing Xu and Wenjie Ji and Jason Alicea and John Preskill} } @article {2864, title = {Spin-Wave Quantum Computing with Atoms in a Single-Mode Cavity}, year = {2021}, month = {9/30/2021}, abstract = {

We present a method for network-capable quantum computing that relies on holographic spin-wave excitations stored collectively in ensembles of qubits. We construct an orthogonal basis of spin waves in a one-dimensional array and show that high-fidelity universal linear controllability can be achieved using only phase shifts, applied in both momentum and position space. Neither single-site addressability nor high single-qubit cooperativity is required, and the spin waves can be read out with high efficiency into a single cavity mode for quantum computing and networking applications.\ 

}, url = {https://arxiv.org/abs/2109.15252}, author = {Kevin C. Cox and Przemyslaw Bienias and David H. Meyer and Paul D. Kunz and Donald P. Fahey and Alexey V. Gorshkov} } @article {2870, title = {Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains}, year = {2021}, month = {9/27/2021}, abstract = {

We address spin transport in the easy-axis Heisenberg spin chain subject to integrability-breaking perturbations. We find that spin transport is subdiffusive with dynamical exponent z=4 up to a timescale that is parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for large finite anisotropy, one eventually recovers diffusion at late times, but with a diffusion constant independent of the strength of the integrability breaking perturbation. We provide numerical evidence for these findings, and explain them by adapting the generalized hydrodynamics framework to nearly integrable dynamics. Our results show that the diffusion constant of near-integrable interacting spin chains is not generically a continuous function of the integrability-breaking parameter.\ 

}, url = {https://arxiv.org/abs/2109.13251}, author = {Jacopo De Nardis and Sarang Gopalakrishnan and Romain Vasseur and Brayden Ware} } @article {2933, title = {Surface code compilation via edge-disjoint paths}, year = {2021}, month = {10/21/2021}, abstract = {

We provide an efficient algorithm to compile quantum circuits for fault-tolerant execution. We target surface codes, which form a 2D grid of logical qubits with nearest-neighbor logical operations. Embedding an input circuit\&$\#$39;s qubits in surface codes can result in long-range two-qubit operations across the grid. We show how to prepare many long-range Bell pairs on qubits connected by edge-disjoint paths of ancillas in constant depth which can be used to perform these long-range operations. This forms one core part of our Edge-Disjoint Paths Compilation (EDPC) algorithm, by easily performing parallel long-range Clifford operations in constant depth. It also allows us to establish a connection between surface code compilation and several well-studied edge-disjoint paths problems. Similar techniques allow us to perform non-Clifford single-qubit rotations far from magic state distillation factories. In this case, we can easily find the maximum set of paths by a max-flow reduction, which forms the other major part of our EDPC algorithm. We compare EDPC to other compilation approaches including a SWAP-based algorithm, and find significantly improved performance for circuits built from parallel CNOTs, and for circuits which implement the multi-controlled X gate.

}, url = {https://arxiv.org/abs/2110.11493}, author = {Michael Beverland and Vadym Kliuchnikov and Eddie Schoute} } @article {2879, title = {Synchronous Values of Games}, year = {2021}, month = {9/29/2021}, abstract = {

We study synchronous values of games, especially synchronous games. It is known that a synchronous game has a perfect strategy if and only if it has a perfect synchronous strategy. However, we give examples of synchronous games, in particular graph colouring games, with synchronous value that is strictly smaller than their ordinary value. Thus, the optimal strategy for a synchronous game need not be synchronous. We derive a formula for the synchronous value of an XOR game as an optimization problem over a spectrahedron involving a matrix related to the cost matrix. We give an example of a game such that the synchronous value of repeated products of the game is strictly increasing. We show that the synchronous quantum bias of the XOR of two XOR games is not multiplicative. Finally, we derive geometric and algebraic conditions that a set of projections that yields the synchronous value of a game must satisfy.

}, url = {https://arxiv.org/abs/2109.14741}, author = {J. William Helton and Hamoon Mousavi and Seyed Sajjad Nezhadi and Vern I. Paulsen and Travis B. Russell} } @article {2774, title = {Testing quantum gravity with interactive information sensing}, year = {2021}, month = {1/27/2021}, abstract = {

We suggest a test of a central prediction of perturbatively quantized general relativity: the coherent communication of quantum information between massive objects through gravity. To do this, we introduce the concept of interactive quantum information sensing, a protocol tailored to the verification of dynamical entanglement generation between a pair of systems. Concretely, we propose to monitor the periodic wavefunction collapse and revival in an atomic interferometer which is gravitationally coupled to a mechanical oscillator. We prove a theorem which shows that, under the assumption of time-translation invariance, this collapse and revival is possible if and only if the gravitational interaction forms an entangling channel. Remarkably, as this approach improves at moderate temperatures and relies primarily upon atomic coherence, our numerical estimates indicate feasibility with current devices.

}, url = {https://arxiv.org/abs/2101.11629}, author = {Daniel Carney and Holger M{\"u}ller and Jacob M. Taylor} } @article {2506, title = {Theory of Trotter Error with Commutator Scaling}, journal = {Phys. Rev. X}, volume = {11}, year = {2021}, month = {2/1/2021}, pages = {49}, chapter = {011020}, abstract = {

The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of prior approaches based on truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, including simulations of second-quantized plane-wave electronic structure, k-local Hamiltonians, rapidly decaying power-law interactions, clustered Hamiltonians, the transverse field Ising model, and quantum ferromagnets, nearly matching or even outperforming the best previous results. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound as a byproduct. Our analysis reproduces known tight bounds for first- and second-order formulas. Our higher-order bound overestimates the complexity of simulating a one-dimensional Heisenberg model with an even-odd ordering of terms by only a factor of 5, and is close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both asymptotic scaling and constant prefactor.

}, doi = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.011020}, url = {https://arxiv.org/abs/1912.08854}, author = {Andrew M. Childs and Yuan Su and Minh C. Tran and Nathan Wiebe and Shuchen Zhu} } @article {2731, title = {A Threshold for Quantum Advantage in Derivative Pricing}, journal = {Quantum}, volume = {5}, year = {2021}, pages = {463}, abstract = {

We give an upper bound on the resources required for valuable quantum advantage in pricing derivatives. To do so, we give the first complete resource estimates for useful quantum derivative pricing, using autocallable and Target Accrual Redemption Forward (TARF) derivatives as benchmark use cases. We uncover blocking challenges in known approaches and introduce a new method for quantum derivative pricing - the re-parameterization method - that avoids them. This method combines pre-trained variational circuits with fault-tolerant quantum computing to dramatically reduce resource requirements. We find that the benchmark use cases we examine require 7.5k logical qubits and a T-depth of 46 million and thus estimate that quantum advantage would require a logical clock speed of 10Mhz. While the resource requirements given here are out of reach of current systems, we hope they will provide a roadmap for further improvements in algorithms, implementations, and planned hardware architectures.\ 

}, doi = {https://doi.org/10.22331/q-2021-06-01-463}, url = {https://arxiv.org/abs/2012.03819}, author = {Shouvanik Chakrabarti and Rajiv Krishnakumar and Guglielmo Mazzola and Nikitas Stamatopoulos and Stefan Woerner and William J. Zeng} } @article {2909, title = {Tight bounds on the convergence of noisy random circuits to uniform}, year = {2021}, month = {12/1/2021}, abstract = {

We study the properties of output distributions of noisy, random circuits. We obtain upper and lower bounds on the expected distance of the output distribution from the uniform distribution. These bounds are tight with respect to the dependence on circuit depth. Our proof techniques also allow us to make statements about the presence or absence of anticoncentration for both noisy and noiseless circuits. We uncover a number of interesting consequences for hardness proofs of sampling schemes that aim to show a quantum computational advantage over classical computation. Specifically, we discuss recent barrier results for depth-agnostic and/or noise-agnostic proof techniques. We show that in certain depth regimes, noise-agnostic proof techniques might still work in order to prove an often-conjectured claim in the literature on quantum computational advantage, contrary to what was thought prior to this work.\ 

}, url = {https://arxiv.org/abs/2112.00716}, author = {Abhinav Deshpande and Bill Fefferman and Alexey V. Gorshkov and Michael Gullans and Pradeep Niroula and Oles Shtanko} } @article {2414, title = {Torus Spectroscopy of the Gross-Neveu-Yukawa Quantum Field Theory: Free Dirac versus Chiral Ising Fixed Point}, journal = {Phys. Rev. B}, volume = {103}, year = {2021}, month = {3/15/2021}, pages = {125128}, abstract = {

We establish the universal torus low-energy spectra at the free Dirac fixed point and at the strongly coupled chiral Ising fixed point and their subtle crossover behaviour in the Gross-Neuveu-Yukawa field theory with nD=4 component Dirac spinors in D=(2+1) dimensions. These fixed points and the field theories are directly relevant for the long-wavelength physics of certain interacting Dirac systems, such as repulsive spinless fermions on the honeycomb lattice or π-flux square lattice. The torus energy spectrum has been shown previously to serve as a characteristic fingerprint of relativistic fixed points and is a powerful tool to discriminate quantum critical behaviour in numerical simulations. Here, we use a combination of exact diagonalization and quantum Monte Carlo simulations of strongly interacting fermionic lattice models, to compute the critical torus energy spectrum on finite-size clusters with periodic boundaries and extrapolate them to the thermodynamic limit. Additionally, we compute the torus energy spectrum analytically using the perturbative expansion in ε=4\−D, which is in good agreement with the numerical results, thereby validating the presence of the chiral Ising fixed point in the lattice models at hand. We show that the strong interaction between the spinor field and the scalar order-parameter field strongly influences the critical torus energy spectrum and we observe prominent multiplicity features related to an emergent symmetry predicted from the quantum field theory. Building on these results we are able to address the subtle crossover physics of the low-energy spectrum flowing from the chiral Ising fixed point to the Dirac fixed point, and analyze earlier flawed attempts to extract Fermi velocity renormalizations from the low-energy spectrum.

}, doi = {https://doi.org/10.1103/PhysRevB.103.125128}, url = {https://arxiv.org/abs/1907.05373}, author = {Michael Schuler and Stephan Hesselmann and Seth Whitsitt and Thomas C. Lang and Stefan Wessel and Andreas M. L{\"a}uchli} } @article {2775, title = {Trading Locality for Time: Certifiable Randomness from Low-Depth Circuits}, journal = {Communications in Mathematical Physics}, volume = {382}, year = {2021}, month = {2/9/2021}, pages = {49 - 86}, abstract = {

The generation of certifiable randomness is the most fundamental informationtheoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion using a\ single quantum device. The protocol calls for the device to implement a simple quantum circuit of constant depth on a 2D lattice of qubits. The output of the circuit can be\ verified classically in linear time, and is guaranteed to contain a polynomial number of\ certified random bits assuming that the device used to generate the output operated using\ a (classical or quantum) circuit of sub-logarithmic depth. This assumption contrasts with\ the locality assumption used for randomness certification based on Bell inequality violation and more recent proposals for randomness certification based on computational\ assumptions. Furthermore, to demonstrate randomness generation it is sufficient for a\ device to sample from the ideal output distribution within constant statistical distance.\ \ Our procedure is inspired by recent work of Bravyi et al. (Science 362(6412):308\–311,\ 2018), who introduced a relational problem that can be solved by a constant-depth quantum circuit, but provably cannot be solved by any classical circuit of sub-logarithmic\ depth. We develop the discovery of Bravyi et al. into a framework for robust randomness\ expansion. Our results lead to a new proposal for a demonstrated quantum advantage\ that has some advantages compared to existing proposals. First, our proposal does not\ rest on any complexity-theoretic conjectures, but relies on the physical assumption that\ the adversarial device being tested implements a circuit of sub-logarithmic depth. Second, success on our task can be easily verified in classical linear time. Finally, our task\ is more noise-tolerant than most other existing proposals that can only tolerate multiplicative error, or require additional conjectures from complexity theory; in contrast, we\ are able to allow a small constant additive error in total variation distance between the\ sampled and ideal distributions.

}, issn = {0010-3616}, doi = {10.1007/s00220-021-03963-w}, url = {https://link.springer.com/content/pdf/10.1007/s00220-021-03963-w.pdf}, author = {Matthew Coudron and Stark, Jalex and Vidick, Thomas} } @article {2764, title = {Trapped electrons and ions as particle detectors}, journal = {Phys. Rev. Lett.}, volume = {127}, year = {2021}, month = {8/5/2021}, abstract = {

Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that these systems can also be used as highly sensitive detectors of passing charged particles, due to the combination of their extreme charge-to-mass ratio and low-noise quantum readout and control. In particular, these systems can be used to detect energy depositions many orders of magnitude below typical ionization scales. As an illustration, we show that current devices can be used to provide competitive sensitivity to models where ambient dark matter particles carry small electric millicharges <}, doi = {https://doi.org/10.1103/PhysRevLett.127.061804}, url = {https://arxiv.org/abs/2104.05737}, author = {Daniel Carney and Hartmut H{\"a}ffner and David C. Moore and J. M. Taylor} } @article {2682, title = {Tunable three-body loss in a nonlinear Rydberg medium}, journal = {Phys. Rev. Lett., in press }, year = {2021}, month = {9/28/2020}, abstract = {

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential to generate novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study a three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wavefunction and analytical estimates based on Fermi\&$\#$39;s Golden Rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

}, url = {https://arxiv.org/abs/2009.13599}, author = {Dalia P. Ornelas Huerta and Przemyslaw Bienias and Alexander N. Craddock and Michael Gullans and Andrew J. Hachtel and Marcin Kalinowski and Mary E. Lyon and Alexey V. Gorshkov and Steven L. Rolston and J. V. Porto} } @article {2450, title = {Ultralight dark matter detection with mechanical quantum sensors}, journal = {New Journal of Physics}, volume = {23}, year = {2021}, month = {3/10/2021}, pages = {023041}, abstract = {

We consider the use of quantum-limited mechanical force sensors to detect ultralight (sub-meV) dark matter candidates which are weakly coupled to the standard model. We show that mechanical sensors with masses around or below the milligram scale, operating around the standard quantum limit, would enable novel searches for dark matter with natural frequencies around the kHz scale. This would complement existing strategies based on torsion balances, atom interferometers, and atomic clock systems

}, issn = {1367-2630}, doi = {https://doi.org/10.1088/1367-2630/abd9e7}, url = {https://arxiv.org/abs/1908.04797}, author = {Daniel Carney and Anson Hook and Zhen Liu and J. M. Taylor and Yue Zhao} } @article {2866, title = {Unifying Quantum and Classical Speed Limits on Observables}, year = {2021}, month = {8/9/2021}, abstract = {

The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit divides into Mandalestam and Tamm\&$\#$39;s original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, generalizing both to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds to the speed of evolution. We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits, and that a preferred basis of \emph{speed operators} serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable.

}, url = {https://arxiv.org/abs/2108.04261}, author = {Luis Pedro Garc{\'\i}a-Pintos and Schuyler Nicholson and Jason R. Green and Adolfo del Campo and Alexey V. Gorshkov} } @article {2862, title = {Using an Atom Interferometer to Infer Gravitational Entanglement Generation}, journal = {PRX Quantum}, volume = {2}, year = {2021}, month = {8/20/2021}, abstract = {

If gravitational perturbations are quantized into gravitons in analogy with the electromagnetic field and photons, the resulting graviton interactions should lead to an entangling interaction between massive objects. We suggest a test of this prediction. To do this, we introduce the concept of interactive quantum information sensing. This novel sensing protocol is tailored to provable verification of weak dynamical entanglement generation between a pair of systems. We show that this protocol is highly robust to typical thermal noise sources. The sensitivity can moreover be increased both using an initial thermal state and/or an initial phase of entangling via a non-gravitational interaction. We outline a concrete implementation testing the ability of the gravitational field to generate entanglement between an atomic interferometer and mechanical oscillator. Preliminary numerical estimates suggest that near-term devices could feasibly be used to perform the experiment.

}, issn = {2691-3399}, doi = {10.1103/prxquantum.2.030330}, url = {http://dx.doi.org/10.1103/PRXQuantum.2.030330}, author = {Carney, Daniel and M{\"u}ller, Holger and Taylor, Jacob M.} } @article {2912, title = {Verified Compilation of Quantum Oracles}, year = {2021}, month = {12/13/2021}, abstract = {

Quantum algorithms often apply classical operations, such as arithmetic or predicate checks, over a quantum superposition of classical data; these so-called oracles are often the largest components of a quantum algorithm. To ease the construction of efficient, correct oracle functions, this paper presents VQO, a high-assurance framework implemented with the Coq proof assistant. The core of VQO is OQASM, the oracle quantum assembly language. OQASM operations move qubits among three different bases via the Quantum Fourier Transform and Hadamard operations, thus admitting important optimizations, but without inducing entanglement and the exponential blowup that comes with it. OQASM\&$\#$39;s design enabled us to prove correct VQO\&$\#$39;s compilers -- from a simple imperative language called OQIMP to OQASM, and from OQASM to SQIR, a general-purpose quantum assembly language -- and allowed us to efficiently test properties of OQASM programs using the QuickChick property-based testing framework. We have used VQO to implement oracles used in Shor\&$\#$39;s and Grover\&$\#$39;s algorithms, as well as several common arithmetic operators. VQO\&$\#$39;s oracles have performance comparable to those produced by Quipper, a state-of-the-art but unverified quantum programming platform.

}, url = {https://arxiv.org/abs/2112.06700}, author = {Liyi Li and Finnegan Voichick and Kesha Hietala and Yuxiang Peng and Xiaodi Wu and Michael Hicks} } @article {2491, title = {A Verified Optimizer for Quantum Circuits}, journal = {Proceedings of the ACM on Programming Languages}, volume = {5}, year = {2021}, month = {11/12/2020}, abstract = {

We present VOQC, the first fully verified compiler for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, which is deeply embedded in Coq. Optimizations and other transformations are expressed as Coq functions, which are proved correct with respect to a semantics of SQIR programs. We evaluate VOQC\&$\#$39;s verified optimizations on a series of benchmarks, and it performs comparably to industrial-strength compilers. VOQC\&$\#$39;s optimizations reduce total gate counts on average by 17.7\% on a benchmark of 29 circuit programs compared to a 10.7\% reduction when using IBM\&$\#$39;s Qiskit compiler.

}, doi = {https://doi.org/10.1145/3434318}, url = {https://arxiv.org/abs/1912.02250}, author = {Kesha Hietala and Robert Rand and Shih-Han Hung and Xiaodi Wu and Michael Hicks} } @article {2299, title = {Accessing scrambling using matrix product operators}, journal = {Nature Physics }, volume = {16}, year = {2020}, month = {2/2020}, pages = {199-204}, abstract = {

Scrambling, a process in which quantum information spreads over a complex quantum system becoming inaccessible to simple probes, happens in generic chaotic quantum many-body systems, ranging from spin chains, to metals, even to black holes. Scrambling can be measured using out-of-time-ordered correlators (OTOCs), which are closely tied to the growth of Heisenberg operators. In this work, we present a general method to calculate OTOCs of local operators in local one-dimensional systems based on approximating Heisenberg operators as matrix-product operators (MPOs). Contrary to the common belief that such tensor network methods work only at early times, we show that the entire early growth region of the OTOC can be captured using an MPO approximation with modest bond dimension. We analytically establish the goodness of the approximation by showing that if an appropriate OTOC is close to its initial value, then the associated Heisenberg operator has low entanglement across a given cut. We use the method to study scrambling in a chaotic spin chain with 201 sites. Based on this data and OTOC results for black holes, local random circuit models, and non-interacting systems, we conjecture a universal form for the dynamics of the OTOC near the wavefront. We show that this form collapses the chaotic spin chain data over more than fifteen orders of magnitude.

}, doi = {https://doi.org/10.1038/s41567-019-0712-4}, url = {https://arxiv.org/abs/1802.00801}, author = {Shenglong Xu and Brian Swingle} } @article {2694, title = {Approximate optimization of MAXCUT with a local spin algorithm}, year = {2020}, month = {8/13/2020}, abstract = {

Local tensor methods are a class of optimization algorithms that was introduced in [Hastings,arXiv:1905.07047v2][1] as a classical analogue of the quantum approximate optimization algorithm (QAOA). These algorithms treat the cost function as a Hamiltonian on spin degrees of freedom and simulate the relaxation of the system to a low energy configuration using local update rules on the spins. Whereas the emphasis in [1] was on theoretical worst-case analysis, we here investigate performance in practice through benchmarking experiments on instances of the MAXCUT problem.Through heuristic arguments we propose formulas for choosing the hyperparameters of the algorithm which are found to be in good agreement with the optimal choices determined from experiment. We observe that the local tensor method is closely related to gradient descent on a relaxation of maxcut to continuous variables, but consistently outperforms gradient descent in all instances tested. We find time to solution achieved by the local tensor method is highly uncorrelated with that achieved by a widely used commercial optimization package; on some MAXCUT instances the local tensor method beats the commercial solver in time to solution by up to two orders of magnitude and vice-versa. Finally, we argue that the local tensor method closely follows discretized, imaginary-time dynamics of the system under the problem Hamiltonian.

}, url = {https://arxiv.org/abs/2008.06054}, author = {Aniruddha Bapat and Stephen P. Jordan} } @article {2154, title = {Approximate Quantum Fourier Transform with O(nlog(n)) T gates}, journal = {npj Quantum Information }, volume = {6}, year = {2020}, month = {3/13/2020}, abstract = {

The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer enables the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete logarithm over Abelian groups, and phase estimation. The standard fault-tolerant implementation of an n-qubit QFT approximates the desired transformation by removing small-angle controlled rotations and synthesizing the remaining ones into Clifford+t gates, incurring the t-count complexity of O(n log2 (n)). In this paper we show how to obtain approximate QFT with the t-count of O(n log(n)). Our approach relies on quantum circuits with measurements and feedforward, and on reusing a special quantum state that induces the phase gradient transformation. We report asymptotic analysis as well as concrete circuits, demonstrating significant advantages in both theory and practice.

}, doi = {https://doi.org/10.1038/s41534-020-0257-5}, url = {https://arxiv.org/abs/1803.04933}, author = {Yunseong Nam and Yuan Su and Dmitri Maslov} } @article {2601, title = {Approximate recovery and relative entropy I. general von Neumann subalgebras}, year = {2020}, month = {6/14/2020}, abstract = {

We prove the existence of a universal recovery channel that approximately recovers states on a v. Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I v. Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary v. Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms. We comment on applications to the quantum null energy condition.

}, url = {https://arxiv.org/abs/2006.08002}, author = {Thomas Faulkner and Stefan Hollands and Brian Swingle and Yixu Wang} } @article {2641, title = {Approximate recovery and relative entropy I. general von Neumann subalgebras}, year = {2020}, month = {6/14/2020}, abstract = {

We prove the existence of a universal recovery channel that approximately recovers states on a v. Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I v. Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary v. Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms. We comment on applications to the quantum null energy condition.

}, url = {https://arxiv.org/abs/2006.08002}, author = {Thomas Faulkner and Stefan Hollands and Brian Swingle and Yixu Wang} } @article {2594, title = {Asymmetric blockade and multi-qubit gates via dipole-dipole interactions}, year = {2020}, month = {6/3/2020}, abstract = {

Due to their strong and tunable interactions, Rydberg atoms can be used to realize fast two-qubit entangling gates. We propose a generalization of a generic two-qubit Rydberg-blockade gate to multi-qubit Rydberg-blockade gates which involve both many control qubits and many target qubits simultaneously. This is achieved by using strong microwave fields to dress nearby Rydberg states, leading to asymmetric blockade in which control-target interactions are much stronger than control-control and target-target interactions. The implementation of these multi-qubit gates can drastically simplify both quantum algorithms and state preparation. To illustrate this, we show that a 25-atom GHZ state can be created using only three gates with an error of 7.8\%.

}, url = {https://arxiv.org/abs/2006.02486}, author = {Jeremy T. Young and Przemyslaw Bienias and Ron Belyansky and Adam M. Kaufman and Alexey V. Gorshkov} } @article {2517, title = {Auditing and Debugging Deep Learning Models via Decision Boundaries: Individual-level and Group-level Analysis}, year = {2020}, month = {1/2/2020}, abstract = {

Deep learning models have been criticized for their lack of easy interpretation, which undermines confidence in their use for important applications. Nevertheless, they are consistently utilized in many applications, consequential to humans\&$\#$39; lives, mostly because of their better performance. Therefore, there is a great need for computational methods that can explain, audit, and debug such models. Here, we use flip points to accomplish these goals for deep learning models with continuous output scores (e.g., computed by softmax), used in social applications. A flip point is any point that lies on the boundary between two output classes: e.g. for a model with a binary yes/no output, a flip point is any input that generates equal scores for \"yes\" and \"no\". The flip point closest to a given input is of particular importance because it reveals the least changes in the input that would change a model\&$\#$39;s classification, and we show that it is the solution to a well-posed optimization problem. Flip points also enable us to systematically study the decision boundaries of a deep learning classifier. The resulting insight into the decision boundaries of a deep model can clearly explain the model\&$\#$39;s output on the individual-level, via an explanation report that is understandable by non-experts. We also develop a procedure to understand and audit model behavior towards groups of people. Flip points can also be used to alter the decision boundaries in order to improve undesirable behaviors. We demonstrate our methods by investigating several models trained on standard datasets used in social applications of machine learning. We also identify the features that are most responsible for particular classifications and misclassifications.

}, url = {https://arxiv.org/abs/2001.00682}, author = {Roozbeh Yousefzadeh and Dianne P. O{\textquoteright}Leary} } @article {2449, title = {Auto-tuning of double dot devices in situ with machine learning}, journal = {Phys. Rev. Applied }, volume = {13}, year = {2020}, month = {4/1/2020}, abstract = {

There are myriad quantum computing approaches, each having its own set of challenges to understand and effectively control their operation. Electrons confined in arrays of semiconductor nanostructures, called quantum dots (QDs), is one such approach. The easy access to control parameters, fast measurements, long qubit lifetimes, and the potential for scalability make QDs especially attractive. However, as the size of the QD array grows, so does the number of parameters needed for control and thus the tuning complexity. The current practice of manually tuning the qubits is a relatively time-consuming procedure and is inherently impractical for scaling up and applications. In this work, we report on the in situ implementation of an auto-tuning protocol proposed by Kalantre et al. [arXiv:1712.04914]. In particular, we discuss how to establish a seamless communication protocol between a machine learning (ML)-based auto-tuner and the experimental apparatus. We then show that a ML algorithm trained exclusively on synthetic data coming from a physical model to quantitatively classify the state of the QD device, combined with an optimization routine, can be used to replace manual tuning of gate voltages in devices. A success rate of over 85 \% is determined for tuning to a double quantum dot regime when at least one of the plunger gates is initiated sufficiently close to the desired state. Modifications to the training network, fitness function, and optimizer are discussed as a path towards further improvement in the success rate when starting both near and far detuned from the target double dot range.

}, doi = {https://doi.org/10.1103/PhysRevApplied.13.034075}, url = {https://arxiv.org/abs/1909.08030}, author = {Justyna P. Zwolak and Thomas McJunkin and Sandesh S. Kalantre and J. P. Dodson and E. R. MacQuarrie and D. E. Savage and M. G. Lagally and S. N. Coppersmith and Mark A. Eriksson and J. M. Taylor} } @article {2581, title = {Back-action evading impulse measurement with mechanical quantum sensors}, journal = {Phys. Rev. A}, volume = {102}, year = {2020}, month = {8/28/2020}, type = {FERMILAB-PUB-19-537-T}, abstract = {

The quantum measurement of any observable naturally leads to noise added by the act of measurement. Approaches to evade or reduce this noise can lead to substantial improvements in a wide variety of sensors, from laser interferometers to precision magnetometers and more. In this paper, we develop a measurement protocol based upon pioneering work by the gravitational wave community which allows for reduction of added noise from measurement by coupling an optical field to the momentum of a small mirror. As a specific implementation, we present a continuous measurement protocol using a double-ring optomechanical cavity. We demonstrate that with experimentally-relevant parameters, this protocol can lead to significant back-action noise evasion, yielding measurement noise below the standard quantum limit over many decades of frequency.

}, doi = {https://doi.org/10.1103/PhysRevA.102.023525}, url = {https://arxiv.org/pdf/1910.11892.pdf}, author = {Sohitri Ghosh and Daniel Carney and Peter Shawhan and J. M. Taylor} } @article {2728, title = {A Black-Box Approach to Post-Quantum Zero-Knowledge in Constant Rounds}, year = {2020}, month = {11/5/2020}, abstract = {

In a recent seminal work, Bitansky and Shmueli (STOC \&$\#$39;20) gave the first construction of a constant round zero-knowledge argument for NP secure against quantum attacks. However, their construction has several drawbacks compared to the classical counterparts. Specifically, their construction only achieves computational soundness, requires strong assumptions of quantum hardness of learning with errors (QLWE assumption) and the existence of quantum fully homomorphic encryption (QFHE), and relies on non-black-box simulation. In this paper, we resolve these issues at the cost of weakening the notion of zero-knowledge to what is called ε-zero-knowledge. Concretely, we construct the following protocols: - We construct a constant round interactive proof for NP that satisfies statistical soundness and black-box ε-zero-knowledge against quantum attacks assuming the existence of collapsing hash functions, which is a quantum counterpart of collision-resistant hash functions. Interestingly, this construction is just an adapted version of the classical protocol by Goldreich and Kahan (JoC \&$\#$39;96) though the proof of ε-zero-knowledge property against quantum adversaries requires novel ideas. - We construct a constant round interactive argument for NP that satisfies computational soundness and black-box ε-zero-knowledge against quantum attacks only assuming the existence of post-quantum one-way functions. At the heart of our results is a new quantum rewinding technique that enables a simulator to extract a committed message of a malicious verifier while simulating verifier\&$\#$39;s internal state in an appropriate sense.

}, url = {https://arxiv.org/abs/2011.02670}, author = {Nai-Hui Chia and Kai-Min Chung and Takashi Yamakawa} } @article {2606, title = {Building Bulk Geometry from the Tensor Radon Transform}, journal = {Journal of High Energy Physics}, volume = {2020}, year = {2020}, month = {12/4/2020}, pages = {1-50}, abstract = {

Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of AdS3/CFT2. We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.

}, url = {https://arxiv.org/abs/2007.00004}, author = {ChunJun Cao and Xiao-Liang Q and Brian Swingle and Eugene Tang} } @article {2526, title = {Can graph properties have exponential quantum speedup?}, year = {2020}, month = {1/28/2020}, abstract = {

Quantum computers can sometimes exponentially outperform classical ones, but only for problems with sufficient structure. While it is well known that query problems with full permutation symmetry can have at most polynomial quantum speedup -- even for partial functions -- it is unclear how far this condition must be relaxed to enable exponential speedup. In particular, it is natural to ask whether exponential speedup is possible for (partial) graph properties, in which the input describes a graph and the output can only depend on its isomorphism class. We show that the answer to this question depends strongly on the input model. In the adjacency matrix model, we prove that the bounded-error randomized query complexity R of any graph property P has R(P)=O(Q(P)6), where Q is the bounded-error quantum query complexity. This negatively resolves an open question of Montanaro and de Wolf in the adjacency matrix model. More generally, we prove R(P)=O(Q(P)3l) for any l-uniform hypergraph property P in the adjacency matrix model. In direct contrast, in the adjacency list model for bounded-degree graphs, we exhibit a promise problem that shows an exponential separation between the randomized and quantum query complexities.

}, url = {https://arxiv.org/abs/2001.10520}, author = {Andrew M. Childs and Daochen Wang} } @article {2575, title = {The Character of Motional Modes for Entanglement and Sympathetic Cooling of Mixed-Species Trapped Ion Chains}, year = {2020}, month = {4/16/2020}, abstract = {

Modular mixed-species ion-trap networks are a promising framework for scalable quantum information processing, where one species acts as a memory qubit and another as a communication qubit. This architecture requires high-fidelity mixed-species entangling gates to transfer information from communication to memory qubits through their collective motion. We investigate the character of the motional modes of a mixed-species ion chain for entangling operations and also sympathetic cooling. We find that the laser power required for high-fidelity entangling gates based on transverse modes is at least an order of magnitude higher than that based on axial modes for widely different masses of the two species. We also find that for even moderate mass differences, the transverse modes are much harder to cool than the axial modes regardless of the ion chain configuration. Therefore, transverse modes conventionally used for operations in single-species ion chains may not be well suited for mixed-species chains with widely different masses.

}, url = {https://arxiv.org/abs/2004.08045}, author = {Ksenia Sosnova and Allison Carter and Christopher Monroe} } @article {2364, title = {Circuit Complexity across a Topological Phase Transition}, journal = {Physical Review Research }, volume = {2}, year = {2020}, month = {03/16/2020}, pages = {013323}, abstract = {

We use Nielsen\&$\#$39;s approach to quantify the circuit complexity in the one-dimensional Kitaev model. In equilibrium, we find that the circuit complexity of ground states exhibits a divergent derivative at the critical point, signaling the presence of a topological phase transition. Out of equilibrium, we study the complexity dynamics after a sudden quench, and find that the steady-state complexity exhibits nonanalytical behavior when quenched across critical points. We generalize our results to the long-range interacting case, and demonstrate that the circuit complexity correctly predicts the critical point between regions with different semi-integer topological numbers. Our results establish a connection between circuit complexity and quantum phase transitions both in and out of equilibrium, and can be easily generalized to topological phase transitions in higher dimensions. Our study opens a new avenue to using circuit complexity as a novel quantity to understand many-body systems.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.013323}, url = {https://arxiv.org/abs/1902.10720}, author = {Fangli Liu and Rex Lundgren and Paraj Titum and James R. Garrison and Alexey V. Gorshkov} } @article {2565, title = {Classical Models of Entanglement in Monitored Random Circuits}, year = {2020}, month = {4/14/2020}, abstract = {

The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms of a classical Markov process for the dynamics of bipartition purities and establish a probabilistic cellular-automaton algorithm to compute entanglement entropy in monitored random circuits on arbitrary graphs. In one dimension, we further relate the evolution of the entropy to a simple classical spin model that naturally generalizes a two-dimensional lattice percolation problem. We also establish a Markov model for the evolution of the zeroth R{\'e}nyi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-R{\'e}nyi-entropy model. Finally, we extend the Markovian description to a more general setting that incorporates continuous-time dynamics, defined by stochastic Hamiltonians and weak local measurements continuously monitoring the system.

}, url = {https://arxiv.org/abs/2004.06736}, author = {Oles Shtanko and Yaroslav A. Kharkov and Luis Pedro Garc{\'\i}a-Pintos and Alexey V. Gorshkov} } @article {2779, title = {Coherent transport of spin by adiabatic passage in quantum dot arrays}, journal = {Physical Review B}, volume = {102}, year = {2020}, month = {9/17/2020}, abstract = {

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (\>95\%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

}, issn = {2469-9950}, doi = {10.1103/PhysRevB.102.155404}, url = {https://arxiv.org/abs/2007.10582}, author = {Michael Gullans and Petta, J. R.} } @article {2683, title = {Coherent transport of spin by adiabatic passage in quantum dot arrays}, journal = {Phys. Rev. B}, volume = {102}, year = {2020}, month = {9/17/2020}, abstract = {

We introduce an adiabatic transfer protocol for spin states in large quantum dot arrays that is based on time-dependent modulation of the Heisenberg exchange interaction in the presence of a magnetic field gradient. We refer to this protocol as spin-CTAP (coherent transport by adiabatic passage) in analogy to a related protocol developed for charge state transfer in quantum dot arrays. The insensitivity of this adiabatic protocol to pulse imperfections has potential advantages for reading out extended spin qubit arrays. When the static exchange interaction varies across the array, a quantum-controlled version of spin-CTAP is possible, where the transfer process is conditional on the spin states in the middle of the array. This conditional operation can be used to generate N-qubit entangled GHZ states. Using a realistic noise model, we analyze the robustness of the spin-CTAP operations and find that high-fidelity (\>95\%) spin eigenstate transfer and GHZ state preparation is feasible in current devices.

}, doi = {https://doi.org/10.1103/PhysRevB.102.155404}, url = {https://arxiv.org/abs/2007.10582}, author = {Michael Gullans and J. R. Petta} } @article {2585, title = {Collisions of room-temperature helium with ultracold lithium and the van der Waals bound state of HeLi}, journal = {Phys. Rev. A }, volume = {101}, year = {2020}, month = {1/6/2020}, abstract = {

We have computed the thermally averaged total, elastic rate coefficient for the collision of a room-temperature helium atom with an ultracold lithium atom. This rate coefficient has been computed as part of the characterization of a cold-atom vacuum sensor based on laser-cooled Li 6 or Li 7 atoms that will operate in the ultrahigh-vacuum (p\< 10\− 6 Pa) and extreme-high-vacuum (p\< 10\− 10 Pa) regimes. The analysis involves computing the X 2 Σ+ HeLi Born-Oppenheimer potential followed by the numerical solution of the relevant radial Schr{\"o}dinger equation. The potential is computed using a single-reference-coupled-cluster electronic-structure method with basis sets of different completeness in order to characterize our uncertainty budget. We predict that the rate coefficient for a 300 K helium gas and a 1 μ K Li gas is 1.467 (13)\× 10\− 9 cm 3/s for He 4+ Li 6 and 1.471 (13)\× 10\− 9 cm 3/s for He 4+ Li 7, where the \…

}, doi = {https://doi.org/10.1103/PhysRevA.101.012702}, author = {Constantinos Makrides and Daniel S Barker and James A Fedchak and Julia Scherschligt and Stephen Eckel and Eite Tiesinga} } @article {2573, title = {Computations with Greater Quantum Depth Are Strictly More Powerful (Relative to an Oracle)}, journal = {Accepted to the Symposium on the Theory of Computing (STOC) 2020 conference}, year = {2020}, month = {4/23/2020}, abstract = {

A conjecture of Jozsa [Jozsa06] states that any polynomial-time quantum computation can be simulated by polylogarithmic-depth quantum computation interleaved with polynomial-depth classical computation. Separately, Aaronson [Aaronson05, Aaronson11, Aaronson14] conjectured that there exists an oracle O such that BQPO\≠(BPPBQNC)O. These conjectures are intriguing allusions to the unresolved potential of combining classical and low-depth quantum computation. In this work we show that the Welded Tree Problem, which is an oracle problem that can be solved in quantum polynomial time as shown by Childs et al. [ChildsCDFGS03], cannot be solved in BPPBQNC, nor can it be solved in the class that Jozsa describes. This proves Aaronson\&$\#$39;s oracle separation conjecture and provides a counterpoint to Jozsa\&$\#$39;s conjecture relative to the Welded Tree oracle problem. More precisely, we define two complexity classes, HQC and JC whose languages are decided by two different families of interleaved quantum-classical circuits. HQC contains BPPBQNC and is therefore relevant to Aaronson\&$\#$39;s conjecture, while JC captures the model of computation that Jozsa considers. We show that the Welded Tree Problem gives an oracle separation between either of {JC,HQC} and BQP. Therefore, even when interleaved with arbitrary polynomial-time classical computation, greater \"quantum depth\" leads to strictly greater computational ability in this relativized setting.

}, doi = {https://doi.org/10.1145/3357713.3384269}, url = {https://arxiv.org/abs/1909.10503}, author = {Matthew Coudron and Sanketh Menda} } @article {2695, title = {Confronting lattice parton distributions with global QCD analysis}, year = {2020}, month = {10/1/2020}, abstract = {

We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions

}, url = {https://arxiv.org/abs/2010.00548}, author = {Jacob Bringewatt and N. Sato and W. Melnitchouk and Jian-Wei Qiu and F. Steffens and M. Constantinou} } @article {2723, title = {Constant-round Blind Classical Verification of Quantum Sampling}, year = {2020}, month = {12/8/2020}, abstract = {

In a recent breakthrough, Mahadev constructed a classical verification of quantum computation (CVQC) protocol for a classical client to delegate decision problems in BQP to an untrusted quantum prover under computational assumptions. In this work, we explore further the feasibility of CVQC with the more general sampling problems in BQP and with the desirable blindness property. We contribute affirmative solutions to both as follows. (1) Motivated by the sampling nature of many quantum applications (e.g., quantum algorithms for machine learning and quantum supremacy tasks), we initiate the study of CVQC for quantum sampling problems (denoted by SampBQP). More precisely, in a CVQC protocol for a SampBQP problem, the prover and the verifier are given an input x\∈{0,1}n and a quantum circuit C, and the goal of the classical client is to learn a sample from the output z\←C(x) up to a small error, from its interaction with an untrusted prover. We demonstrate its feasibility by constructing a four-message CVQC protocol for SampBQP based on the quantum Learning With Error assumption. (2) The blindness of CVQC protocols refers to a property of the protocol where the prover learns nothing, and hence is blind, about the client\&$\#$39;s input. It is a highly desirable property that has been intensively studied for the delegation of quantum computation. We provide a simple yet powerful generic compiler that transforms any CVQC protocol to a blind one while preserving its completeness and soundness errors as well as the number of rounds. Applying our compiler to (a parallel repetition of) Mahadev\&$\#$39;s CVQC protocol for BQP and our CVQC protocol for SampBQP yields the first constant-round blind CVQC protocol for BQP and SampBQP respectively, with negligible completeness and soundness errors.

}, url = {https://arxiv.org/abs/2012.04848}, author = {Kai-Min Chung and Yi Lee and Han-Hsuan Lin and Xiaodi Wu} } @article {2572, title = {Constructing Multipartite Bell inequalities from stabilizers}, year = {2020}, month = {2/5/2020}, abstract = {

Bell inequality with self-testing property has played an important role in quantum information field with both fundamental and practical applications. However, it is generally challenging to find Bell inequalities with self-testing property for multipartite states and actually there are not many known candidates. In this work, we propose a systematical framework to construct Bell inequalities from stabilizers which are maximally violated by general stabilizer states, with two observables for each local party. We show that the constructed Bell inequalities can self-test any stabilizer state which is essentially device-independent, if and only if these stabilizers can uniquely determine the state in a device-dependent manner. This bridges the gap between device-independent and device-dependent verification methods. Our framework can provide plenty of Bell inequalities for self-testing stabilizer states. Among them, we give two families of Bell inequalities with different advantages: (1) a family of Bell inequalities with a constant ratio of quantum and classical bounds using 2N correlations, (2) Single pair inequalities improving on all previous robustness self-testing bounds using N+1 correlations, which are both efficient and suitable for realizations in multipartite systems. Our framework can not only inspire more fruitful multipartite Bell inequalities from conventional verification methods, but also pave the way for their practical applications.

}, url = {https://arxiv.org/abs/2002.01843}, author = {Qi Zhao and You Zhou} } @article {2719, title = {Continuous symmetries and approximate quantum error correction}, journal = {Phys. Rev. X}, volume = {10}, year = {2020}, month = {10/26/2020}, abstract = {

Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two important principles. If a logical quantum system is encoded into n physical subsystems, we say that the code is covariant with respect to a symmetry group G if a G transformation on the logical system can be realized by performing transformations on the individual subsystems. For a G-covariant code with G a continuous group, we derive a lower bound on the error correction infidelity following erasure of a subsystem. This bound approaches zero when the number of subsystems n or the dimension d of each subsystem is large. We exhibit codes achieving approximately the same scaling of infidelity with n or d as the lower bound. Leveraging tools from representation theory, we prove an approximate version of the Eastin-Knill theorem: If a code admits a universal set of transversal gates and corrects erasure with fixed accuracy, then, for each logical qubit, we need a number of physical qubits per subsystem that is inversely proportional to the error parameter. We construct codes covariant with respect to the full logical unitary group, achieving good accuracy for large d (using random codes) or n (using codes based on W-states). We systematically construct codes covariant with respect to general groups, obtaining natural generalizations of qubit codes to, for instance, oscillators and rotors. In the context of the AdS/CFT correspondence, our approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the Eastin-Knill theorem, and our five-rotor code can be stacked to form a covariant holographic code.

}, doi = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.041018}, url = {https://arxiv.org/abs/1902.07714}, author = {Philippe Faist and Sepehr Nezami and Victor V. Albert and Grant Salton and Fernando Pastawski and Patrick Hayden and John Preskill} } @article {2637, title = {Critical Theory for the Breakdown of Photon Blockade}, year = {2020}, month = {6/9/2020}, abstract = {

Photon blockade is the result of the interplay between the quantized nature of light and strong optical nonlinearities, whereby strong photon-photon repulsion prevents a quantum optical system from absorbing multiple photons. We theoretically study a single atom coupled to the light field, described by the resonantly driven Jaynes--Cummings model, in which case the photon blockade breaks down in a second order phase transition at a critical drive strength. We show that this transition is associated to the spontaneous breaking of an anti-unitary PT-symmetry. Within a semiclassical approximation we calculate the expectation values of observables in the steady state. We then move beyond the semiclassical approximation and approach the critical point from the disordered (blockaded) phase by reducing the Lindblad quantum master equation to a classical rate equation that we solve. The width of the steady-state distribution in Fock space is found to diverge as we approach the critical point with a simple power-law, allowing us to calculate the critical scaling of steady state observables without invoking mean-field theory. We propose a simple physical toy model for biased diffusion in the space of occupation numbers, which captures the universal properties of the steady state. We list several experimental platforms where this phenomenon may be observed.

}, url = {https://arxiv.org/abs/2006.05593}, author = {Jonathan B. Curtis and Igor Boettcher and Jeremy T. Young and Mohammad F. Maghrebi and Howard Carmichael and Alexey V. Gorshkov and Michael Foss-Feig} } @article {2514, title = {Destructive Error Interference in Product-Formula Lattice Simulation}, journal = {Phys. Rev. Lett. }, volume = {124}, year = {2020}, month = {6/4/2020}, abstract = {

Quantum computers can efficiently simulate the dynamics of quantum systems. In this paper, we study the cost of digitally simulating the dynamics of several physically relevant systems using the first-order product formula algorithm. We show that the errors from different Trotterization steps in the algorithm can interfere destructively, yielding a much smaller error than previously estimated. In particular, we prove that the total error in simulating a nearest-neighbor interacting system of n sites for time t using the first-order product formula with r time slices is O(nt/r+nt3/r2) when nt2/r is less than a small constant. Given an error tolerance ε, the error bound yields an estimate of max{O(n2t/ε),O(n2t3/2/ε1/2)} for the total gate count of the simulation. The estimate is tighter than previous bounds and matches the empirical performance observed in Childs et al. [PNAS 115, 9456-9461 (2018)]. We also provide numerical evidence for potential improvements and conjecture an even tighter estimate for the gate count.\ 

}, doi = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.220502}, url = {https://arxiv.org/abs/1912.11047}, author = {Minh C. Tran and Su-Kuan Chu and Yuan Su and Andrew M. Childs and Alexey V. Gorshkov} } @article {2411, title = {Discrete Time Crystals}, journal = {Annual Review of Condensed Matter Physics }, volume = {11}, year = {2020}, month = {3/10/2020}, pages = {467-499}, abstract = {

Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new non-equilibrium phases of matter. In particular, we focus on \"discrete time crystals\", which are many-body phases of matter characterized by a spontaneously broken discrete time translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a non-equilibrium phenomenon, which is stabilized by many-body interactions, with no analog in non-interacting systems. We explain the theory behind several proposed models of discrete time crystals, and compare a number of recent realizations, in different experimental contexts.\ 

}, doi = {https://doi.org/10.1146/annurev-conmatphys-031119-050658}, url = {https://arxiv.org/abs/1905.13232}, author = {Dominic V. Else and Christopher Monroe and Chetan Nayak and Norman Y. Yao} } @article {2688, title = {Distinct Critical Behaviors from the Same State in Quantum Spin and Population Dynamics Perspectives}, year = {2020}, month = {9/10/2020}, abstract = {

There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same matrix. However, that vector is the wavefunction amplitude in the quantum spin model, whereas it is the probability itself in the population model. We show that this seemingly minor difference has significant consequences: phase transitions which are discontinuous in the spin system become continuous when viewed through the population perspective, and transitions which are continuous become governed by new critical exponents. We introduce a more general class of models which encompasses both cases, and that can be solved exactly in a mean-field limit. Numerical results are also presented for a number of one-dimensional chains with power-law interactions. We see that well-worn spin models of quantum statistical mechanics can contain unexpected new physics and insights when treated as population-dynamical models and beyond, motivating further studies.\ 

}, url = {https://arxiv.org/abs/2009.05064}, author = {Christopher L. Baldwin and S. Shivam and S. L. Sondhi and M. Kardar} } @article {2388, title = {Distributional property testing in a quantum world}, journal = {Proceedings of ITCS 2020}, volume = {25}, year = {2020}, month = {02/02/2019}, pages = {1-25}, abstract = {

A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing closeness between unknown distributions, testing independence between two distributions, and estimating the Shannon / von Neumann entropy of distributions. The distributions can be either classical or quantum, however our quantum algorithms require coherent quantum access to a process preparing the samples. Our results build on the recent technique of quantum singular value transformation, combined with more standard tricks such as divide-and-conquer. The presented approach is a natural fit for distributional property testing both in the classical and the quantum case, demonstrating the first speed-ups for testing properties of density operators that can be accessed coherently rather than only via sampling; for classical distributions our algorithms significantly improve the precision dependence of some earlier results.

}, doi = {http://dx.doi.org/10.4230/LIPIcs.ITCS.2020.25}, url = {https://arxiv.org/abs/1902.00814}, author = {Andras Gilyen and Tongyang Li} } @article {2778, title = {Dynamical Purification Phase Transition Induced by Quantum Measurements}, journal = {Physical Review X}, volume = {10}, year = {2020}, month = {7/30/2020}, abstract = {

Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling interactions within the system can result in a dynamical purification phase transition between (i) a phase that locally purifies at a constant system-size-independent rate, and (ii) a \"mixed\" phase where the purification time diverges exponentially in the system size. The residual entropy density in the mixed phase implies the existence of a quantum error-protected subspace where quantum information is reliably encoded against the future non-unitary evolution of the system. We show that these codes are of potential relevance to fault-tolerant quantum computation as they are often highly degenerate and satisfy optimal tradeoffs between encoded information densities and error thresholds. In spatially local models in 1+1 dimensions, this phase transition for mixed initial states occurs concurrently with a recently identified class of entanglement phase transitions for pure initial states. The mutual information of an initially completely-mixed state in 1+1 dimensions grows sublinearly in time due to the formation of the error protected subspace. The purification transition studied here also generalizes to systems with long-range interactions, where conventional notions of entanglement transitions have to be reformulated. Purification dynamics is likely a more robust probe of the transition in experiments, where imperfections generically reduce entanglement and drive the system towards mixed states. We describe the motivations for studying this novel class of non-equilibrium quantum dynamics in the context of advanced quantum computing platforms and fault-tolerant quantum computation.

}, doi = {10.1103/PhysRevX.10.041020}, url = {https://arxiv.org/abs/1905.05195}, author = {Michael Gullans and Huse, David A.} } @article {2584, title = {Effective gaps are not effective: quasipolynomial classical simulation of obstructed stoquastic Hamiltonians}, year = {2020}, month = {4/21/2020}, abstract = {

All known examples confirming the possibility of an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (AQC) exploit symmetries that constrain adiabatic dynamics to effective, symmetric subspaces. The symmetries produce large effective eigenvalue gaps, which in turn make adiabatic computation efficient. We present a classical algorithm to efficiently sample from the effective subspace of a k-local stoquastic Hamiltonian H, without a priori knowledge of its symmetries (or near-symmetries). Our algorithm maps any k-local Hamiltonian to a graph G=(V,E) with |V|=O(poly(n)) where n is the number of qubits. Given the well-known result of Babai, we exploit graph isomorphism to study the automorphisms of G and arrive at an algorithm quasi-polynomial in |V| for producing samples from the effective subspace eigenstates of H. Our results rule out exponential separations between stoquastic AQC and classical computation that arise from hidden symmetries in k-local Hamiltonians. Furthermore, our graph representation of H is not limited to stoquastic Hamiltonians and may rule out corresponding obstructions in non-stoquastic cases, or be useful in studying additional properties of k-local Hamiltonians.

}, url = {https://arxiv.org/abs/2004.08681}, author = {Jacob Bringewatt and Michael Jarret} } @article {2540, title = {Efficient randomness certification by quantum probability estimation}, journal = {Phys. Rev. Research }, volume = {2}, year = {2020}, month = {1/7/2020}, abstract = {

For practical applications of quantum randomness generation, it is important to certify and further produce a fixed block of fresh random bits with as few trials as possible. Consequently, protocols with high finite-data efficiency are preferred. To yield such protocols with respect to quantum side information, we develop quantum probability estimation. Our approach is applicable to device-independent as well as device-dependent scenarios, and it generalizes techniques from previous works [Miller and Shi, SIAM J. Comput. 46, 1304 (2017); Arnon-Friedman et al., Nat. Commun. 9, 459 (2018)]. Quantum probability estimation can adapt to changing experimental conditions, allows stopping the experiment as soon as the prespecified randomness goal is achieved, and can tolerate imperfect knowledge of the input distribution. Moreover, the randomness rate achieved at constant error is asymptotically optimal. For the device-independent scenario, our approach certifies the amount of randomness available in experimental results without first searching for relations between randomness and violations of fixed Bell inequalities. We implement quantum probability estimation for device-independent randomness generation in the CHSH Bell-test configuration, and we show significant improvements in finite-data efficiency, particularly at small Bell violations which are typical in current photonic loophole-free Bell tests.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.013016}, author = {Yanbao Zhang and Honghao Fu and Emanuel Knill} } @article {2627, title = {Efficient Simulation of Random States and Random Unitaries}, journal = {In: Canteaut A., Ishai Y. (eds) Advances in Cryptology {\textendash} EUROCRYPT 2020. Lecture Notes in Computer Science, Springer, Cham}, volume = {12107}, year = {2020}, month = {5/1/2020}, pages = {759-787}, type = {inproceedings}, abstract = {

We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access.

This problem has previously only been considered for restricted adversaries. Against adversaries with an a priori bound on the number of queries, it is well-known that t-designs suffice. Against polynomial-time adversaries, one can use pseudorandom states (PRS) and pseudorandom unitaries (PRU), as defined in a recent work of Ji, Liu, and Song; unfortunately, no provably secure construction is known for PRUs.

In our setting, we are concerned with unbounded adversaries. Nonetheless, we are able to give stateful quantum algorithms which simulate the ideal object in both settings of interest. In the case of Haar-random states, our simulator is polynomial-time, has negligible error, and can also simulate verification and reflection through the simulated state. This yields an immediate application to quantum money: a money scheme which is information-theoretically unforgeable and untraceable. In the case of Haar-random unitaries, our simulator takes polynomial space, but simulates both forward and inverse access with zero error.

These results can be seen as the first significant steps in developing a theory of lazy sampling for random quantum objects.

}, doi = {https://doi.org/10.1007/978-3-030-45727-3_26}, author = {Gorjan Alagic and Christian Majenz and Alexander Russell} } @article {2331, title = {Efficiently computable bounds for magic state distillation}, journal = {Phys. Rev. Lett. }, volume = {124}, year = {2020}, month = {3/6/2020}, abstract = {

Magic state manipulation is a crucial component in the leading approaches to realizing scalable, fault-tolerant, and universal quantum computation. Related to magic state manipulation is the resource theory of magic states, for which one of the goals is to characterize and quantify quantum \"magic.\" In this paper, we introduce the family of thauma measures to quantify the amount of magic in a quantum state, and we exploit this family of measures to address several open questions in the resource theory of magic states. As a first application, we use the min-thauma to bound the regularized relative entropy of magic. As a consequence of this bound, we find that two classes of states with maximal mana, a previously established magic measure, cannot be interconverted in the asymptotic regime at a rate equal to one. This result resolves a basic question in the resource theory of magic states and reveals a fundamental difference between the resource theory of magic states and other resource theories such as entanglement and coherence. As a second application, we establish the hypothesis testing thauma as an efficiently computable benchmark for the one-shot distillable magic, which in turn leads to a variety of bounds on the rate at which magic can be distilled, as well as on the overhead of magic state distillation. Finally, we prove that the max-thauma can outperform mana in benchmarking the efficiency of magic state distillation.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.124.090505}, url = {https://arxiv.org/abs/1812.10145}, author = {Xin Wang and Mark M. Wilde and Yuan Su} } @article {2457, title = {Entanglement Bounds on the Performance of Quantum Computing Architectures}, journal = {Phys. Rev. Research}, volume = {2}, year = {2020}, month = {9/22/2020}, abstract = {

There are many possible architectures for future quantum computers that designers will need to choose between. However, the process of evaluating a particular connectivity graph\&$\#$39;s performance as a quantum architecture can be difficult. In this paper, we establish a connection between a quantity known as the isoperimetric number and a lower bound on the time required to create highly entangled states. The metric we propose counts resources based on the use of two-qubit unitary operations, while allowing for arbitrarily fast measurements and classical feedback. We describe how these results can be applied to the evaluation of the hierarchical architecture proposed in Phys. Rev. A 98, 062328 (2018). We also show that the time-complexity bound we place on the creation of highly-entangled states can be saturated up to a multiplicative factor logarithmic in the number of qubits.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.033316}, url = {https://arxiv.org/abs/1908.04802}, author = {Zachary Eldredge and Leo Zhou and Aniruddha Bapat and James R. Garrison and Abhinav Deshpande and Frederic T. Chong and Alexey V. Gorshkov} } @article {2677, title = {Entanglement entropy scaling transition under competing monitoring protocols}, year = {2020}, month = {08/19/2020}, abstract = {

Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works has been primarily on engineering the non-equilibrium steady state, we investigate the build-up of entanglement in the quantum trajectories. Specifically, we analyze the competition between two different dissipation channels arising from two incompatible continuous monitoring protocols. The first protocol locks the phase of neighboring sites upon registering a quantum jump, thereby generating a long-range entanglement through the system, while the second one destroys the coherence via dephasing mechanism. By studying the unraveling of stochastic quantum trajectories associated with the continuous monitoring protocols, we present a transition for the scaling of the averaged trajectory entanglement entropies, from critical scaling to area-law behavior. Our work provides novel insights into the occurrence of a measurement-induced phase transition within a continuous monitoring protocol.

}, url = {https://arxiv.org/abs/2008.08619}, author = {Mathias Van Regemortel and Ze-Pei Cian and Alireza Seif and Hossein Dehghani and Mohammad Hafezi} } @article {2567, title = {Exotic photonic molecules via Lennard-Jones-like potentials}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {9/19/2020}, abstract = {

Ultracold systems offer an unprecedented level of control of interactions between atoms. An important challenge is to achieve a similar level of control of the interactions between photons. Towards this goal, we propose a realization of a novel Lennard-Jones-like potential between photons coupled to the Rydberg states via electromagnetically induced transparency (EIT). This potential is achieved by tuning Rydberg states to a F{{\"o}}rster resonance with other Rydberg states. We consider few-body problems in 1D and 2D geometries and show the existence of self-bound clusters (\"molecules\") of photons. We demonstrate that for a few-body problem, the multi-body interactions have a significant impact on the geometry of the molecular ground state. This leads to phenomena without counterparts in conventional systems: For example, three photons in 2D preferentially arrange themselves in a line-configuration rather than in an equilateral-triangle configuration. Our result opens a new avenue for studies of many-body phenomena with strongly interacting photons.

}, doi = {https://doi.org/10.1103/PhysRevLett.125.093601}, url = {https://arxiv.org/abs/2003.07864}, author = {Przemyslaw Bienias and Michael Gullans and Marcin Kalinowski and Alexander N. Craddock and Dalia P. Ornelas-Huerta and Steven L. Rolston and J. V. Porto and Alexey V. Gorshkov} } @article {2329, title = {Experimental Low-Latency Device-Independent Quantum Randomness}, journal = {Phys. Rev. Lett. }, volume = {124}, year = {2020}, month = {12/24/2019}, abstract = {

Applications of randomness such as private key generation and public randomness beacons require small blocks of certified random bits on demand. Device-independent quantum random number generators can produce such random bits, but existing quantum-proof protocols and loophole-free implementations suffer from high latency, requiring many hours to produce any random bits. We demonstrate device-independent quantum randomness generation from a loophole-free Bell test with a more efficient quantum-proof protocol, obtaining multiple blocks of 512 bits with an average experiment time of less than 5 min per block and with certified error bounded by 2\−64\≈5.42\×10\−20.

}, doi = {https://doi.org/10.1103/PhysRevLett.124.010505}, url = {https://arxiv.org/abs/1812.07786}, author = {Yanbao Zhang and Lynden K. Shalm and Joshua C. Bienfang and Martin J. Stevens and Michael D. Mazurek and Sae Woo Nam and Carlos Abell{\'a}n and Waldimar Amaya and Morgan W. Mitchell and Honghao Fu and Carl Miller and Alan Mink and Emanuel Knill} } @article {2640, title = {An exponential ramp in the quadratic Sachdev-Ye-Kitaev model}, year = {2020}, month = {6/26/2020}, abstract = {

A long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.

}, url = {https://arxiv.org/abs/2006.15152}, author = {Michael Winer and Shao-Kai Jian and Brian Swingle} } @article {2686, title = {Fault-Tolerant Operation of a Quantum Error-Correction Code}, year = {2020}, month = {9/24/2020}, abstract = {

Quantum error correction protects fragile quantum information by encoding it in a larger quantum system whose extra degrees of freedom enable the detection and correction of errors. An encoded logical qubit thus carries increased complexity compared to a bare physical qubit. Fault-tolerant protocols contain the spread of errors and are essential for realizing error suppression with an error-corrected logical qubit. Here we experimentally demonstrate fault-tolerant preparation, rotation, error syndrome extraction, and measurement on a logical qubit encoded in the 9-qubit Bacon-Shor code. For the logical qubit, we measure an average fault-tolerant preparation and measurement error of 0.6\% and a transversal Clifford gate with an error of 0.3\% after error correction. The result is an encoded logical qubit whose logical fidelity exceeds the fidelity of the entangling operations used to create it. We compare these operations with non-fault-tolerant protocols capable of generating arbitrary logical states, and observe the expected increase in error. We directly measure the four Bacon-Shor stabilizer generators and are able to detect single qubit Pauli errors. These results show that fault-tolerant quantum systems are currently capable of logical primitives with error rates lower than their constituent parts. With the future addition of intermediate measurements, the full power of scalable quantum error-correction can be achieved.\ 

}, url = {https://arxiv.org/abs/2009.11482}, author = {Laird Egan and Dripto M. Debroy and Crystal Noel and Andrew Risinger and Daiwei Zhu and Debopriyo Biswas and Michael Newman and Muyuan Li and Kenneth R. Brown and Marko Cetina and Christopher Monroe} } @article {2648, title = {Feedback Induced Magnetic Phases in Binary Bose-Einstein Condensates}, year = {2020}, month = {7/14/2020}, abstract = {

Weak measurement in tandem with real-time feedback control is a new route toward engineering novel non-equilibrium quantum matter. Here we develop a theoretical toolbox for quantum feedback control of multicomponent Bose-Einstein condensates (BECs) using backaction-limited weak measurements in conjunction with spatially resolved feedback. Feedback in the form of a single-particle potential can introduce effective interactions that enter into the stochastic equation governing system dynamics. The effective interactions are tunable and can be made analogous to Feshbach resonances -- spin-independent and spin-dependent -- but without changing atomic scattering parameters. Feedback cooling prevents runaway heating due to measurement backaction and we present an analytical model to explain its effectiveness. We showcase our toolbox by studying a two-component BEC using a stochastic mean-field theory, where feedback induces a phase transition between easy-axis ferromagnet and spin-disordered paramagnet phases. We present the steady-state phase diagram as a function of intrinsic and effective spin-dependent interaction strengths. Our result demonstrates that closed-loop quantum control of Bose-Einstein condensates is a powerful new tool for quantum engineering in cold-atom systems.

}, url = {https://arxiv.org/abs/2007.07266}, author = {Hilary M. Hurst and Shangjie Guo and I. B. Spielman} } @article {2461, title = {Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries}, journal = {Phys. Rev. Lett. }, volume = {125}, year = {2020}, month = {7/22/2020}, abstract = {

We study the connection between the charging power of quantum batteries and the fluctuations of the stored work. We prove that in order to have a non-zero rate of change of the extractable work, the state ρW of the battery cannot be an eigenstate of a {\textquoteleft}\emph{work operator}\&$\#$39;, defined by F \≡ HW + β\−1log(ρW), where HW is the Hamiltonian of the battery and β is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the stored work upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine.\ 

}, doi = {10.1103/PhysRevLett.125.040601}, url = {https://arxiv.org/abs/1909.03558}, author = {Luis Pedro Garc{\'\i}a-Pintos and Alioscia Hamma and Adolfo del Campo} } @article {2375, title = {Gravitational Direct Detection of Dark Matter}, journal = {Phys. Rev. D}, volume = {102}, year = {2020}, month = {10/13/2020}, type = {FERMILAB-PUB-19-082-AE-T}, abstract = {

The only coupling dark matter is guaranteed to have with the standard model is through gravity. Here we propose a concept for direct dark matter detection using only this gravitational coupling, enabling a new regime of detection. Leveraging dramatic advances in the ability to create, maintain, and probe quantum states of massive objects, we suggest that an array of quantum-limited impulse sensors may be capable of detecting the correlated gravitational force created by a passing dark matter particle. We present two concrete realizations of this scheme, using either mechanical resonators or freely-falling masses. With currently available technology, a meter-scale apparatus of this type could detect any dark matter candidate around the Planck mass or heavier.

}, doi = {https://doi.org/10.1103/PhysRevD.102.072003}, url = {https://arxiv.org/abs/1903.00492}, author = {Daniel Carney and Sohitri Ghosh and Gordan Krnjaic and J. M. Taylor} } @article {2577, title = {Hierarchy of linear light cones with long-range interactions}, journal = {Physical Review X}, volume = {10}, year = {2020}, month = {5/29/2020}, abstract = {

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a \"linear light cone,\" which expands at an emergent velocity analogous to the speed of light. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance r interact with potential energy V(r)\∝1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same α, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, commutators of local operators \⟨ψ|[Ox(t),Oy]|ψ\⟩ are negligible in every state |ψ\⟩ when |x\−y|≳vt, where v is finite when α\>3 (Lieb-Robinson light cone); in a typical state |ψ\⟩ drawn from the infinite temperature ensemble, v is finite when α\>52 (Frobenius light cone); in non-interacting systems, v is finite in every state when α\>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones, and their tightness, also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that quantum state transfer and many-body quantum chaos are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

}, doi = {https://doi.org/10.1103/PhysRevX.10.031009}, url = {https://arxiv.org/abs/2001.11509}, author = {Minh C. Tran and Chi-Fang Chen and Adam Ehrenberg and Andrew Y. Guo and Abhinav Deshpande and Yifan Hong and Zhe-Xuan Gong and Alexey V. Gorshkov and Andrew Lucas} } @article {2498, title = {Hilbert-Space Fragmentation from Strict Confinement}, journal = {Phys. Rev. Lett.}, volume = {124}, year = {2020}, month = {5/22/2020}, abstract = {

We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most of the previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of Z2 gauge theory coupled to fermionic matter, leading to a hierarchy of time scales for motion of the fermions. This model can be realized experimentally in two complementary settings.

}, doi = {https://doi.org/10.1103/PhysRevLett.124.207602}, url = {https://arxiv.org/abs/1912.04300}, author = {Zhi-Cheng Yang and Fangli Liu and Alexey V. Gorshkov and Thomas Iadecola} } @article {2629, title = {The impossibility of efficient quantum weak coin flipping}, journal = {STOC 2020: Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing }, year = {2020}, month = {6/2020}, pages = {916-929}, abstract = {

How can two parties with competing interests carry out a fair coin flip across a quantum communication channel? This problem (quantum weak coin-flipping) was formalized more than 15 years ago, and, despite some phenomenal theoretical progress, practical quantum coin-flipping protocols with vanishing bias have proved hard to find. In the current work we show that there is a reason that practical weak quantum coin-flipping is difficult: any quantum weak coin-flipping protocol with bias є must use at least exp( Ω (1/\√є )) rounds of communication. This is a large improvement over the previous best known lower bound of Ω ( log log(1/є )) due to Ambainis from 2004. Our proof is based on a theoretical construction (the two-variable profile function) which may find further applications.

}, doi = {https://doi.org/10.1145/3357713.3384276}, author = {Carl Miller} } @article {2625, title = {Impossibility of Quantum Virtual Black-Box Obfuscation of Classical Circuits}, year = {2020}, month = {5/13/2020}, abstract = {

Virtual black-box obfuscation is a strong cryptographic primitive: it encrypts a circuit while maintaining its full input/output functionality. A remarkable result by Barak et al. (Crypto 2001) shows that a general obfuscator that obfuscates classical circuits into classical circuits cannot exist. A promising direction that circumvents this impossibility result is to obfuscate classical circuits into quantum states, which would potentially be better capable of hiding information about the obfuscated circuit. We show that, under the assumption that learning-with-errors (LWE) is hard for quantum computers, this quantum variant of virtual black-box obfuscation of classical circuits is generally impossible. On the way, we show that under the presence of dependent classical auxiliary input, even the small class of classical point functions cannot be quantum virtual black-box obfuscated.

}, url = {https://arxiv.org/abs/2005.06432}, author = {Gorjan Alagic and Zvika Brakerski and Yfke Dulek and Christian Schaffner} } @article {2602, title = {Information scrambling at finite temperature in local quantum systems}, year = {2020}, month = {5/21/2020}, abstract = {

This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, m, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature T. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O(N) non-linear sigma model, which is analytically tractable at large N. Using the ladder diagram technique, we find that operators spread at a speed T/m\−\−\−\−\√ at low temperatures, T<}, url = {https://arxiv.org/abs/2005.10814}, author = {Subhayan Sahu and Brian Swingle} } @article {2643, title = {Information scrambling at finite temperature in local quantum systems}, year = {2020}, month = {5/21/2020}, abstract = {

This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, m, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature T. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O(N) non-linear sigma model, which is analytically tractable at large N. Using the ladder diagram technique, we find that operators spread at a speed T/m\−\−\−\−\√ at low temperatures, T<}, url = {https://arxiv.org/abs/2005.10814}, author = {Subhayan Sahu and Brian Swingle} } @article {2593, title = {Limits on Classical Simulation of Free Fermions with Dissipation}, year = {2020}, month = {5/21/2020}, abstract = {

Free-fermionic systems are a valuable, but limited, class of many-body problems efficiently simulable on a classical computer. We examine how classical simulability of noninteracting fermions is modified in the presence of Markovian dissipation described by quadratic Lindblad operators, including, for example, incoherent transitions or pair losses. On the one hand, we establish three broad classes of Markovian dynamics that are efficiently simulable classically, by devising efficient algorithms. On the other hand, we demonstrate that, in the worst case, simulating Markovian dynamics with quadratic Lindblad operators is at least as hard as simulating universal quantum circuits. This result is applicable to an experimentally relevant setting in cold atomic systems, where magnetic Feshbach resonances can be used to engineer the desired dissipation. For such systems, our hardness result provides a direct scheme for dissipation-assisted quantum computing with a potential significant advantage in the speed of two-qubit gates and, therefore, in error tolerance.

}, url = {https://arxiv.org/abs/2005.10840}, author = {Oles Shtanko and Abhinav Deshpande and Paul S. Julienne and Alexey V. Gorshkov} } @article {2720, title = {Localization and criticality in antiblockaded 2D Rydberg atom arrays}, year = {2020}, month = {12/7/2020}, abstract = {

Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under anti-blockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime\&$\#$39;s existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally.\ 

}, url = {https://arxiv.org/abs/2012.03946}, author = {Fangli Liu and Zhi-Cheng Yang and Przemyslaw Bienias and Thomas Iadecola and Alexey V. Gorshkov} } @article {2466, title = {Machine learning the thermodynamic arrow of time}, journal = {Nat. Phys.}, year = {2020}, month = {09/21/2020}, pages = {1-9}, abstract = {

The mechanism by which thermodynamics sets the direction of time\&$\#$39;s arrow has long fascinated scientists. Here, we show that a machine learning algorithm can learn to discern the direction of time\&$\#$39;s arrow when provided with a system\&$\#$39;s microscopic trajectory as input. The performance of our algorithm matches fundamental bounds predicted by nonequilibrium statistical mechanics. Examination of the algorithm\&$\#$39;s decision-making process reveals that it discovers the underlying thermodynamic mechanism and the relevant physical observables. Our results indicate that machine learning techniques can be used to study systems out of equilibrium, and ultimately to uncover physical principles.

}, doi = {https://doi.org/10.1038/s41567-020-1018-2}, url = {https://arxiv.org/abs/1909.12380}, author = {Alireza Seif and Mohammad Hafezi and Christopher Jarzynski} } @article {2531, title = {Many-Body Dephasing in a Trapped-Ion Quantum Simulator}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {8/24/2020}, abstract = {

How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this work, we observe and analyse the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles and observe the experimental evidence for the theoretically predicted regime of many-body dephasing. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions even for the long-time non-integrable dynamics. We find that the measured fluctuations are exponentially suppressed with increasing system size, consistent with theoretical predictions.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.125.120605}, url = {https://arxiv.org/abs/2001.02477}, author = {Harvey B. Kaplan and Lingzhen Guo and Wen Lin Tan and Arinjoy De and Florian Marquardt and Guido Pagano and Christopher Monroe} } @article {2687, title = {Mechanical Quantum Sensing in the Search for Dark Matter}, year = {2020}, month = {8/13/2020}, type = {FERMILAB-PUB-20-378-QIS-T}, abstract = {

Numerous astrophysical and cosmological observations are best explained by the existence of dark matter, a mass density which interacts only very weakly with visible, baryonic matter. Searching for the extremely weak signals produced by this dark matter strongly motivate the development of new, ultra-sensitive detector technologies. Paradigmatic advances in the control and readout of massive mechanical systems, in both the classical and quantum regimes, have enabled unprecedented levels of sensitivity. In this white paper, we outline recent ideas in the potential use of a range of solid-state mechanical sensing technologies to aid in the search for dark matter in a number of energy scales and with a variety of coupling mechanisms.

}, url = {https://arxiv.org/abs/2008.06074}, author = {D. Carney and G. Krnjaic and D. C. Moore and C. A. Regal and G. Afek and S. Bhave and B. Brubaker and T. Corbitt and J. Cripe and N. Crisosto and A.Geraci and S. Ghosh and J. G. E. Harris and A. Hook and E. W. Kolb and J. Kunjummen and R. F. Lang and T. Li and T. Lin and Z. Liu and J. Lykken and L. Magrini and J. Manley and N. Matsumoto and A. Monte and F. Monteiro and T. Purdy and C. J. Riedel and R. Singh and S. Singh and K. Sinha and J. M. Taylor and J. Qin and D. J. Wilson and Y. Zhao} } @article {2595, title = {Minimal model for fast scrambling}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {9/22/2020}, abstract = {

We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two exactly solvable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled non-linear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results can be verified with state-of-the-art quantum simulators.

}, doi = {https://doi.org/10.1103/PhysRevLett.125.130601}, url = {https://arxiv.org/abs/2005.05362}, author = {Ron Belyansky and Przemyslaw Bienias and Yaroslav A. Kharkov and Alexey V. Gorshkov and Brian Swingle} } @article {2692, title = {More of the Bulk from Extremal Area Variations}, journal = {Classical and Quantum Gravity}, volume = {38}, year = {2020}, month = {12/24/2020}, pages = {047001}, abstract = {

It was shown recently, building on work of Alexakis, Balehowksy, and Nachman that the geometry of (some portion of) a manifold with boundary is uniquely fixed by the areas of a foliation of two-dimensional disk-shaped surfaces anchored to the boundary. In the context of AdS/CFT, this implies that (a portion of) a four-dimensional bulk geometry can be fixed uniquely from the entanglement entropies of disk-shaped boundary regions, subject to several constraints. In this Note, we loosen some of these constraints, in particular allowing for the bulk foliation of extremal surfaces to be local and removing the constraint of disk topology; these generalizations ensure uniqueness of more of the deep bulk geometry by allowing for e.g. surfaces anchored on disconnected asymptotic boundaries, or HRT surfaces past a phase transition. We also explore in more depth the generality of the local foliation requirement, showing that even in a highly dynamical geometry like AdS-Vaidya it is satisfied.

}, doi = {https://iopscience.iop.org/article/10.1088/1361-6382/abcfd0/pdf}, url = {https://arxiv.org/abs/2009.07850}, author = {Ning Bao and ChunJun Cao and Sebastian Fischetti and Jason Pollack and Yibo Zhong} } @article {2556, title = {Nearly optimal time-independent reversal of a spin chain}, journal = {accepted for publication in Physical Review Research}, year = {2020}, month = {3/5/2020}, abstract = {

We propose a time-independent Hamiltonian protocol for the reversal of qubit ordering in a chain of N spins. Our protocol has an easily implementable nearest-neighbor, transverse-field Ising model Hamiltonian with time-independent, non-uniform couplings. Under appropriate normalization, we implement this state reversal three times faster than a naive approach using SWAP gates, in time comparable to a protocol of Raussendorf [Phys. Rev. A 72, 052301 (2005)] that requires dynamical control. We also prove lower bounds on state reversal by using results on the entanglement capacity of Hamiltonians and show that we are within a factor 1.502(1+1/N) of the shortest time possible. Our lower bound holds for all nearest-neighbor qubit protocols with arbitrary finite ancilla spaces and local operations and classical communication. Finally, we extend our protocol to an infinite family of nearest-neighbor, time-independent Hamiltonian protocols for state reversal. This includes chains with nearly uniform coupling that may be especially feasible for experimental implementation.\ 

}, url = {https://arxiv.org/abs/2003.02843}, author = {Aniruddha Bapat and Eddie Schoute and Alexey V. Gorshkov and Andrew M. Childs} } @article {2560, title = {Noncommuting conserved charges in quantum many-body thermalization}, journal = {Phys. Rev. E }, volume = {101}, year = {2020}, month = {4/15/2020}, abstract = {

In statistical mechanics, a small system exchanges conserved quantities\—heat, particles, electric charge, etc.\—with a bath. The small system thermalizes to the canonical ensemble or the grand canonical ensemble, etc., depending on the quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system\&$\#$39;s long-time state was dubbed \“the non-Abelian thermal state (NATS).\” We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

}, doi = {https://doi.org/10.1103/PhysRevE.101.042117}, url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.042117}, author = {Nicole Yunger Halpern and Michael E. Beverland and Amir Kalev} } @article {2363, title = {Non-equilibrium fixed points of coupled Ising models}, journal = {Phys. Rev. X }, volume = {10}, year = {2020}, month = {2/26/2020}, abstract = {

Driven-dissipative systems can exhibit non-equilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions present in these systems generically exhibit an effectively classical equilibrium behavior in spite of their quantum non-equilibrium origin. In this paper, we show that multicritical points in driven-dissipative systems can give rise to genuinely non-equilibrium behavior. We investigate a non-equilibrium driven-dissipative model of interacting bosons that exhibits two distinct phase transitions: one from a high- to a low-density phase---reminiscent of a liquid-gas transition---and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) Z2 symmetry. They, however, coalesce at a multicritical point giving rise to a non-equilibrium model of coupled Ising-like order parameters described by a Z2\×Z2 symmetry. Using a dynamical renormalization-group approach, we show that a pair of non-equilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents, spiraling phase boundaries, and a complex Liouvillian gap even close to the phase transition. As direct evidence of the non-equilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes \"hotter\" and \"hotter\" at longer and longer wavelengths. Finally, we argue that this non-equilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.

}, doi = {https://doi.org/10.1103/PhysRevX.10.011039}, url = {https://arxiv.org/abs/1903.02569}, author = {Jeremy T. Young and Alexey V. Gorshkov and Michael Foss-Feig and Mohammad F. Maghrebi} } @article {2642, title = {Non-equilibrium steady state phases of the interacting Aubry-Andre-Harper model}, year = {2020}, month = {5/21/2020}, abstract = {

Here we study the phase diagram of the Aubry-Andre-Harper model in the presence of strong interactions as the strength of the quasiperiodic potential is varied. Previous work has established the existence of many-body localized phase at large potential strength; here, we find a rich phase diagram in the delocalized regime characterized by spin transport and unusual correlations. We calculate the non-equilibrium steady states of a boundary-driven strongly interacting Aubry-Andre-Harper model by employing the time-evolving block decimation algorithm on matrix product density operators. From these steady states, we extract spin transport as a function of system size and quasiperiodic potential strength. This data shows spin transport going from superdiffusive to subdiffusive well before the localization transition; comparing to previous results, we also find that the transport transition is distinct from a transition observed in the speed of operator growth in the model. We also investigate the correlation structure of the steady state and find an unusual oscillation pattern for intermediate values of the potential strength. The unusual spin transport and quantum correlation structure suggest multiple dynamical phases between the much-studied thermal and many-body-localized phases.

}, url = {https://arxiv.org/abs/2005.10835}, author = {Yongchan Yoo and Junhyun Lee and Brian Swingle} } @article {2485, title = {Non-interactive classical verification of quantum computation}, journal = {Theory of Cryptography Conference (TCC)}, volume = {Lecture Notes in Computer Science 12552}, year = {2020}, month = {3/9/2020}, pages = {153-180}, abstract = {

In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. In this work, we show that this same task can in fact be performed non-interactively and in zero-knowledge.
Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We begin by making the first message instance-independent and moving it to an offline setup phase. We then establish a parallel repetition theorem for the resulting three-message protocol, with an asymptotically optimal rate. This, in turn, enables an application of the Fiat-Shamir heuristic, eliminating the second message and giving a non-interactive protocol. Finally, we employ classical non-interactive zero-knowledge (NIZK) arguments and classical fully homomorphic encryption (FHE) to give a zero-knowledge variant of this construction. This yields the first purely classical NIZK argument system for QMA, a quantum analogue of NP.
We establish the security of our protocols under standard assumptions in quantum-secure cryptography. Specifically, our protocols are secure in the Quantum Random Oracle Model, under the assumption that Learning with Errors is quantumly hard. The NIZK construction also requires circuit-private FHE.

}, url = {https://arxiv.org/abs/1911.08101}, author = {Gorjan Alagic and Andrew M. Childs and Alex B. Grilo and Shih-Han Hung} } @article {2571, title = {A note on blind contact tracing at scale with applications to the COVID-19 pandemic}, year = {2020}, month = {4/10/2020}, abstract = {

The current COVID-19 pandemic highlights the utility of contact tracing, when combined with case isolation and social distancing, as an important tool for mitigating the spread of a disease [1]. Contact tracing provides a mechanism of identifying individuals with a high likelihood of previous exposure to a contagious disease, allowing additional precautions to be put in place to prevent continued transmission. Here we consider a cryptographic approach to contact tracing based on secure two-party computation (2PC). We begin by considering the problem of comparing a set of location histories held by two parties to determine whether they have come within some threshold distance while at the same time maintaining the privacy of the location histories. We propose a solution to this problem using pre-shared keys, adapted from an equality testing protocol due to Ishai et al [2]. We discuss how this protocol can be used to maintain privacy within practical contact tracing scenarios, including both app-based approaches and approaches which leverage location history held by telecoms and internet service providers. We examine the efficiency of this approach and show that existing infrastructure is sufficient to support anonymised contact tracing at a national level.

}, url = {https://arxiv.org/abs/2004.05116}, author = {Jack K. Fitzsimons and Atul Mantri and Robert Pisarczyk and Tom Rainforth and Zhikuan Zhao} } @article {2568, title = {On-demand indistinguishable single photons from an efficient and pure source based on a Rydberg ensemble}, year = {2020}, month = {3/4/2020}, abstract = {

Single photons coupled to atomic systems have shown to be a promising platform for developing quantum technologies. Yet a bright on-demand, highly pure and highly indistinguishable single-photon source compatible with atomic platforms is lacking. In this work, we demonstrate such a source based on a strongly interacting Rydberg system. The large optical nonlinearities in a blockaded Rydberg ensemble convert coherent light into a single-collective excitation that can be coherently retrieved as a quantum field. We observe a single-transverse-mode efficiency up to 0.18(2), g(2)=2.0(1.5)\×10\−4, and indistinguishability of 0.982(7), making this system promising for scalable quantum information applications. Accounting for losses, we infer a generation probability up to 0.40(4). Furthermore, we investigate the effects of contaminant Rydberg excitations on the source efficiency. Finally, we introduce metrics to benchmark the performance of on-demand single-photon sources.\ 

}, url = {https://arxiv.org/abs/2003.02202}, author = {Dalia P. Ornelas-Huerta and Alexander N. Craddock and Elizabeth A. Goldschmidt and Andrew J. Hachtel and Yidan Wang and P. Bienias and Alexey V. Gorshkov and Steve L. Rolston and James V. Porto} } @article {2732, title = {One-shot dynamical resource theory}, year = {2020}, month = {12/4/2020}, abstract = {

A fundamental problem in resource theory is to study the manipulation of the resource. Focusing on a general dynamical resource theory of quantum channels, here we consider tasks of one-shot resource distillation and dilution with a single copy of the resource. For any target of unitary channel or pure state preparation channel, we establish a universal strategy to determine upper and lower bounds on rates that convert between any given resource and the target. We show that the rates are related to resource measures based on the channel robustness and the channel hypothesis testing entropy, with regularization factors of the target resource measures. The strategy becomes optimal with converged bounds when the channel robustness is finite and measures of the target resource collapse to the same value. The single-shot result also applies to asymptotic parallel manipulation of channels to obtain asymptotic resource conversion rates. We give several examples of dynamical resources, including the purity, classical capacity, quantum capacity, non-uniformity, coherence, and entanglement of quantum channels. Our results are applicable to general dynamical resource theories with potential applications in quantum communication, fault-tolerant quantum computing, and quantum thermodynamics.

}, url = {https://arxiv.org/abs/2012.02781}, author = {Xiao Yuan and Pei Zeng and Minbo Gao and Qi Zhao} } @article {2456, title = {The operator L{\'e}vy flight: light cones in chaotic long-range interacting systems}, journal = {Phys. Rev. Lett. }, volume = {124}, year = {2020}, month = {7/6/2020}, abstract = {

We propose a generic light cone phase diagram for chaotic long-range r\−α interacting systems, where a linear light cone appears for α\≥d+1/2 in d dimension. Utilizing the dephasing nature of quantum chaos, we argue that the universal behavior of the squared commutator is described by a stochastic model, for which the exact phase diagram is known. We provide an interpretation in terms of the L{\'e}vy flights and show that this suffices to capture the scaling of the squared commutator. We verify these phenomena in numerical computation of a long-range spin chain with up to 200 sites.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.124.180601}, url = {https://arxiv.org/abs/1909.08646}, author = {Tianci Zhou and Shenglong Xu and Xiao Chen and Andrew Guo and Brian Swingle} } @article {2635, title = {Optical quantum memory with optically inaccessible noble-gas spins}, year = {2020}, month = {7/17/2020}, abstract = {

Optical quantum memories, which store and preserve the quantum state of photons, rely on a coherent mapping of the photonic state onto matter states that are optically accessible. Here we outline a new physical mechanism to map the state of photons onto the long-lived but optically inaccessible collective state of noble-gas spins. The mapping employs the coherent spin-exchange interaction arising from random collisions with alkali vapor. We analyze optimal strategies for high-efficiency storage and retrieval of non-classical light at various parameter regimes. Based on these strategies, we identify feasible experimental conditions for realizing efficient quantum memories with noble-gas spins having hours-long coherence times at room temperature and above

}, url = {https://arxiv.org/abs/2007.08770}, author = {Or Katz and Eran Reches and Roy Shaham and Alexey V. Gorshkov and Ofer Firstenberg} } @article {2632, title = {Optimal control for quantum detectors}, year = {2020}, month = {5/12/2020}, abstract = {

Quantum systems are promising candidates for sensing of weak signals as they can provide unrivaled performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-to-noise-ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. We further generalize, using numerical techniques, these results to the background noise being a correlated Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences such as CPMG are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.

}, url = {https://arxiv.org/abs/2005.05995}, author = {Paraj Titum and Kevin M. Schultz and Alireza Seif and Gregory D. Quiroz and B. D. Clader} } @article {2495, title = {Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning}, journal = {Quantum }, volume = {4}, year = {2020}, month = {5/26/2020}, abstract = {

We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an n-mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on \⌈log3(2n+1)\⌉ qubits. The mapping has a simple structure and is optimal in the sense that it is impossible to construct Pauli operators in any fermion-to-qubit mapping acting nontrivially on less than log3(2n) qubits on average. We apply it to the problem of learning k-fermion reduced density matrix (RDM), a problem relevant in various quantum simulation applications. We show that using the ternary-tree mapping one can determine the elements of all k-fermion RDMs, to precision ϵ, by repeating a single quantum circuit for ≲(2n+1)kϵ\−2 times. This result is based on a method we develop here that allows one to determine the elements of all k-qubit RDMs, to precision ϵ, by repeating a single quantum circuit for ≲3kϵ\−2 times, independent of the system size. This improves over existing schemes for determining qubit RDMs.

}, doi = {https://doi.org/10.22331/q-2020-06-04-276}, url = {https://arxiv.org/abs/1910.10746}, author = {Zhang Jiang and Amir Kalev and Wojciech Mruczkiewicz and Hartmut Neven} } @article {2721, title = {Optimal Measurement of Field Properties with Quantum Sensor Networks}, year = {2020}, month = {11/2/2020}, abstract = {

We consider a quantum sensor network of qubit sensors coupled to a field f(x⃗ ;θ⃗ ) analytically parameterized by the vector of parameters θ⃗ . The qubit sensors are fixed at positions x⃗ 1,\…,x⃗ d. While the functional form of f(x⃗ ;θ⃗ ) is known, the parameters θ⃗\  are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function q(θ⃗ ) of these parameters and construct the optimal protocols that achieve these bounds. Our results are obtained from a combination of techniques from quantum information theory and duality theorems for linear programming. They can be applied to many problems, including optimal placement of quantum sensors, field interpolation, and the measurement of functionals of parametrized fields.

}, url = {https://arxiv.org/abs/2011.01259}, author = {Timothy Qian and Jacob Bringewatt and Igor Boettcher and Przemyslaw Bienias and Alexey V. Gorshkov} } @article {2564, title = {Optimal Protocols in Quantum Annealing and QAOA Problems}, year = {2020}, month = {3/19/2020}, abstract = {

Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or \"bang-bang\") structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. Through simulations of various transverse field Ising models, we demonstrate that bang-anneal-bang protocols are more common. The general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

}, url = {https://arxiv.org/abs/2003.08952}, author = {Lucas T. Brady and Christopher L. Baldwin and Aniruddha Bapat and Yaroslav Kharkov and Alexey V. Gorshkov} } @article {2689, title = {Optimal state transfer and entanglement generation in power-law interacting systems}, year = {2020}, month = {10/6/2020}, abstract = {

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law (1/rα) interactions. For all power-law exponents α between d and 2d+1, where d is the dimension of the system, the protocol yields a polynomial speedup for α\>2d and a superpolynomial speedup for α\≤2d, compared to the state of the art. For all α\>d, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states.\ 

}, url = {https://arxiv.org/abs/2010.02930}, author = {Minh C. Tran and Abhinav Deshpande and Andrew Y. Guo and Andrew Lucas and Alexey V. Gorshkov} } @article {2515, title = {Optimal Two-Qubit Circuits for Universal Fault-Tolerant Quantum Computation}, year = {2020}, month = {1/16/2020}, abstract = {

We study two-qubit circuits over the Clifford+CS gate set which consists of Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes with magic state distillation. However, since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is desirable to construct circuits that use few CS gates. In the present paper, we introduce an algorithm to construct optimal circuits for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and efficiently produces a Clifford+CS circuit for U using the least possible number of CS gates. Because our algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for the operator. We give a formal description of these normal forms as walks over certain graphs and use this description to derive an asymptotic lower bound of 5log(1/epsilon)+O(1) on the number CS gates required to epsilon-approximate any 4x4 unitary matrix.\ 

}, url = {https://arxiv.org/abs/2001.05997}, author = {Andrew N. Glaudell and Neil J. Ross and J. M. Taylor} } @article {1951, title = {Parallel Device-Independent Quantum Key Distribution}, journal = {IEEE Transactions on Information Theory}, volume = {66}, year = {2020}, month = {09/2020}, pages = {5567-5584}, abstract = {

A prominent application of quantum cryptography is the distribution of cryptographic keys that are provably secure. Such security proofs were extended by Vazirani and Vidick ( Physical Review Letters , 113, 140501, 2014) to the device-independent (DI) scenario, where the users do not need to trust the integrity of the underlying quantum devices. The protocols analyzed by them and by subsequent authors all require a sequential execution of N multiplayer games, where N is the security parameter. In this work, we prove the security of a protocol where all games are executed in parallel. Besides decreasing the number of time-steps necessary for key generation, this result reduces the security requirements for DI-QKD by allowing arbitrary information leakage of each user\’s inputs within his or her lab. To the best of our knowledge, this is the first parallel security proof for a fully device-independent QKD protocol. Our protocol tolerates a constant level of device imprecision and achieves a linear key rate.

}, doi = {https://doi.org/10.1109/TIT.2020.2986740}, url = {https://arxiv.org/abs/1703.05426}, author = {Rahul Jain and Carl Miller and Yaoyun Shi} } @article {2582, title = {Position Space Decoherence From Long-Range Interaction With Background Gas}, journal = {Bulletin of the American Physical Society}, year = {2020}, month = {06/05/2020}, type = {Invited paper of the DAMOP20 Meeting of The American Physical Society}, abstract = {

Experiments in matter wave interferometry and optomechanics are increasing the spatial extent of wavefunctions of massive quantum systems; this gives rise to new sources of decoherence that must be characterized. Here\ we calculate the position space decoherence of a quantum particle due to interaction\ with a fluctuating classical background gas for several different force laws. We begin\ with the calculation of this effect for the Newton potential. To our knowledge, this\ calculation has not been done before. We then solve the same problem in the case\ of a Yukawa interaction, which interpolates between our long-range force result and\ the well-studied formula for collisional decoherence from a contact interaction. Unlike the contact interaction case, where the decoherence rate becomes independent\ of distance for large quantum particle separations, we observe that a long-range\ interaction leads to quadratic scaling of the decoherence rate with distance even at\ large separations. This work is relevant to the generation of massive superposition\ in optomechanical and atom beam experiments, and to conclude we comment on\ the use of this decoherence signal for gravitational detection of dark matter.\ 

}, url = {http://meetings.aps.org/Meeting/DAMOP20/Session/S08.5}, author = {Jonathan Kunjummen and Daniel Carney and J. M. Taylor} } @article {2558, title = {On the Principles of Differentiable Quantum Programming Languages}, year = {2020}, month = {4/2/2020}, abstract = {

Variational Quantum Circuits (VQCs), or the so-called quantum neural-networks, are predicted to be one of the most important near-term quantum applications, not only because of their similar promises as classical neural-networks, but also because of their feasibility on near-term noisy intermediate-size quantum (NISQ) machines. The need for gradient information in the training procedure of VQC applications has stimulated the development of auto-differentiation techniques for quantum circuits. We propose the first formalization of this technique, not only in the context of quantum circuits but also for imperative quantum programs (e.g., with controls), inspired by the success of differentiable programming languages in classical machine learning. In particular, we overcome a few unique difficulties caused by exotic quantum features (such as quantum no-cloning) and provide a rigorous formulation of differentiation applied to bounded-loop imperative quantum programs, its code-transformation rules, as well as a sound logic to reason about their correctness. Moreover, we have implemented our code transformation in OCaml and demonstrated the resource-efficiency of our scheme both analytically and empirically. We also conduct a case study of training a VQC instance with controls, which shows the advantage of our scheme over existing auto-differentiation for quantum circuits without controls.

}, doi = {https://doi.org/10.1145/3385412.3386011}, url = {https://arxiv.org/abs/2004.01122}, author = {Shaopeng Zhu and Shih-Han Hung and Shouvanik Chakrabarti and Xiaodi Wu} } @article {2604, title = {Probing many-body localization on a noisy quantum computer}, year = {2020}, month = {6/22/2020}, abstract = {

A disordered system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer without error correction is challenging because even weak coupling to a thermal environment destroys most signatures of localization. Fortunately, spectral functions of local operators are known to contain features that can survive the presence of noise. In these spectra, discrete peaks and a soft gap at low frequencies compared to the thermal phase indicate localization. Here, we present the computation of spectral functions on a trapped-ion quantum computer for a one-dimensional Heisenberg model with disorder. Further, we design an error-mitigation technique which is effective at removing the noise from the measurement allowing clear signatures of localization to emerge as the disorder increases. Thus, we show that spectral functions can serve as a robust and scalable diagnostic of many-body localization on the current generation of quantum computers.\ 

}, url = {https://arxiv.org/abs/2006.12355}, author = {D. Zhu and S. Johri and N. H. Nguyen and C. Huerta Alderete and K. A. Landsman and N. M. Linke and C. Monroe and A. Y. Matsuura} } @article {2586, title = {Probing XY phase transitions in a Josephson junction array with tunable frustration}, year = {2020}, month = {1/22/2020}, abstract = {

The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations. These transitions have been extensively studied in the context of two-dimensional XY models -- coupled compasses -- and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U(1)] and discrete chiral (Z2) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U(1) part.

}, url = {https://arxiv.org/abs/2001.07877}, author = {R. Cosmic and K. Kawabata and Y. Ashida and H. Ikegami and S. Furukawa and P. Patil and J. M. Taylor and Y. Nakamura} } @article {2726, title = {Programmable Quantum Annealers as Noisy Gibbs Samplers}, year = {2020}, month = {12/16/2020}, abstract = {

Drawing independent samples from high-dimensional probability distributions represents the major computational bottleneck for modern algorithms, including powerful machine learning frameworks such as deep learning. The quest for discovering larger families of distributions for which sampling can be efficiently realized has inspired an exploration beyond established computing methods and turning to novel physical devices that leverage the principles of quantum computation. Quantum annealing embodies a promising computational paradigm that is intimately related to the complexity of energy landscapes in Gibbs distributions, which relate the probabilities of system states to the energies of these states. Here, we study the sampling properties of physical realizations of quantum annealers which are implemented through programmable lattices of superconducting flux qubits. Comprehensive statistical analysis of the data produced by these quantum machines shows that quantum annealers behave as samplers that generate independent configurations from low-temperature noisy Gibbs distributions. We show that the structure of the output distribution probes the intrinsic physical properties of the quantum device such as effective temperature of individual qubits and magnitude of local qubit noise, which result in a non-linear response function and spurious interactions that are absent in the hardware implementation. We anticipate that our methodology will find widespread use in characterization of future generations of quantum annealers and other emerging analog computing devices.

}, url = {https://arxiv.org/abs/2012.08827}, author = {Marc Vuffray and Carleton Coffrin and Yaroslav A. Kharkov and Andrey Y. Lokhov} } @article {2207, title = {Quantum algorithms and lower bounds for convex optimization}, journal = {Quantum}, volume = {4}, year = {2020}, month = {12/18/2019}, abstract = {

While recent work suggests that quantum computers can speed up the solution of semidefinite programs, little is known about the quantum complexity of more general convex optimization. We present a quantum algorithm that can optimize a convex function over an n-dimensional convex body using O~(n) queries to oracles that evaluate the objective function and determine membership in the convex body. This represents a quadratic improvement over the best-known classical algorithm. We also study limitations on the power of quantum computers for general convex optimization, showing that it requires Ω~(n\−\−\√) evaluation queries and Ω(n\−\−\√) membership queries.

}, doi = {https://doi.org/10.22331/q-2020-01-13-221}, url = {https://arxiv.org/abs/1809.01731}, author = {Shouvanik Chakrabarti and Andrew M. Childs and Tongyang Li and Xiaodi Wu} } @article {2696, title = {Quantum Algorithms for Simulating the Lattice Schwinger Model}, journal = {Quantum}, volume = {4}, year = {2020}, month = {8/5/2020}, type = {INT-PUB-20-008}, abstract = {

The Schwinger model (quantum electrodynamics in 1+1 dimensions) is a testbed for the study of quantum gauge field theories. We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In particular, we perform a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and give upper bounds on the resources needed for simulations in both scenarios. In lattice units, we find a Schwinger model on N/2 physical sites with coupling constant x\−1/2 and electric field cutoff x\−1/2Λ can be simulated on a quantum computer for time 2xT using a number of T-gates or CNOTs in O\˜(N3/2T3/2x\−\−\√Λ) for fixed operator error. This scaling with the truncation Λ is better than that expected from algorithms such as qubitization or QDRIFT. Furthermore, we give scalable measurement schemes and algorithms to estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density. Finally, we bound the root-mean-square error in estimating this observable via simulation as a function of the diamond distance between the ideal and actual CNOT channels. This work provides a rigorous analysis of simulating the Schwinger model, while also providing benchmarks against which subsequent simulation algorithms can be tested.\ 

}, doi = {https://doi.org/10.22331/q-2020-08-10-306}, url = {https://arxiv.org/abs/2002.11146}, author = {Alexander F. Shaw and Pavel Lougovski and Jesse R. Stryker and Nathan Wiebe} } @article {2702, title = {Quantum algorithms for the polynomial eigenvalue problems}, year = {2020}, month = {10/28/2020}, abstract = {

Polynomial eigenvalue problems (PEPs) arise in a variety of science and engineering applications, and many breakthroughs in the development of classical algorithms to solve PEPs have been made in the past decades. Here we attempt to solve PEPs in a quantum computer. Firstly, for generalized eigenvalue problems (GEPs) $A\x = \lambda B\x$ with A,B symmetric, and B positive definite, we give a quantum algorithm based on block-encoding and quantum phase estimation. In a more general case when B is invertible, B\−1A is diagonalizable and all the eigenvalues are real, we propose a quantum algorithm based on the Fourier spectral method to solve ordinary differential equations (ODEs). The inputs of our algorithms can be any desired states, and the outputs are superpositions of the eigenpairs. The complexities are polylog in the matrix size and linear in the precision. The dependence on precision is optimal. Secondly, we show that when B is singular, any quantum algorithm uses at least Ω(n\−\−\√) queries to compute the eigenvalues, where n is the matrix size. Thirdly, based on the linearization method and the connection between PEPs and higher-order ODEs, we provide two quantum algorithms to solve PEPs by extending the quantum algorithm for GEPs. We also give detailed complexity analysis of the algorithm for two special types of quadratic eigenvalue problems that are important in practice. Finally, under an extra assumption, we propose a quantum algorithm to solve PEPs when the eigenvalues are complex.

}, url = {https://arxiv.org/abs/2010.15027}, author = {Changpeng Shao and Jin-Peng Liu} } @article {2626, title = {On Quantum Chosen-Ciphertext Attacks and Learning with Errors}, journal = {Cryptography}, volume = {4}, year = {2020}, month = {3/21/2020}, pages = {10}, abstract = {

Large-scale quantum computing poses a major threat to classical public-key cryptography. Recently, strong \“quantum access\” security models have shown that numerous symmetric-key cryptosystems are also vulnerable. In this paper, we consider classical encryption in a model that grants the adversary quantum oracle access to encryption and decryption, but where we restrict the latter to non-adaptive (i.e., pre-challenge) queries only. We formalize this model using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. We show that the standard pseudorandom function ( PRF )-based encryption schemes are QCCA1 -secure when instantiated with quantum-secure primitives. Our security proofs use a strong bound on quantum random-access codes with shared randomness. Revisiting plain IND\−CPA -secure Learning with Errors ( LWE ) encryption, we show that leaking only a single quantum decryption query (and no other leakage or queries of any kind) allows the adversary to recover the full secret key with constant success probability. Information-theoretically, full recovery of the key in the classical setting requires at least a linear number of decryption queries. Our results thus challenge the notion that LWE is unconditionally \“just as secure\” quantumly as it is classically. The algorithm at the core of our attack is a new variant of the well-known Bernstein\–Vazirani algorithm. Finally, we emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.

}, doi = {https://doi.org/10.3390/cryptography4010010}, author = {Gorjan Alagic and Stacey Jeffery and Maris Ozols and Alexander Poremba} } @article {2680, title = {Quantum coding with low-depth random circuits}, year = {2020}, month = {10/19/2020}, abstract = {

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity in D\≥1 spatial dimensions to generate quantum error-correcting codes. For random stabilizer codes and the erasure channel, we find strong evidence that a depth O(logN) random circuit is necessary and sufficient to converge (with high probability) to zero failure probability for any finite amount below the channel capacity for any D. Previous results on random circuits have only shown that O(N1/D) depth suffices or that O(log3N) depth suffices for all-to-all connectivity (D\→\∞). We then study the critical behavior of the erasure threshold in the so-called moderate deviation limit, where both the failure probability and the distance to the channel capacity converge to zero with N. We find that the requisite depth scales like O(logN) only for dimensions D\≥2, and that random circuits require O(N\−\−\√) depth for D=1. Finally, we introduce an \"expurgation\" algorithm that uses quantum measurements to remove logical operators that cause the code to fail by turning them into either additional stabilizers or into gauge operators in a subsystem code. With such targeted measurements, we can achieve sub-logarithmic depth in D\≥2 spatial dimensions below capacity without increasing the maximum weight of the check operators. We find that for any rate beneath the capacity, high-performing codes with thousands of logical qubits are achievable with depth 4-8 expurgated random circuits in D=2 dimensions. These results indicate that finite-rate quantum codes are practically relevant for near-term devices and may significantly reduce the resource requirements to achieve fault tolerance for near-term applications.\ 

}, url = {https://arxiv.org/abs/2010.09775}, author = {Michael Gullans and Stefan Krastanov and David A. Huse and Liang Jiang and Steven T. Flammia} } @article {2557, title = {Quantum Coupon Collector}, journal = {Proceedings of the 15th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2020), Leibniz International Proceedings in Informatics}, volume = {158}, year = {2020}, month = {2/18/2020}, pages = {10:1-10:17}, abstract = {

We study how efficiently a k-element set S\⊆[n] can be learned from a uniform superposition |S\⟩ of its elements. One can think of |S\⟩=\∑i\∈S|i\⟩/|S|\−\−\−\√ as the quantum version of a uniformly random sample over S, as in the classical analysis of the {\textquoteleft}{\textquoteleft}coupon collector problem.\&$\#$39;\&$\#$39; We show that if k is close to n, then we can learn S using asymptotically fewer quantum samples than random samples. In particular, if there are n\−k=O(1) missing elements then O(k) copies of |S\⟩ suffice, in contrast to the Θ(klogk) random samples needed by a classical coupon collector. On the other hand, if n\−k=Ω(k), then Ω(klogk) quantum samples are~necessary. More generally, we give tight bounds on the number of quantum samples needed for every k and n, and we give efficient quantum learning algorithms. We also give tight bounds in the model where we can additionally reflect through |S\⟩. Finally, we relate coupon collection to a known example separating proper and improper PAC learning that turns out to show no separation in the quantum case.

}, doi = {10.4230/LIPIcs.TQC.2020.10}, url = {https://arxiv.org/abs/2002.07688}, author = {Srinivasan Arunachalam and Aleksandrs Belovs and Andrew M. Childs and Robin Kothari and Ansis Rosmanis and Ronald de Wolf} } @article {2583, title = {Quantum Lifshitz criticality in a frustrated two-dimensional XY model}, journal = {Phys. Rev. B }, volume = {101}, year = {2020}, month = {01/09/2020}, abstract = {

Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states,
driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point.
Quantum fluctuations change the nature of the transition. In particular, it has been argued previously that in the\ two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a\ Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition\ problem for the 2D frustrated XY model. Specifically, we show that, unlike the SU (2) symmetric Lifshitz case,\ in the XY model, the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical\ exponents in the N{\'e}el and in the spin spiral state and relate these to properties of the SL. We also solve the\ transition problem at a finite temperature and discuss the role of topological excitations.

}, doi = {https://doi.org/10.1103/PhysRevB.101.035114}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.101.035114}, author = {Yaroslav A. Kharkov and Jaan Oitmaa and Oleg P. Sushkov} } @article {2497, title = {Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry}, journal = {Phys. Rev. A}, volume = {102}, year = {2020}, month = {9/11/2020}, abstract = {

We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincar{\'e} disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Our analysis also reveals in which sense discrete hyperbolic lattices emulate the continuous geometry of negatively curved space and thus can be used to resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

}, doi = {https://doi.org/10.1103/PhysRevA.102.032208}, url = {https://arxiv.org/abs/1910.12318}, author = {Igor Boettcher and Przemyslaw Bienias and Ron Belyansky and Alicia J. Koll{\'a}r and Alexey V. Gorshkov} } @article {2646, title = {Quantum simulation with hybrid tensor networks}, year = {2020}, month = {7/2/2020}, abstract = {

Tensor network theory and quantum simulation are respectively the key classical and quantum methods in understanding many-body quantum physics. Here we show hybridization of these two seemingly independent methods, inheriting both their distinct advantageous features of efficient representations of many-body wave functions. We introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors. As an example, we demonstrate efficient quantum simulation with hybrid tree tensor networks that use quantum hardware whose size is significantly smaller than the one of the target system. We numerically test our method for finding the ground state of 1D and 2D spin systems of up to 8\×8 and 4\×3 qubits with operations only acting on 8+1 and 4+1 qubits, respectively. Our approach paves the way to the near-term quantum simulation of large practical problems with intermediate size quantum hardware, with potential applications in quantum chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.

}, url = {https://arxiv.org/abs/2007.00958}, author = {Xiao Yuan and Jinzhao Sun and Junyu Liu and Qi Zhao and You Zhou} } @article {2333, title = {Quantum spectral methods for differential equations}, journal = {Commun. Math. Phys. }, volume = {375}, year = {2020}, month = {2/18/2020}, pages = {1427-1457}, abstract = {

Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a d-dimensional system of linear equations or linear differential equations with complexity poly(logd). While several of these algorithms approximate the solution to within ε with complexity poly(log(1/ε)), no such algorithm was previously known for differential equations with time-dependent coefficients. Here we develop a quantum algorithm for linear ordinary differential equations based on so-called spectral methods, an alternative to finite difference methods that approximates the solution globally. Using this approach, we give a quantum algorithm for time-dependent initial and boundary value problems with complexity poly(logd,log(1/ε)).

}, doi = {https://doi.org/10.1007/s00220-020-03699-z}, url = {https://arxiv.org/abs/1901.00961}, author = {Andrew M. Childs and Jin-Peng Liu} } @article {2570, title = {Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer}, year = {2020}, month = {2/6/2020}, abstract = {

The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range of quantum algorithms. Here we present the circuit-based implementation of a discrete-time quantum walk in position space on a five-qubit trapped-ion quantum processor. We encode the space of walker positions in particular multi-qubit states and program the system to operate with different quantum walk parameters, experimentally realizing a Dirac cellular automaton with tunable mass parameter. The quantum walk circuits and position state mapping scale favorably to a larger model and physical systems, allowing the implementation of any algorithm based on discrete-time quantum walks algorithm and the dynamics associated with the discretized version of the Dirac equation.

}, url = {https://arxiv.org/abs/2002.02537}, author = {C. Huerta Alderete and Shivani Singh and Nhung H. Nguyen and Daiwei Zhu and Radhakrishnan Balu and Christopher Monroe and C. M. Chandrashekar and Norbert M. Linke} } @article {2628, title = {Quantum-Access-Secure Message Authentication via Blind-Unforgeability}, journal = {In: Canteaut A., Ishai Y. (eds) Advances in Cryptology {\textendash} EUROCRYPT 2020. Lecture Notes in Computer Science, Springer, Cham}, volume = {12-17}, year = {2020}, month = {5/1/2020}, pages = {788-817 }, type = {inproceedings}, abstract = {

Formulating and designing authentication of classical messages in the presence of adversaries with quantum query access has been a longstanding challenge, as the familiar classical notions of unforgeability do not directly translate into meaningful notions in the quantum setting. A particular difficulty is how to fairly capture the notion of \“predicting an unqueried value\” when the adversary can query in quantum superposition.

We propose a natural definition of unforgeability against quantum adversaries called blind unforgeability. This notion defines a function to be predictable if there exists an adversary who can use \“partially blinded\” oracle access to predict values in the blinded region. We support the proposal with a number of technical results. We begin by establishing that the notion coincides with EUF-CMA in the classical setting and go on to demonstrate that the notion is satisfied by a number of simple guiding examples, such as random functions and quantum-query-secure pseudorandom functions. We then show the suitability of blind unforgeability for supporting canonical constructions and reductions. We prove that the \“hash-and-MAC\” paradigm and the Lamport one-time digital signature scheme are indeed unforgeable according to the definition. To support our analysis, we additionally define and study a new variety of quantum-secure hash functions called Bernoulli-preserving.

Finally, we demonstrate that blind unforgeability is strictly stronger than a previous definition of Boneh and Zhandry [EUROCRYPT \’13, CRYPTO \’13] and resolve an open problem concerning this previous definition by constructing an explicit function family which is forgeable yet satisfies the definition.

}, doi = {https://doi.org/10.1007/978-3-030-45727-3_27}, author = {Gorjan Alagic and Christian Majenz and Alexander Russell and Fang Song} } @article {2716, title = {Quasi-polynomial Time Approximation of Output Probabilities of Constant-depth, Geometrically-local Quantum Circuits}, journal = {Accepted to QIP 2021}, year = {2020}, month = {12/10/2020}, abstract = {

We present a classical algorithm that, for any 3D geometrically-local, constant-depth quantum circuit C, and any bit string x\∈{0,1}n, can compute the quantity |\<x|C|0\⊗n\>|2 to within any inverse-polynomial additive error in quasi-polynomial time. It is known that it is $\#$P-hard to compute this same quantity to within 2\−n2 additive error [Mov20]. The previous best known algorithm for this problem used O(2n1/3poly(1/ε)) time to compute probabilities to within additive error ε [BGM20]. Notably, the [BGM20] paper included an elegant polynomial time algorithm for the same estimation task with 2D circuits, which makes a novel use of 1D Matrix Product States carefully tailored to the 2D geometry of the circuit in question. Surprisingly, it is not clear that it is possible to extend this use of MPS to address the case of 3D circuits in polynomial time. This raises a natural question as to whether the computational complexity of the 3D problem might be drastically higher than that of the 2D problem. In this work we address this question by exhibiting a quasi-polynomial time algorithm for the 3D case. In order to surpass the technical barriers encountered by previously known techniques we are forced to pursue a novel approach: Our algorithm has a Divide-and-Conquer structure, constructing a recursive sub-division of the given 3D circuit using carefully designed block-encodings, each creating a 3D-local circuit on at most half the number of qubits as the original. This division step is then applied recursively, expressing the original quantity as a weighted sum of smaller and smaller 3D-local quantum circuits. A central technical challenge is to control correlations arising from the entanglement that may exist between the different circuit \"pieces\" produced this way.

}, url = {https://arxiv.org/abs/2012.05460}, author = {Nolan J. Coble and Matthew Coudron} } @article {2820, title = {Quasi-polynomial time approximation of output probabilities of geometrically-local, shallow quantum circuits}, year = {2020}, month = {12/10/2020}, abstract = {

We present a classical algorithm that, for any 3D geometrically-local, polylogarithmic-depth quantum circuit C acting on n qubits, and any bit string x\∈{0,1}n, can compute the quantity |\<x|C|0\⊗n\>|2 to within any inverse-polynomial additive error in quasi-polynomial time. It is known that it is $\#$P-hard to compute this same quantity to within 2\−n2 additive error [Mov20, KMM21]. The previous best known algorithm for this problem used O(2n1/3poly(1/ϵ)) time to compute probabilities to within additive error ϵ [BGM20]. Notably, the [BGM20] paper included an elegant polynomial time algorithm for this estimation task restricted to 2D circuits, which makes a novel use of 1D Matrix Product States (MPS) carefully tailored to the 2D geometry of the circuit in question. Surprisingly, it is not clear that it is possible to extend this use of MPS to address the case of 3D circuits in polynomial time. This raises a natural question as to whether the computational complexity of the 3D problem might be drastically higher than that of the 2D problem. In this work we address this question by exhibiting a quasi-polynomial time algorithm for the 3D case. In order to surpass the technical barriers encountered by previously known techniques we are forced to pursue a novel approach.
Our algorithm has a Divide-and-Conquer structure, demonstrating how to approximate the desired quantity via several instantiations of the same problem type, each involving 3D-local circuits on about half the number of qubits as the original. This division step is then applied recursively, expressing the original quantity as a weighted combination of smaller and smaller 3D-local quantum circuits. A central technical challenge is to control correlations arising from entanglement that may exist between the different circuit {\textquoteleft}{\textquoteleft}pieces\" produced this way.

}, url = {https://arxiv.org/abs/2012.05460}, author = {Nolan J. Coble and Matthew Coudron} } @article {2563, title = {Random Quantum Batteries}, journal = {Phys. Rev. Research }, volume = {2}, year = {2020}, month = {5/5/2020}, abstract = {

Quantum nano-devices are fundamental systems in quantum thermodynamics that have been the subject of profound interest in recent years. Among these, quantum batteries play a very important role. In this paper we lay down a theory of random quantum batteries and provide a systematic way of computing the average work and work fluctuations in such devices by investigating their typical behavior. We show that the performance of random quantum batteries exhibits typicality and depends only on the spectral properties of the time evolving operator, the initial state and the measuring Hamiltonian. At given revival times a random quantum battery features a quantum advantage over classical random batteries. Our method is particularly apt to be used both for exactly solvable models like the Jaynes-Cummings model or in perturbation theory, e.g., systems subject to harmonic perturbations. We also study the setting of quantum adiabatic random batteries.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.023095}, url = {https://arxiv.org/abs/1908.08064}, author = {Francesco Caravelli and Ghislaine Coulter-De Wit and Luis Pedro Garc{\'\i}a-Pintos and Alioscia Hamma} } @article {2727, title = {Raw Image Deblurring}, year = {2020}, month = {12/8/2020}, abstract = {

Deep learning-based blind image deblurring plays an essential role in solving image blur since all existing kernels are limited in modeling the real world blur. Thus far, researchers focus on powerful models to handle the deblurring problem and achieve decent results. For this work, in a new aspect, we discover the great opportunity for image enhancement (e.g., deblurring) directly from RAW images and investigate novel neural network structures benefiting RAW-based learning. However, to the best of our knowledge, there is no available RAW image deblurring dataset. Therefore, we built a new dataset containing both RAW images and processed sRGB images and design a new model to utilize the unique characteristics of RAW images. The proposed deblurring model, trained solely from RAW images, achieves the state-of-art performance and outweighs those trained on processed sRGB images. Furthermore, with fine-tuning, the proposed model, trained on our new dataset, can generalize to other sensors. Additionally, by a series of experiments, we demonstrate that existing deblurring models can also be improved by training on the RAW images in our new dataset. Ultimately, we show a new venue for further opportunities based on the devised novel raw-based deblurring method and the brand-new Deblur-RAW dataset.

}, url = {https://arxiv.org/abs/2012.04264}, author = {Chih-Hung Liang and Yu-An Chen and Yueh-Cheng Liu and Winston H. Hsu} } @article {2685, title = {Ray-based classification framework for high-dimensional data}, journal = {Proceedings of the Machine Learning and the Physical Sciences Workshop at NeurIPS 2020, Vancouver, Canada}, year = {2020}, month = {10/1/2020}, abstract = {

While classification of arbitrary structures in high dimensions may require complete quantitative information, for simple geometrical structures, low-dimensional qualitative information about the boundaries defining the structures can suffice. Rather than using dense, multi-dimensional data, we propose a deep neural network (DNN) classification framework that utilizes a minimal collection of one-dimensional representations, called \emph{rays}, to construct the \"fingerprint\" of the structure(s) based on substantially reduced information. We empirically study this framework using a synthetic dataset of double and triple quantum dot devices and apply it to the classification problem of identifying the device state. We show that the performance of the ray-based classifier is already on par with traditional 2D images for low dimensional systems, while significantly cutting down the data acquisition cost.

}, url = {https://arxiv.org/abs/2010.00500}, author = {Justyna P. Zwolak and Sandesh S. Kalantre and Thomas McJunkin and Brian J. Weber and J. M. Taylor} } @article {2636, title = {Realizing and Probing Baryonic Excitations in Rydberg Atom Arrays}, year = {2020}, month = {7/14/2020}, abstract = {

We propose a realization of mesonic and baryonic quasiparticle excitations in Rydberg atom arrays with programmable interactions. Recent experiments have shown that such systems possess a Z3-ordered crystalline phase whose low-energy quasiparticles are defects in the crystalline order. By engineering a Z3-translational-symmetry breaking field on top of the Rydberg-blockaded Hamiltonian, we show that different types of defects experience confinement, and as a consequence form mesonic or baryonic quasiparticle excitations. We illustrate the formation of these quasiparticles by studying a quantum chiral clock model related to the Rydberg Hamiltonian. We then propose an experimental protocol involving out-of-equilibrium dynamics to directly probe the spectrum of the confined excitations. We show that the confined quasiparticle spectrum can limit quantum information spreading in this system. This proposal is readily applicable to current Rydberg experiments, and the method can be easily generalized to more complex confined excitations (e.g. {\textquoteleft}tetraquarks\&$\#$39;, {\textquoteleft}pentaquarks\&$\#$39;) in phases with Zq order for q\>3.\ 

}, url = {https://arxiv.org/abs/2007.07258}, author = {Fangli Liu and Seth Whitsitt and Przemyslaw Bienias and Rex Lundgren and Alexey V. Gorshkov} } @article {2681, title = {Resonant enhancement of three-body loss between strongly interacting photons}, year = {2020}, month = {10/19/2020}, abstract = {

Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong or even stronger than two-body interactions. The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly-interacting, and topological phases of matter. Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored. Using a renormalization group technique to solve the three-body Schr{\"o}dinger equation, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons. We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiment

}, url = {https://arxiv.org/abs/2010.09772}, author = {Marcin Kalinowski and Yidan Wang and Przemyslaw Bienias and Michael Gullans and Dalia P. Ornelas-Huerta and Alexander N. Craddock and Steven L. Rolston and J. V. Porto and Hans Peter B{\"u}chler and Alexey V. Gorshkov} } @article {2718, title = {Robust Encoding of a Qubit in a Molecule}, journal = {Phys. Rev. X}, volume = {10}, year = {2020}, month = {9/1/2020}, abstract = {

We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of rotational states of a rigid body. These codes, which protect against both drift in the body\’s orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules as well as nuclear states of molecules and atoms. We also describe codes associated with general non-Abelian groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.

}, doi = {https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.031050}, url = {https://arxiv.org/abs/1911.00099}, author = {Victor V. Albert and Jacob P. Covey and John Preskill} } @article {2501, title = {Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning}, journal = {to appear in Proceedings of STOC 2020}, year = {2020}, month = {6/18/2020}, abstract = {

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang\&$\#$39;s breakthrough quantum-inspired algorithm for recommendation systems [STOC\&$\#$39;19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gily{\'e}n et al. [STOC\&$\#$39;19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all recent results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: l2-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.

}, doi = {https://doi.org/10.1145/3357713.3384314}, url = {https://arxiv.org/abs/1910.06151}, author = {Nai-Hui Chia and Andras Gilyen and Tongyang Li and Han-Hsuan Lin and Ewin Tang and Chunhao Wang} } @article {2693, title = {Search for composite dark matter with optically levitated sensors}, journal = {Phys. Rev. Lett. }, volume = {125}, year = {2020}, month = {11/2/2020}, abstract = {

Results are reported from a search for a class of composite dark matter models with feeble, long-range interactions with normal matter. We search for impulses arising from passing dark matter particles by monitoring the mechanical motion of an optically levitated nanogram mass over the course of several days. Assuming such particles constitute the dominant component of dark matter, this search places upper limits on their interaction with neutrons of αn\≤1.2\×10\−7 at 95\% confidence for dark matter masses between 1--10 TeV and mediator masses mφ\≤0.1 eV. Due to the large enhancement of the cross-section for dark matter to coherently scatter from a nanogram mass (\∼1029 times that for a single neutron) and the ability to detect momentum transfers as small as \∼200 MeV/c, these results provide sensitivity to certain classes of composite dark matter models that substantially exceeds existing searches, including those employing kg-scale or ton-scale targets. Extensions of these techniques can enable directionally-sensitive searches for a broad class of previously inaccessible heavy dark matter candidates.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.125.181102}, url = {https://arxiv.org/abs/2007.12067}, author = {Fernando Monteiro and Gadi Afek and Daniel Carney and Gordan Krnjaic and Jiaxiang Wang and David C. Moore} } @article {2678, title = {Secure Quantum Two-Party Computation: Impossibility and Constructions}, year = {2020}, month = {10/15/2020}, abstract = {

Secure two-party computation considers the problem of two parties computing a joint function of their private inputs without revealing anything beyond the output of the computation. In this work, we take the first steps towards understanding the setting in which the two parties want to evaluate a joint quantum functionality while using only a classical channel between them. Our first result indicates that it is in general impossible to realize a two-party quantum functionality against malicious adversaries with black-box simulation, relying only on classical channels. The negative result stems from reducing the existence of a black-box simulator to an extractor for classical proof of quantum knowledge, which in turn leads to violation of the quantum no-cloning. Next, we introduce the notion of oblivious quantum function evaluation (OQFE). An OQFE is a two-party quantum cryptographic primitive with one fully classical party (Alice) whose input is (a classical description of a) quantum unitary, U, and a quantum party (Bob) whose input is a quantum state, ψ. In particular, Alice receives a classical output corresponding to the measurement of U(ψ) while Bob receives no output. In OQFE, Bob remains oblivious to Alice\&$\#$39;s input, while Alice learns nothing about ψ more than what can be learned from the output. We present two constructions, one secure against semi-honest parties and the other against malicious parties. Due to the no-go result mentioned above, we consider what is arguably the best possible notion obtainable in our model concerning malicious adversaries: one-sided simulation security. Our protocol relies on the assumption of injective homomorphic trapdoor OWFs, which in turn rely on the LWE problem. As a result, we put forward a first, simple and modular, construction of one-sided quantum two-party computation and quantum oblivious transfer over classical networks.

}, url = {https://arxiv.org/abs/2010.07925}, author = {Michele Ciamp and Alexandru Cojocaru and Elham Kashefi and Atul Mantri} } @article {2610, title = {Security Limitations of Classical-Client Delegated Quantum Computing}, year = {2020}, month = {7/3/2020}, abstract = {

Secure delegated quantum computing allows a computationally weak client to outsource an arbitrary quantum computation to an untrusted quantum server in a privacy-preserving manner. One of the promising candidates to achieve classical delegation of quantum computation is classical-client remote state preparation (RSPCC), where a client remotely prepares a quantum state using a classical channel. However, the privacy loss incurred by employing RSPCC as a sub-module is unclear.
In this work, we investigate this question using the Constructive Cryptography framework by Maurer and Renner (ICS\&$\#$39;11). We first identify the goal of RSPCC as the construction of ideal RSP resources from classical channels and then reveal the security limitations of using RSPCC. First, we uncover a fundamental relationship between constructing ideal RSP resources (from classical channels) and the task of cloning quantum states. Any classically constructed ideal RSP resource must leak to the server the full classical description (possibly in an encoded form) of the generated quantum state, even if we target computational security only. As a consequence, we find that the realization of common RSP resources, without weakening their guarantees drastically, is impossible due to the no-cloning theorem. Second, the above result does not rule out that a specific RSPCC protocol can replace the quantum channel at least in some contexts, such as the Universal Blind Quantum Computing (UBQC) protocol of Broadbent et al. (FOCS \&$\#$39;09). However, we show that the resulting UBQC protocol cannot maintain its proven composable security as soon as RSPCC is used as a subroutine. Third, we show that replacing the quantum channel of the above UBQC protocol by the RSPCC protocol QFactory of Cojocaru et al. (Asiacrypt \&$\#$39;19), preserves the weaker, game-based, security of UBQC.

}, url = {https://arxiv.org/abs/2007.01668}, author = {Christian Badertscher and Alexandru Cojocaru and L{\'e}o Colisson and Elham Kashefi and Dominik Leichtle and Atul Mantri and Petros Wallden} } @article {2403, title = {Signaling and Scrambling with Strongly Long-Range Interactions}, journal = {Physical Review A}, volume = {102}, year = {2020}, month = {7/8/2020}, abstract = {

Strongly long-range interacting quantum systems---those with interactions decaying as a power-law 1/rα in the distance r on a D-dimensional lattice for α\≤D---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for α\≤D/2. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all α\<D. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture.\ 

}, doi = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.010401}, url = {https://arxiv.org/abs/1906.02662}, author = {Andrew Y. Guo and Minh C. Tran and Andrew M. Childs and Alexey V. Gorshkov and Zhe-Xuan Gong} } @article {2600, title = {Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion}, year = {2020}, month = {6/3/2020}, abstract = {

We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the dynamics due to the diagonal component of the Hamiltonian from the dynamics generated by its off-diagonal part, which we encode using the linear combination of unitaries technique. Our method has an optimal dependence on the desired precision and, as we illustrate, generally requires considerably fewer resources than the current state-of-the-art. We provide an analysis of resource costs for several sample models.

}, url = {https://arxiv.org/abs/2006.02539}, author = {Amir Kalev and Itay Hen} } @article {2377, title = {Simulating large quantum circuits on a small quantum computer}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {12/8/2020}, abstract = {

Limited quantum memory is one of the most important constraints for near-term quantum devices. Understanding whether a small quantum computer can simulate a larger quantum system, or execute an algorithm requiring more qubits than available, is both of theoretical and practical importance. In this Letter, we introduce cluster parameters K and d of a quantum circuit. The tensor network of such a circuit can be decomposed into clusters of size at most d with at most K qubits of inter-cluster quantum communication. Our main result is a simulation scheme of any (K,d)-clustered quantum circuit on a d-qubit machine in time roughly 2O(K). An important application of our result is the simulation of clustered quantum systems---such as large molecules---that can be partitioned into multiple significantly smaller clusters with weak interactions among them. Another potential application is quantum optimization: we demonstrate numerically that variational quantum eigensolvers can still perform well when restricted to clustered circuits, thus making it feasible to study large quantum systems on small quantum devices.

}, doi = {https://doi.org/10.1103/PhysRevLett.125.150504}, url = {https://arxiv.org/abs/1904.00102}, author = {Tianyi Peng and Aram Harrow and Maris Ozols and Xiaodi Wu} } @article {2672, title = {A Sparse Model of Quantum Holography}, year = {2020}, month = {8/5/2020}, abstract = {

We study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, k, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed k. We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when k is of order unity. In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic. Our argument proceeds by constructing a path integral for the sparse model which reproduces the conventional SYK path integral plus gapped fluctuations. The sparsity of the model permits larger scale numerical calculations than previously possible, the results of which are consistent with the path integral analysis. Additionally, we show that the sparsity of the model considerably reduces the cost of quantum simulation algorithms. This makes the sparse SYK model the most efficient currently known route to simulate a holographic model of quantum gravity. We also define and study a sparse supersymmetric SYK model, with similar conclusions to the non-supersymmetric case. Looking forward, we argue that the class of models considered here constitute an interesting and relatively unexplored sparse frontier in quantum many-body physics.

}, url = {https://arxiv.org/abs/2008.02303}, author = {Shenglong Xu and Leonard Susskind and Yuan Su and Brian Swingle} } @article {2644, title = {Spin-Mediated Mott Excitons}, year = {2020}, month = {4/22/2020}, abstract = {

Motivated by recent experiments on Mott insulators, in both iridates and ultracold atoms, we theoretically study the effects of magnetic order on the Mott-Hubbard excitons. In particular, we focus on spin-mediated doublon-holon pairing in Hubbard materials. We use several complementary theoretical techniques: mean-field theory to describe the spin degrees of freedom, the self-consistent Born approximation to characterize individual charge excitations across the Hubbard gap, and the Bethe-Salpeter equation to identify bound states of doublons and holons. The binding energy of the Hubbard exciton is found to increase with increasing the N{{\'e}}el order parameter, while the exciton mass decreases. We observe that these trends rely significantly on the retardation of the effective interaction, and require consideration of multiple effects from changing the magnetic order. Our results are consistent with the key qualitative trends observed in recent experiments on iridates. Moreover, the findings could have direct implications on ultracold atom Mott insulators, where the Hubbard model is the exact description of the system and the microscopic degrees of freedom can be directly accessed.\ 

}, url = {https://arxiv.org/abs/2004.10825}, author = {T. -S. Huang and Christopher L. Baldwin and M. Hafezi and V. Galitski} } @article {2676, title = {Status Report on the Second Round of the NIST Post-Quantum Cryptography Standardization Process}, journal = {NISTIR 8309}, year = {2020}, month = {07/2020}, abstract = {

The National Institute of Standards and Technology is in the process of selecting one or more public-key cryptographic algorithms through a public, competition-like process. The new public-key cryptography standards will specify one or more additional digital signatures, public-key encryption, and key-establishment algorithms to augment Federal Information Processing Standard (FIPS) 186-4, Digital Signature Standard (DSS), as well as NIST Special Publication (SP) 800-56A Revision 3, Recommendation for Pair-Wise Key-Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B Revision 2, Recommendation for Pair-Wise Key Establishment Using Integer Factorization Cryptography. It is intended that these algorithms will be capable of protecting sensitive information well into the foreseeable future, including after the advent of quantum computers.

The NIST Post-Quantum Cryptography Standardization Process began in 2017 with 69 candidate algorithms that met both the minimum acceptance criteria and submission requirements. The first round lasted until January 2019, during which candidate algorithms were evaluated based on their security, performance, and other characteristics. NIST selected 26 algorithms to advance to the second round for more analysis. This report describes the evaluation and selection process, based on public feedback and internal review, of the second-round candidates. The report summarizes the 26 second-round candidate algorithms and identifies those selected to move forward to the third round of the competition. The third-round finalist public-key encryption and key-establishment algorithms are Classic McEliece, CRYSTALS-KYBER, NTRU, and SABER. The third-round finalists for digital signatures are CRYSTALS-DILITHIUM, FALCON, and Rainbow. These finalists will be considered for standardization at the end of the third round. In addition, eight alternate candidate algorithms will also advance to the third round: BIKE, FrodoKEM, HQC, NTRU Prime, SIKE, GeMSS, Picnic, and SPHINCS+. These additional candidates are still being considered for standardization, although this is unlikely to occur at the end of the third round. NIST hopes that the announcement of these finalists and additional candidates will serve to focus the cryptographic community\’s attention during the next round.

}, doi = {https://doi.org/10.6028/NIST.IR.8309}, author = {Gorjan Alagic and Jacob Alperin-Sheriff and Daniel Apon and David Cooper and Quynh Dang and John Kelsey and Yi-Kai Liu and Carl Miller and Dustin Moody and Rene Peralta and Ray Perlner and Angela Robinson and Daniel Smith-Tone} } @article {2579, title = {Studying viral populations with tools from quantum spin chains}, year = {2020}, month = {3/24/2020}, abstract = {

We study Eigen\&$\#$39;s model of quasi-species, characterized by sequences that replicate with a specified fitness and mutate independently at single sites. The evolution of the population vector in time is then closely related to that of quantum spins in imaginary time. We employ multiple perspectives and tools from interacting quantum systems to examine growth and collapse of realistic viral populations, specifically certain HIV proteins. All approaches used, including the simplest perturbation theory, give consistent results.

}, url = {https://arxiv.org/abs/2003.10668}, author = {Saumya Shivam and Christopher L. Baldwin and John Barton and Mehran Kardar and S. L. Sondhi} } @article {2722, title = {Sublinear classical and quantum algorithms for general matrix games}, journal = {To appear in the Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI 2021)}, year = {2020}, month = {12/11/2020}, abstract = {

We investigate sublinear classical and quantum algorithms for matrix games, a fundamental problem in optimization and machine learning, with provable guarantees. Given a matrix A\∈Rn\×d, sublinear algorithms for the matrix game minx\∈Xmaxy\∈Yy⊤Ax were previously known only for two special cases: (1) Y being the l1-norm unit ball, and (2) X being either the l1- or the l2-norm unit ball. We give a sublinear classical algorithm that can interpolate smoothly between these two cases: for any fixed q\∈(1,2], we solve the matrix game where X is a lq-norm unit ball within additive error ε in time O~((n+d)/ε2). We also provide a corresponding sublinear quantum algorithm that solves the same task in time O~((n\−\−\√+d\−\−\√)poly(1/ε)) with a quadratic improvement in both n and d. Both our classical and quantum algorithms are optimal in the dimension parameters n and d up to poly-logarithmic factors. Finally, we propose sublinear classical and quantum algorithms for the approximate Carath{\'e}odory problem and the lq-margin support vector machines as applications.

}, url = {https://arxiv.org/abs/2012.06519}, author = {Tongyang Li and Chunhao Wang and Shouvanik Chakrabarti and Xiaodi Wu} } @conference {2599, title = {Symmetries, graph properties, and quantum speedups}, booktitle = {Proceedings of the 61st IEEE Symposium on Foundations of Computer Science (FOCS 2020), pp. 649{\textendash}660 (2020)}, year = {2020}, month = {6/23/2020}, abstract = {

Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup?
In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups.
In contrast, in the adjacency list model for bounded-degree graphs (where graph symmetry is manifested differently), we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013).

}, doi = {https://doi.org/10.1109/FOCS46700.2020.00066}, url = {https://arxiv.org/abs/2006.12760}, author = {Shalev Ben-David and Andrew M. Childs and Andras Gilyen and William Kretschmer and Supartha Podder and Daochen Wang} } @article {2690, title = {Symmetry breaking and error correction in open quantum systems}, journal = {Phys. Rev. Lett. }, volume = {125}, year = {2020}, month = {8/6/2020}, pages = {240405}, abstract = {

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system---a Lindbladian---a unitary symmetry can be imposed in a \"weak\" or a \"strong\" way. We characterize the possible Zn symmetry breaking transitions for both cases. In the case of Z2, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially-protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correctio

}, doi = {https://doi.org/10.1103/PhysRevLett.125.240405}, url = {https://arxiv.org/abs/2008.02816}, author = {Simon Lieu and Ron Belyansky and Jeremy T. Young and Rex Lundgren and Victor V. Albert and Alexey V. Gorshkov} } @article {2519, title = {Time evolution of correlation functions in quantum many-body systems}, journal = {Phys. Rev. Lett}, volume = {124}, year = {2020}, month = {3/19/2020}, abstract = {

We give rigorous analytical results on the temporal behavior of two-point correlation functions --also known as dynamical response functions or Green\&$\#$39;s functions-- in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times \⟨A(t)B\⟩β\→\⟨A\⟩β\⟨B\⟩β, thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For auto-correlation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values, and does not increase with system size. We give numerical examples that show that this bound is a good estimate in non-integrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.

}, doi = {https://doi.org/10.1103/PhysRevLett.124.110605}, url = {https://arxiv.org/abs/1906.11280}, author = {{\'A}lvaro M. Alhambra and Jonathon Riddell and Luis Pedro Garc{\'\i}a-Pintos} } @article {2402, title = {Time-dependent Hamiltonian simulation with L1-norm scaling}, journal = {Quantum}, volume = {4}, year = {2020}, month = {4/20/2020}, abstract = {

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For the case of sparse Hamiltonian simulation, the gate complexity scales with the L1 norm \∫t0dτ||H(τ)||max, whereas the best previous results scale with tmaxτ\∈[0,t]||H(τ)||max. We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schr{\"o}dinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. By leveraging the L1-norm information, we obtain polynomial speedups for semi-classical simulations of scattering processes in quantum chemistry.

}, doi = {https://doi.org/10.22331/q-2020-04-20-254}, url = {https://arxiv.org/abs/1906.07115}, author = {Dominic W. Berry and Andrew M. Childs and Yuan Su and Xin Wang and Nathan Wiebe} } @article {2518, title = {Time-information uncertainty relations in thermodynamics}, journal = {Nat. Phys.}, year = {2020}, month = {09/21/2020}, abstract = {

Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we show that rates of energy and entropy exchange are subject to a speed limit -- a time-information uncertainty relation -- imposed by the rates of change in the information content of the system. This uncertainty relation bounds the time that elapses before the change in a thermodynamic quantity has the same magnitude as its initial standard deviation. From this general bound, we establish a family of speed limits for heat, work, entropy production, and entropy flow depending on the experimental constraints on the system. In all of these inequalities, the time scale of transient dynamical fluctuations is universally bounded by the Fisher information. Moreover, they all have a mathematical form that mirrors the Mandelstam-Tamm version of the time-energy uncertainty relation in quantum mechanics. These bounds on the speed of arbitrary observables apply to transient systems away from thermodynamic equilibrium, independent of the physical assumptions about the stochastic dynamics or their function.\ 

}, doi = {https://doi.org/10.1038/s41567-020-0981-y}, url = {https://arxiv.org/abs/2001.05418}, author = {Schuyler B. Nicholson and Luis Pedro Garc{\'\i}a-Pintos and Adolfo del Campo and Jason R. Green} } @article {2453, title = {Towards analog quantum simulations of lattice gauge theories with trapped ions}, journal = {Physical Review Research }, volume = {2}, year = {2020}, month = {4/8/2020}, abstract = {

Gauge field theories play a central role in modern physics and are at the heart of the Standard Model of elementary particles and interactions. Despite significant progress in applying classical computational techniques to simulate gauge theories, it has remained a challenging task to compute the real-time dynamics of systems described by gauge theories. An exciting possibility that has been explored in recent years is the use of highly-controlled quantum systems to simulate, in an analog fashion, properties of a target system whose dynamics are difficult to compute. Engineered atom-laser interactions in a linear crystal of trapped ions offer a wide range of possibilities for quantum simulations of complex physical systems. Here, we devise practical proposals for analog simulation of simple lattice gauge theories whose dynamics can be mapped onto spin-spin interactions in any dimension. These include 1+1D quantum electrodynamics, 2+1D Abelian Chern-Simons theory coupled to fermions, and 2+1D pure Z2 gauge theory. The scheme proposed, along with the optimization protocol applied, will have applications beyond the examples presented in this work, and will enable scalable analog quantum simulation of Heisenberg spin models in any number of dimensions and with arbitrary interaction strengths.

}, doi = {https://doi.org/10.1103/PhysRevResearch.2.023015}, url = {https://arxiv.org/abs/1908.03210}, author = {Zohreh Davoudi and Mohammad Hafezi and Christopher Monroe and Guido Pagano and Alireza Seif and Andrew Shaw} } @article {2609, title = {Transport and dynamics in the frustrated two-bath spin-boson model}, year = {2020}, month = {7/7/2020}, abstract = {

We study the strong coupling dynamics as well as transport properties of photons in the two-bath spin-boson model, in which a spin-1/2 particle is frustratingly coupled to two independent Ohmic bosonic baths. Using a combination of numerical and analytical methods, we show that the frustration in this model gives rise to rich physics in a very wide range of energies. This is in contrast to the one-bath spin-boson model, where the non-trivial physics occurs at an energy scale close to the renormalized spin frequency. The renormalized spin frequency in the two-bath spin-boson model is still important, featuring in different observables, including the non-equiblirum dynamics of both the spin and the baths along with the elastic transport properties of a photon. The latter however reveals a much more complex structure. The elastic scattering displays non-monotonic behavior at high frequencies, and is very different in the two channels: intra- and inter-bath scattering. The photon can also be inelastically scattered, a process in which it is split into several photons of smaller energies. We show that such inelastic processes are highly anisotropic, with the outgoing particles being preferentially emitted into only one of the baths. Moreover, the inelastic scattering rate is parameterically larger than in the one-bath case, and can even exceed the total elastic rate. Our results can be verified with state-of-the-art circuit and cavity quantum electrodynamics experiments.\ 

}, url = {https://arxiv.org/abs/2007.03690}, author = {Ron Belyansky and Seth Whitsitt and Rex Lundgren and Yidan Wang and Andrei Vrajitoarea and Andrew A. Houck and Alexey V. Gorshkov} } @article {2673, title = {Understanding the Frauchiger-Renner Argument}, year = {2020}, month = {9/4/2020}, abstract = {

In 2018, Daniela Frauchiger and Renato Renner published an article in Nature Communications entitled {\textquoteleft}Quantum theory cannot consistently describe the use of itself.\&$\#$39; I clarify the significance of the result and point out a common and persistent misunderstanding of the argument, which has been attacked as flawed from a variety of interpretational perspectives.

}, url = {https://arxiv.org/abs/2008.08538}, author = {Jeffrey Bub} } @article {2494, title = {Unitary Subharmonic Response and Floquet Majorana Modes}, journal = {Phys. Rev. Lett.}, volume = {125}, year = {2020}, month = {10/13/2020}, abstract = {

Detection and manipulation of excitations with non-Abelian statistics, such as Majorana fermions, are essential for creating topological quantum computers. To this end, we show the connection between the existence of such localized particles and the phenomenon of unitary subharmonic response (SR) in periodically driven systems. In particular, starting from highly non-equilibrium initial states, the unpaired Majorana modes exhibit spin oscillations with twice the driving period, are localized, and can have exponentially long lifetimes in clean systems. While the lifetime of SR is limited in translationally invariant systems, we show that disorder can be engineered to stabilize the subharmonic response of Majorana modes. A viable observation of this phenomenon can be achieved using modern multi-qubit hardware, such as superconducting circuits and cold atomic systems

}, doi = {https://doi.org/10.1103/PhysRevLett.125.086804}, url = {https://arxiv.org/abs/1911.05795}, author = {Oles Shtanko and Ramis Movassagh} } @article {2578, title = {Universal one-dimensional discrete-time quantum walks and their implementation on near term quantum hardware}, year = {2020}, month = {1/30/2020}, abstract = {

Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. Quantum walks represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves onto the multi-qubit states in a quantum processor, we present different configurations of quantum circuits for the implementation of discrete-time quantum walks in one-dimensional position space. With example circuits for a five qubit machine we address scalability to higher dimensions and larger quantum processors.

}, url = {https://arxiv.org/abs/2001.11197}, author = {Shivani Singh and Cinthia H. Alderete and Radhakrishnan Balu and Christopher Monroe and Norbert M. Linke and C. M. Chandrashekar} } @article {2562, title = {Accelerated Variational Quantum Eigensolver}, journal = {Phys. Rev. Lett. }, volume = {122}, year = {2019}, month = {3/25/2019}, abstract = {

The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision ε, QPE requires O(1) repetitions of circuits with depth O(1/ε), whereas each expectation estimation subroutine within VQE requires O(1/ε2) samples from circuits with depth O(1). We propose a generalised VQE algorithm that interpolates between these two regimes via a free parameter α\∈[0,1] which can exploit quantum coherence over a circuit depth of O(1/εα) to reduce the number of samples to O(1/ε2(1\−α)). Along the way, we give a new routine for expectation estimation under limited quantum resources that is of independent interest.

}, doi = {https://doi.org/10.1103/PhysRevLett.122.140504}, url = {https://arxiv.org/abs/1802.00171}, author = {Daochen Wang and Oscar Higgott and Stephen Brierley} } @article {2493, title = {An approximate description of quantum states}, year = {2019}, month = {2019/11/13}, abstract = {

We introduce an approximate description of an N-qubit state, which contains sufficient information to estimate the expectation value of any observable with precision independent of N. We show, in fact, that the error in the estimation of the observables\&$\#$39; expectation values decreases as the inverse of the square root of the number of the system\&$\#$39;s identical preparations and increases, at most, linearly in a suitably defined, N-independent, seminorm of the observables. Building the approximate description of the N-qubit state only requires repetitions of single-qubit rotations followed by single-qubit measurements and can be considered for implementation on today\&$\#$39;s Noisy Intermediate-Scale Quantum (NISQ) computers. The access to the expectation values of all observables for a given state leads to an efficient variational method for the determination of the minimum eigenvalue of an observable. The method represents one example of the practical significance of the approximate description of the N-qubit state. We conclude by briefly discussing extensions to generative modelling and with fermionic operators

}, url = {https://arxiv.org/abs/1910.10543}, author = {Marco Paini and Amir Kalev} } @article {2321, title = {Bang-bang control as a design principle for classical and quantum optimization algorithms}, journal = {Quantum Information \& Computation }, volume = {19}, year = {2019}, month = {8/1/2019}, pages = {424-446}, abstract = {

Physically motivated classical heuristic optimization algorithms such as simulated annealing (SA) treat the objective function as an energy landscape, and allow walkers to escape local minima. It has been argued that quantum properties such as tunneling may give quantum algorithms advantage in finding ground states of vast, rugged cost landscapes. Indeed, the Quantum Adiabatic Algorithm (QAO) and the recent Quantum Approximate Optimization Algorithm (QAOA) have shown promising results on various problem instances that are considered classically hard. Here, we argue that the type of control strategy used by the optimization algorithm may be crucial to its success. Along with SA, QAO and QAOA, we define a new, bang-bang version of simulated annealing, BBSA, and study the performance of these algorithms on two well-studied problem instances from the literature. Both classically and quantumly, the successful control strategy is found to be bang-bang, exponentially outperforming the quasistatic analogues on the same instances. Lastly, we construct O(1)-depth QAOA protocols for a class of symmetric cost functions, and provide an accompanying physical picture.

}, url = {https://arxiv.org/abs/1812.02746}, author = {Aniruddha Bapat and Stephen Jordan} } @article {2516, title = {Beyond Spontaneous Emission: Giant Atom Bounded in Continuum}, year = {2019}, month = {12/20/2019}, abstract = {

The quantum coupling of individual superconducting qubits to microwave photons leads to remarkable experimental opportunities. Here we consider the phononic case where the qubit is coupled to an electromagnetic surface acoustic wave antenna that enables supersonic propagation of the qubit oscillations. This can be considered as a giant atom that is many phonon wavelengths long. We study an exactly solvable toy model that captures these effects, and find that this non-Markovian giant atom has a suppressed relaxation, as well as an effective vacuum coupling between a qubit excitation and a localized wave packet of sound, even in the absence of a cavity for the sound waves. Finally, we consider practical implementations of these ideas in current surface acoustic wave devices.\ 

}, url = {https://arxiv.org/abs/1912.09980}, author = {Shangjie Guo and Yidan Wang and Thomas Purdy and J. M. Taylor} } @article {2373, title = {Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization}, year = {2019}, month = {02/19/2019}, abstract = {

The many-body localization transition in quasiperiodic systems has been extensively studied in recent ultracold atom experiments. At intermediate quasiperiodic potential strength, a surprising Griffiths-like regime with slow dynamics appears in the absence of random disorder and mobility edges. In this work, we study the interacting Aubry-Andre model, a prototype quasiperiodic system, as a function of incommensurate potential strength using a novel dynamical measure, information scrambling, in a large system of 200 lattice sites. Between the thermal phase and the many-body localized phase, we find an intermediate dynamical phase where the butterfly velocity is zero and information spreads in space as a power-law in time. This is in contrast to the ballistic spreading in the thermal phase and logarithmic spreading in the localized phase. We further investigate the entanglement structure of the many-body eigenstates in the intermediate phase and find strong fluctuations in eigenstate entanglement entropy within a given energy window, which is inconsistent with the eigenstate thermalization hypothesis. Machine-learning on the entanglement spectrum also reaches the same conclusion. Our large-scale simulations suggest that the intermediate phase with vanishing butterfly velocity could be responsible for the slow dynamics seen in recent experiments.

}, url = {https://arxiv.org/abs/1902.07199}, author = {Shenglong Xu and Xiao Li and Yi-Ting Hsu and Brian Swingle and Sankar Das Sarma} } @article {2271, title = {Canonical forms for single-qutrit Clifford+T operators}, journal = {Annals of Physics}, volume = {406}, year = {2019}, month = {8/19/2019}, pages = {54-70}, abstract = {

We introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the single-qutrit Clifford+T circuits implementing a given operator our canonical form uses the least number of T gates. Finally, we provide an algorithm which inputs the description of an operator (as a matrix or a circuit) and constructs the canonical form for this operator. The algorithm runs in time linear in the number of T gates. Our results provide a higher-dimensional generalization of prior work by Matsumoto and Amano who introduced similar canonical forms for single-qubit Clifford+T circuits.\ 

}, doi = {https://doi.org/10.1016/j.aop.2019.04.001}, url = {https://arxiv.org/abs/1803.05047}, author = {Andrew N. Glaudell and Neil J. Ross and J. M. Taylor} } @article {2374, title = {Chaos in a quantum rotor model}, year = {2019}, month = {01/29/2019}, abstract = {

We study scrambling in a model consisting of a number N of M-component quantum rotors coupled by random infinite-range interactions. This model is known to have both a paramagnetic phase and a spin glass phase separated by second order phase transition. We calculate in perturbation theory the squared commutator of rotor fields at different sites in the paramagnetic phase, to leading non-trivial order at large N and large M. This quantity diagnoses the onset of quantum chaos in this system, and we show that the squared commutator grows exponentially with time, with a Lyapunov exponent proportional to 1M. At high temperature, the Lyapunov exponent limits to a value set by the microscopic couplings, while at low temperature, the exponent exhibits a T4 dependence on temperature T.\ 

}, url = {https://arxiv.org/abs/1901.10446}, author = {Gong Cheng and Brian Swingle} } @article {2372, title = {A characterization of quantum chaos by two-point correlation functions}, year = {2019}, month = {02/28/2019}, abstract = {

We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

}, url = {https://arxiv.org/abs/1902.11086}, author = {Hrant Gharibyan and Masanori Hanada and Brian Swingle and Masaki Tezuka} } @article {2361, title = {Circuit Transformations for Quantum Architectures}, journal = {Proceedings of TQC 2019, LIPIcs}, volume = {135 }, year = {2019}, month = {02/25/2019}, chapter = {1-3:24}, abstract = {

Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits to architecture qubits. To achieve this, we first consider the qubit movement subproblem and use the routing via matchings framework to prove tighter bounds on parallel routing. In practice, we only need to perform partial permutations, so we generalize routing via matchings to that setting. We give new routing procedures for common architecture graphs and for the generalized hierarchical product of graphs, which produces subgraphs of the Cartesian product. Secondly, for serial routing, we consider the token swapping framework and extend a 4-approximation algorithm for general graphs to support partial permutations. We apply these routing procedures to give several circuit transformations, using various heuristic qubit placement subroutines. We implement these transformations in software and compare their performance for large quantum circuits on grid and modular architectures, identifying strategies that work well in practice.

}, doi = {https://doi.org/10.4230/LIPIcs.TQC.2019.3}, url = {https://arxiv.org/abs/1902.09102}, author = {Andrew M. Childs and Eddie Schoute and Cem M. Unsal} } @article {2451, title = {Classifying single-qubit noise using machine learning}, year = {2019}, month = {8/30/2019}, abstract = {

Quantum characterization, validation, and verification (QCVV) techniques are used to probe, characterize, diagnose, and detect errors in quantum information processors (QIPs). An important component of any QCVV protocol is a mapping from experimental data to an estimate of a property of a QIP. Machine learning (ML) algorithms can help automate the development of QCVV protocols, creating such maps by learning them from training data. We identify the critical components of \"machine-learned\" QCVV techniques, and present a rubric for developing them. To demonstrate this approach, we focus on the problem of determining whether noise affecting a single qubit is coherent or stochastic (incoherent) using the data sets originally proposed for gate set tomography. We leverage known ML algorithms to train a classifier distinguishing these two kinds of noise. The accuracy of the classifier depends on how well it can approximate the \"natural\" geometry of the training data. We find GST data sets generated by a noisy qubit can reliably be separated by linear surfaces, although feature engineering can be necessary. We also show the classifier learned by a support vector machine (SVM) is robust under finite-sample noise.\ 

}, url = {https://arxiv.org/abs/1908.11762}, author = {Travis L. Scholten and Yi-Kai Liu and Kevin Young and Robin Blume-Kohout} } @article {2407, title = {Competing (Semi)-Selfish Miners in Bitcoin}, year = {2019}, month = {06/11/2019}, abstract = {

The Bitcoin protocol prescribes certain behavior by the miners who are responsible for maintaining and extending the underlying blockchain; in particular, miners who successfully solve a puzzle, and hence can extend the chain by a block, are supposed to release that block immediately. Eyal and Sirer showed, however, that a selfish miner is incentivized to deviate from the protocol and withhold its blocks under certain conditions. The analysis by Eyal and Sirer, as well as in followup work, considers a \emph{single} deviating miner (who may control a large fraction of the hashing power in the network) interacting with a remaining pool of honest miners. Here, we extend this analysis to the case where there are \emph{multiple} (non-colluding) selfish miners. We find that with multiple strategic miners, specific deviations from honest mining by multiple strategic agents can outperform honest mining, even if individually miners would not be incentivised to be dishonest. This previous point effectively renders the Bitcoin protocol to be less secure than previously thought.\ 

}, url = {https://arxiv.org/abs/1906.04502}, author = {Francisco J. Marmolejo-Coss{\'\i}o and Eric Brigham and Benjamin Sela and Jonathan Katz} } @article {2406, title = {Complexity phase diagram for interacting and long-range bosonic Hamiltonians}, year = {2019}, month = {06/10/2019}, abstract = {

Recent years have witnessed a growing interest in topics at the intersection of many-body physics and complexity theory. Many-body physics aims to understand and classify emergent behavior of systems with a large number of particles, while complexity theory aims to classify computational problems based on how the time required to solve the problem scales as the problem size becomes large. In this work, we use insights from complexity theory to classify phases in interacting many-body systems. Specifically, we demonstrate a \"complexity phase diagram\" for the Bose-Hubbard model with long-range hopping. This shows how the complexity of simulating time evolution varies according to various parameters appearing in the problem, such as the evolution time, the particle density, and the degree of locality. We find that classification of complexity phases is closely related to upper bounds on the spread of quantum correlations, and protocols to transfer quantum information in a controlled manner. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.\ 

}, url = {https://arxiv.org/abs/1906.04178}, author = {Nishad Maskara and Abhinav Deshpande and Minh C. Tran and Adam Ehrenberg and Bill Fefferman and Alexey V. Gorshkov} } @article {2264, title = {Confined Dynamics in Long-Range Interacting Quantum Spin Chains}, journal = {Phys. Rev. Lett.}, volume = {122 }, year = {2019}, month = {04/17/2019}, abstract = {

We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/rα) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic bound states in high-energy physics. We show that these bound states have dramatic consequences for the non-equilibrium dynamics following a global quantum quench, such as suppressed spreading of quantum information and oscillations of order parameters. The masses of these bound states can be read out from the Fourier spectrum of these oscillating order parameters. We then use a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement. The masses of the bound states predicted by this model are in good quantitative agreement with exact diagonalization results. Moreover, we illustrate that these bound states lead to weak thermalization of local observables for initial states with energy near the bottom of the many-body energy spectrum. Our work is readily applicable to current trapped-ion experiments.

}, doi = {https://doi.org/10.1103/PhysRevLett.122.150601}, url = {https://arxiv.org/abs/1810.02365}, author = {Fangli Liu and Rex Lundgren and Paraj Titum and Guido Pagano and Jiehang Zhang and Christopher Monroe and Alexey V. Gorshkov} } @article {2533, title = {Development of Quantum InterConnects for Next-Generation Information Technologies}, year = {2019}, month = {12/13/2019}, abstract = {

Just as classical information technology rests on a foundation built of interconnected information-processing systems, quantum information technology (QIT) must do the same. A critical component of such systems is the interconnect, a device or process that allows transfer of information between disparate physical media, for example, semiconductor electronics, individual atoms, light pulses in optical fiber, or microwave fields. While interconnects have been well engineered for decades in the realm of classical information technology, quantum interconnects (QuICs) present special challenges, as they must allow the transfer of fragile quantum states between different physical parts or degrees of freedom of the system. The diversity of QIT platforms (superconducting, atomic, solid-state color center, optical, etc.) that will form a quantum internet poses additional challenges. As quantum systems scale to larger size, the quantum interconnect bottleneck is imminent, and is emerging as a grand challenge for QIT. For these reasons, it is the position of the community represented by participants of the NSF workshop on Quantum Interconnects that accelerating QuIC research is crucial for sustained development of a national quantum science and technology program. Given the diversity of QIT platforms, materials used, applications, and infrastructure required, a convergent research program including partnership between academia, industry and national laboratories is required. This document is a summary from a U.S. National Science Foundation supported workshop held on 31 October - 1 November 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum interconnects over the next 2-5 years.\ 

}, url = {https://arxiv.org/abs/1912.06642}, author = {David Awschalom and Karl K. Berggren and Hannes Bernien and Sunil Bhave and Lincoln D. Carr and Paul Davids and Sophia E. Economou and Dirk Englund and Andrei Faraon and Marty Fejer and Saikat Guha and Martin V. Gustafsson and Evelyn Hu and Liang Jiang and Jungsang Kim and Boris Korzh and Prem Kumar and Paul G. Kwiat and Marko Lon{\v c}ar and Mikhail D. Lukin and David A. B. Miller and Christopher Monroe and Sae Woo Nam and Prineha Narang and Jason S. Orcutt} } @article {2405, title = {Equilibration to the non-Abelian thermal state in quantum many-body physics}, year = {2019}, month = {6/21/2019}, abstract = {

In statistical mechanics, a small system exchanges conserved charges---heat, particles, electric charge, etc.---with a bath. The small system thermalizes to the canonical ensemble, or the grand canonical ensemble, etc., depending on the charges. The charges are usually represented by operators assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system\&$\#$39;s long-time state was dubbed \"the non-Abelian thermal state (NATS).\" We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which form the system of interest. The conserved charges manifest as spin components. Heisenberg interactions push the charges between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting charges from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.\ 

}, url = {https://arxiv.org/abs/1906.09227}, author = {Nicole Yunger Halpern and Michael E. Beverland and Amir Kalev} } @article {2174, title = {Faster quantum simulation by randomization}, journal = {Quantum }, volume = {3}, year = {2019}, month = {08/28/2019}, abstract = {

Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and surprisingly efficient. We show that by simply randomizing how the summands are ordered, one can prove stronger bounds on the quality of approximation and thereby give more efficient simulations. Indeed, we show that these bounds can be asymptotically better than previous bounds that exploit commutation between the summands, despite using much less information about the structure of the Hamiltonian. Numerical evidence suggests that our randomized algorithm may be advantageous even for near-term quantum simulation.

}, doi = {https://doi.org/10.22331/q-2019-09-02-182}, url = {https://arxiv.org/abs/1805.08385}, author = {Andrew M. Childs and Aaron Ostrander and Yuan Su} } @article {2535, title = {Feshbach resonances in p-wave three-body recombination within Fermi-Fermi mixtures of open-shell 6Li and closed-shell 173Yb atoms}, year = {2019}, month = {12/10/2019}, abstract = {

We report on observations and modeling of interspecies magnetic Feshbach resonances in dilute ultracold mixtures of open-shell alkali-metal 6Li and closed-shell 173Yb atoms with temperatures just above quantum degeneracy for both fermionic species. Resonances are located by detecting magnetic-field-dependent atom loss due to three-body recombination. We resolve closely-located resonances that originate from a weak separation-dependent hyperfine coupling between the electronic spin of 6Li and the nuclear spin of 173Yb, and confirm their magnetic field spacing by ab initio electronic-structure calculations. Through quantitative comparisons of theoretical atom-loss profiles and experimental data at various temperatures between 1 μK and 20 μK, we show that three-body recombination in fermionic mixtures has a p-wave Wigner threshold behavior leading to characteristic asymmetric loss profiles. Such resonances can be applied towards the formation of ultracold doublet ground-state molecules and quantum simulation of superfluid p-wave pairing.

}, url = {https://arxiv.org/abs/1912.04874}, author = {Alaina Green and Hui Li and Jun Hui See Toh and Xinxin Tang and Katherine McCormick and Ming Li and Eite Tiesinga and Svetlana Kotochigova and Subhadeep Gupta} } @article {2409, title = {Floquet engineering of optical lattices with spatial features and periodicity below the diffraction limit}, year = {2019}, month = {06/18/2019}, abstract = {

Floquet engineering or coherent time periodic driving of quantum systems has been successfully used to synthesize Hamiltonians with novel properties. In ultracold atomic systems, this has led to experimental realizations of artificial gauge fields, topological band structures, and observation of dynamical localization, to name just a few. Here we present a Floquet-based framework to stroboscopically engineer Hamiltonians with spatial features and periodicity below the diffraction limit of light used to create them by time-averaging over various configurations of a 1D optical Kronig-Penney (KP) lattice. The KP potential is a lattice of narrow subwavelength barriers spaced by half the optical wavelength (λ/2) and arises from the non-linear optical response of the atomic dark state. Stroboscopic control over the strength and position of this lattice requires time-dependent adiabatic manipulation of the dark state spin composition. We investigate adiabaticity requirements and shape our time-dependent light fields to respect the requirements. We apply this framework to show that a λ/4-spaced lattice can be synthesized using realistic experimental parameters as an example, discuss mechanisms that limit lifetimes in these lattices, explore candidate systems and their limitations, and treat adiabatic loading into the ground band of these lattices.

}, url = {https://arxiv.org/abs/1906.07646}, author = {S. Subhankar and P. Bienias and P. Titum and T-C. Tsui and Y. Wang and Alexey V. Gorshkov and S. L. Rolston and J. V. Porto} } @article {2276, title = {Fluctuation-induced torque on a topological insulator out of thermal equilibrium}, journal = {Phys. Rev. Lett.}, volume = {123}, year = {2019}, month = {8/1/2019}, abstract = {

Topological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well-understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. Utilizing the Keldysh framework, we investigate the universal nonequilibrium response of the TI to the temperature difference with the environment. Finally, we argue that experimental observation of this effect is within reach.

}, doi = {https://doi.org/10.1103/PhysRevLett.123.055901}, url = {https://arxiv.org/abs/1811.06080}, author = {M. F. Maghrebi and Alexey V. Gorshkov and J. D. Sau} } @article {2441, title = {Framework for Hamiltonian simulation and beyond: standard-form encoding, qubitization, and quantum signal processing}, journal = {Quantum Views }, volume = {3}, year = {2019}, month = {08/13/2019}, abstract = {
This is a Perspective on \"Hamiltonian Simulation by Qubitization\" by Guang Hao Low and Isaac L. Chuang, published in Quantum 3, 163 (2019).
}, doi = {https://doi.org/10.22331/qv-2019-08-13-21}, url = {https://quantum-journal.org/views/qv-2019-08-13-21/}, author = {Yuan Su} } @article {1995, title = {Graphical Methods in Device-Independent Quantum Cryptography}, journal = {Quantum}, volume = {3}, year = {2019}, month = {05/20/2019}, abstract = {

We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a recent result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical exposition of a proof of this result and implement parts of it in the Globular proof assistant.

}, doi = {https://doi.org/10.22331/q-2019-05-27-146}, url = {https://arxiv.org/abs/1705.09213}, author = {Spencer Breiner and Carl Miller and Neil J. Ross} } @article {2369, title = {Ground-state energy estimation of the water molecule on a trapped ion quantum computer}, year = {2019}, month = {03/07/2019}, abstract = {

Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly-interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here, we describe a scalable co-design framework for solving chemistry problems on a trapped ion quantum computer, and apply it to compute the ground-state energy of the water molecule. The robust operation of the trapped ion quantum computer yields energy estimates with errors approaching the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics.

}, url = {https://arxiv.org/abs/1902.10171}, author = {Yunseong Nam and Jwo-Sy Chen and Neal C. Pisenti and Kenneth Wright and Conor Delaney and Dmitri Maslov and Kenneth R. Brown and Stewart Allen and Jason M. Amini and Joel Apisdorf and Kristin M. Beck and Aleksey Blinov and Vandiver Chaplin and Mika Chmielewski and Coleman Collins and Shantanu Debnath and Andrew M. Ducore and Kai M. Hudek and Matthew Keesan and Sarah M. Kreikemeier and Jonathan Mizrahi and Phil Solomon and Mike Williams and Jaime David Wong-Campos and Christopher Monroe and Jungsang Kim} } @article {2365, title = {Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks}, journal = {Phys. Rev. A}, volume = {100}, year = {2019}, month = {10/7/2019}, abstract = {

We generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

}, doi = {https://doi.org/10.1103/PhysRevA.100.042304}, url = {https://arxiv.org/abs/1901.09042}, author = {Kevin Qian and Zachary Eldredge and Wenchao Ge and Guido Pagano and Christopher Monroe and James V. Porto and Alexey V. Gorshkov} } @article {2400, title = {How Low Can Vacuum Energy Go When Your Fields Are Finite-Dimensional?}, year = {2019}, month = {05/11/2019}, abstract = {

According to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many degrees of freedom may be localized to any given region of space. In this essay, we explore the viewpoint that quantum field theory may emerge from an underlying theory that is locally finite-dimensional, and we construct a locally finite-dimensional version of a Klein-Gordon scalar field using generalized Clifford algebras. Demanding that the finite-dimensional field operators obey a suitable version of the canonical commutation relations makes this construction essentially unique. We then find that enforcing local finite dimensionality in a holographically consistent way leads to a huge suppression of the quantum contribution to vacuum energy, to the point that the theoretical prediction becomes plausibly consistent with observations.

}, url = {https://arxiv.org/abs/1905.11199}, author = {ChunJun Cao and Aidan Chatwin-Davies and Ashmeet Singh} } @article {2143, title = {Interacting Qubit-Photon Bound States with Superconducting Circuits}, journal = {Phys. Rev. }, volume = {X 9}, year = {2019}, month = {2018/01/30}, abstract = {

Qubits strongly coupled to a photonic crystal give rise to many exotic physical scenarios, beginning with single and multi-excitation qubit-photon dressed bound states comprising induced spatially localized photonic modes, centered around the qubits, and the qubits themselves. The localization of these states changes with qubit detuning from the band-edge, offering an avenue of in situ control of bound state interaction. Here, we present experimental results from a device with two qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and inter-bound state interactions. We observe a fourth-order two photon virtual process between bound states indicating strong coupling between the photonic crystal and qubits. Due to their localization-dependent interaction, these states offer the ability to create one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits\&$\#$39; spatial organization, a key criterion for realization of certain quantum many-body models. The widely tunable, strong and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems of bound states.

}, doi = {https://doi.org/10.1103/PhysRevX.9.011021}, url = {http://arxiv.org/abs/1801.10167}, author = {Neereja M. Sundaresan and Rex Lundgren and Guanyu Zhu and Alexey V. Gorshkov and Andrew A. Houck} } @article {2366, title = {Interaction-induced transition in the quantum chaotic dynamics of a disordered metal}, journal = {Ann. Phys. }, volume = {405}, year = {2019}, month = {03/25/2019}, abstract = {

We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups.

}, doi = {https://doi.org/10.1016/j.aop.2019.03.008}, url = {https://arxiv.org/abs/1709.09296}, author = {S. V. Syzranov and Alexey V. Gorshkov and V. M. Galitski} } @article {2459, title = {Interference of Temporally Distinguishable Photons Using Frequency-Resolved Detection}, journal = {Phys. Rev. Lett. }, volume = {123}, year = {2019}, month = {9/24/2019}, abstract = {

We demonstrate quantum interference of three photons that are distinguishable in time, by resolving them in the conjugate parameter, frequency. We show that the multiphoton interference pattern in our setup can be manipulated by tuning the relative delays between the photons, without the need for reconfiguring the optical network. Furthermore, we observe that the symmetries of our optical network and the spectral amplitude of the input photons are manifested in the interference pattern. Moreover, we demonstrate time-reversed HOM-like interference in the spectral correlations using time-bin entangled photon pairs. By adding a time-varying dispersion using a phase modulator, our setup can be used to realize dynamically reconfigurable and scalable boson sampling in the time domain as well as frequency-resolved multiboson correlation sampling.

}, doi = {https://doi.org/10.1103/PhysRevLett.123.123603}, url = {https://arxiv.org/abs/1904.03222}, author = {Venkata Vikram Orre and Elizabeth A. Goldschmidt and Abhinav Deshpande and Alexey V. Gorshkov and Vincenzo Tamma and Mohammad Hafezi and Sunil Mittal} } @article {2370, title = {Interpreting Neural Networks Using Flip Points}, year = {2019}, month = {03/20/2019}, abstract = {

Neural networks have been criticized for their lack of easy interpretation, which undermines confidence in their use for important applications. Here, we introduce a novel technique, interpreting a trained neural network by investigating its flip points. A flip point is any point that lies on the boundary between two output classes: e.g. for a neural network with a binary yes/no output, a flip point is any input that generates equal scores for \"yes\" and \"no\". The flip point closest to a given input is of particular importance, and this point is the solution to a well-posed optimization problem. This paper gives an overview of the uses of flip points and how they are computed. Through results on standard datasets, we demonstrate how flip points can be used to provide detailed interpretation of the output produced by a neural network. Moreover, for a given input, flip points enable us to measure confidence in the correctness of outputs much more effectively than softmax score. They also identify influential features of the inputs, identify bias, and find changes in the input that change the output of the model. We show that distance between an input and the closest flip point identifies the most influential points in the training data. Using principal component analysis (PCA) and rank-revealing QR factorization (RR-QR), the set of directions from each training input to its closest flip point provides explanations of how a trained neural network processes an entire dataset: what features are most important for classification into a given class, which features are most responsible for particular misclassifications, how an adversary might fool the network, etc. Although we investigate flip points for neural networks, their usefulness is actually model-agnostic.

}, url = {https://arxiv.org/abs/1903.08789}, author = {Roozbeh Yousefzadeh and Dianne P. O{\textquoteright}Leary} } @article {2454, title = {Investigating Decision Boundaries of Trained Neural Networks}, year = {2019}, month = {8/7/2019}, abstract = {

Deep learning models have been the subject of study from various perspectives, for example, their training process, interpretation, generalization error, robustness to adversarial attacks, etc. A trained model is defined by its decision boundaries, and therefore, many of the studies about deep learning models speculate about the decision boundaries, and sometimes make simplifying assumptions about them. So far, finding exact points on the decision boundaries of trained deep models has been considered an intractable problem. Here, we compute exact points on the decision boundaries of these models and provide mathematical tools to investigate the surfaces that define the decision boundaries. Through numerical results, we confirm that some of the speculations about the decision boundaries are accurate, some of the computational methods can be improved, and some of the simplifying assumptions may be unreliable, for models with nonlinear activation functions. We advocate for verification of simplifying assumptions and approximation methods, wherever they are used. Finally, we demonstrate that the computational practices used for finding adversarial examples can be improved and computing the closest point on the decision boundary reveals the weakest vulnerability of a model against adversarial attack.

}, url = {https://arxiv.org/abs/1908.02802}, author = {Roozbeh Yousefzadeh and Dianne P O{\textquoteright}Leary} } @article {2310, title = {Limitations of semidefinite programs for separable states and entangled games}, journal = {Commun. Math. Phys.}, volume = {366}, year = {2019}, month = {03/04/2019}, chapter = {423-468}, abstract = {

Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These are based on new limitations on the sum-of-squares (SoS) hierarchy in approximating two particularly important sets in quantum information theory, where previously no ω(1)-round integrality gaps were known: the set of separable (i.e. unentangled) states, or equivalently, the 2\→4 norm of a matrix, and the set of quantum correlations; i.e. conditional probability distributions achievable with local measurements on a shared entangled state. In both cases no-go theorems were previously known based on computational assumptions such as the Exponential Time Hypothesis (ETH) which asserts that 3-SAT requires exponential time to solve. Our unconditional results achieve the same parameters as all of these previous results (for separable states) or as some of the previous results (for quantum correlations). In some cases we can make use of the framework of Lee-Raghavendra-Steurer (LRS) to establish integrality gaps for any SDP, not only the SoS hierarchy. Our hardness result on separable states also yields a dimension lower bound of approximate disentanglers, answering a question of Watrous and Aaronson et al. These results can be viewed as limitations on the monogamy principle, the PPT test, the ability of Tsirelson-type bounds to restrict quantum correlations, as well as the SDP hierarchies of Doherty-Parrilo-Spedalieri, Navascues-Pironio-Acin and Berta-Fawzi-Scholz.

}, doi = {https://doi.org/10.1007/s00220-019-03382-y}, url = {https://arxiv.org/abs/1612.09306}, author = {Aram W. Harrow and Anand Natarajan and Xiaodi Wu} } @article {2195, title = {Locality and digital quantum simulation of power-law interactions}, journal = {Phys. Rev. X 9, 031006}, volume = {9}, year = {2019}, month = {07/10/2019}, abstract = {

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α\>3D (where D is the number of dimensions).

}, doi = {https://doi.org/10.1103/PhysRevX.9.031006}, url = {https://arxiv.org/abs/1808.05225}, author = {Minh C. Tran and Andrew Y. Guo and Yuan Su and James R. Garrison and Zachary Eldredge and Michael Foss-Feig and Andrew M. Childs and Alexey V. Gorshkov} } @article {2458, title = {Locality and Heating in Periodically Driven, Power-law Interacting Systems}, journal = {Phys. Rev. A }, volume = {100}, year = {2019}, month = {2019/11/12}, abstract = {

We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power-law 1/rα. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for α\>D. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for α\>2D. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.\ 

}, doi = {https://doi.org/10.1103/PhysRevA.100.052103}, url = {https://arxiv.org/abs/1908.02773}, author = {Minh C. Tran and Adam Ehrenberg and Andrew Y. Guo and Paraj Titum and Dmitry A. Abanin and Alexey V. Gorshkov} } @article {2253, title = {Locality, Quantum Fluctuations, and Scrambling}, journal = {Phys. Rev. X }, volume = {9}, year = {2019}, month = {9/18/2019}, abstract = {

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large N models exhibiting exponential growth of OTOCs and a sharp chaos wavefront and other random circuit models showing a diffusively broadened wavefront. In this paper we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wavefront. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a cross-over to a diffusively broadened wavefront. At small N we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively-broadened wavefront.

}, doi = {https://doi.org/10.1103/PhysRevX.9.031048}, url = {https://arxiv.org/abs/1805.05376}, author = {Shenglong Xu and Brian Swingle} } @article {2465, title = {Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems}, year = {2019}, month = {9/11/2019}, abstract = {

We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type of dynamics that occurs depends on whether or not the Fermi level of the initial state is near the energy of the delocalized states present in these models. If the Fermi level of the initial state is near the energy of the delocalized states, we observe an interesting slow logarithmic-like growth of the momentum-space entanglement entropy followed by an eventual saturation. Otherwise, the momentum-space entanglement entropy is found to rapidly saturate. We also find that the momentum-space entanglement spectrum reveals the presence of delocalized states in these models for long times after the quench and the many-body entanglement gap decays logarithmically in time when the Fermi level is near the energy of the delocalized states.

}, url = {https://arxiv.org/abs/1909.05140}, author = {Rex Lundgren and Fangli Liu and Pontus Laurell and Gregory A. Fiete} } @article {2496, title = {On the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model}, year = {2019}, month = {2019/10/9}, abstract = {

The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this work, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents, including those, such as the dynamical critical exponent, that have not been previously considered. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely non-equilibrium. We derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that capture the system\&$\#$39;s long-time memory as well as its non-equilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.

}, url = {https://arxiv.org/abs/1910.04319}, author = {Rex Lundgren and Alexey V. Gorshkov and Mohammad F. Maghrebi} } @article {2332, title = {Nearly optimal lattice simulation by product formulas}, journal = {Phys. Rev. Lett. }, volume = {123}, year = {2019}, month = {12/17/2019}, abstract = {

Product formulas provide a straightforward yet surprisingly efficient approach to quantum simulation. We show that this algorithm can simulate an n-qubit Hamiltonian with nearest-neighbor interactions evolving for time t using only (nt)1+o(1) gates. While it is reasonable to expect this complexity---in particular, this was claimed without rigorous justification by Jordan, Lee, and Preskill---we are not aware of a straightforward proof. Our approach is based on an analysis of the local error structure of product formulas, as introduced by Descombes and Thalhammer and significantly simplified here. We prove error bounds for canonical product formulas, which include well-known constructions such as the Lie-Trotter-Suzuki formulas. We also develop a local error representation for time-dependent Hamiltonian simulation, and we discuss generalizations to periodic boundary conditions, constant-range interactions, and higher dimensions. Combined with a previous lower bound, our result implies that product formulas can simulate lattice Hamiltonians with nearly optimal gate complexity.

}, doi = {https://doi.org/10.1103/PhysRevLett.123.050503}, url = {https://arxiv.org/abs/1901.00564}, author = {Andrew M. Childs and Yuan Su} } @article {2544, title = {New stepsizes for the gradient method}, journal = {Optim Lett }, year = {2019}, month = {1/28/2019}, abstract = {

Gradient methods are famous for their simplicity and low complexity, which attract more and more attention for large scale optimization problems. A good stepsize plays an important role to construct an efficient gradient method. This paper proposes a new framework to generate stepsizes for gradient methods applied to convex quadratic function minimization problems. By adopting different criterions, we propose four new gradient methods. For 2-dimensional unconstrained problems with convex quadratic objective functions, we prove that the new methods either terminate in finite iterations or converge R-superlinearly; for n-dimensional problems, we prove that all the new methods converge R-linearly. Numerical experiments show that the new methods enjoy lower complexity and outperform the existing gradient methods.

}, doi = {https://doi.org/10.1007/s11590-019-01512-y}, author = {Cong Sun and Jin-Peng Liu} } @article {2219, title = {On non-adaptive quantum chosen-ciphertext attacks and Learning with Errors}, journal = {14th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2019, June 3-5, 2019, University of Maryland, College Park, Maryland, USA}, year = {2019}, pages = {1:1-1:23 }, abstract = {

Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong \"quantum access\" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model which grants the adversary quantum oracle access to encryption and decryption, but where the latter is restricted to non-adaptive (i.e., pre-challenge) queries only. We define this model formally using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. Using a bound on quantum random-access codes, we show that the standard PRF- and PRP-based encryption schemes are QCCA1-secure when instantiated with quantum-secure primitives. We then revisit standard IND-CPA-secure Learning with Errors (LWE) encryption and show that leaking just one quantum decryption query (and no other queries or leakage of any kind) allows the adversary to recover the full secret key with constant success probability. In the classical setting, by contrast, recovering the key uses a linear number of decryption queries, and this is optimal. The algorithm at the core of our attack is a (large-modulus version of) the well-known Bernstein-Vazirani algorithm. We emphasize that our results should *not* be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.\ 

}, doi = {https://doi.org/10.4230/LIPIcs.TQC.2019.1}, url = {https://arxiv.org/abs/1808.09655}, author = {Gorjan Alagic and Stacey Jeffery and Maris Ozols and Alexander Poremba} } @article {2460, title = {Nondestructive cooling of an atomic quantum register via state-insensitive Rydberg interactions}, year = {2019}, month = {7/28/2019}, abstract = {

We propose a protocol for sympathetically cooling neutral atoms without destroying the quantum information stored in their internal states. This is achieved by designing state-insensitive Rydberg interactions between the data-carrying atoms and cold auxiliary atoms. The resulting interactions give rise to an effective phonon coupling, which leads to the transfer of heat from the data atoms to the auxiliary atoms, where the latter can be cooled by conventional methods. This can be used to extend the lifetime of quantum storage based on neutral atoms and can have applications for long quantum computations. The protocol can also be modified to realize state-insensitive interactions between the data and the auxiliary atoms but tunable and non-trivial interactions among the data atoms, allowing one to simultaneously cool and simulate a quantum spin-model.\ 

}, url = {https://arxiv.org/abs/1907.11156}, author = {Ron Belyansky and Jeremy T. Young and Przemyslaw Bienias and Zachary Eldredge and Adam M. Kaufman and Peter Zoller and Alexey V. Gorshkov} } @article {2464, title = {Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits}, year = {2019}, month = {8/16/2019}, abstract = {

Kliuchnikov, Maslov, and Mosca proved in 2012 that a 2\×2 unitary matrix V can be exactly represented by a single-qubit Clifford+T circuit if and only if the entries of V belong to the ring Z[1/2\–\√,i]. Later that year, Giles and Selinger showed that the same restriction applies to matrices that can be exactly represented by a multi-qubit Clifford+T circuit. These number-theoretic characterizations shed new light upon the structure of Clifford+T circuits and led to remarkable developments in the field of quantum compiling. In the present paper, we provide number-theoretic characterizations for certain restricted Clifford+T circuits by considering unitary matrices over subrings of Z[1/2\–\√,i]. We focus on the subrings Z[1/2], Z[1/2\–\√], Z[1/-2\−\−\√], and Z[1/2,i], and we prove that unitary matrices with entries in these rings correspond to circuits over well-known universal gate sets. In each case, the desired gate set is obtained by extending the set of classical reversible gates {X,CX,CCX} with an analogue of the Hadamard gate and an optional phase gate.

}, url = {https://arxiv.org/abs/1908.06076}, author = {Matthew Amy and Andrew N. Glaudell and Neil J. Ross} } @article {2520, title = {Observation of Domain Wall Confinement and Dynamics in a Quantum Simulator}, year = {2019}, month = {12/23/2019}, abstract = {

Confinement is a ubiquitous mechanism in nature, whereby particles feel an attractive force that increases without bound as they separate. A prominent example is color confinement in particle physics, in which baryons and mesons are produced by quark confinement. Analogously, confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here, we report the first observation of magnetic domain wall confinement in interacting spin chains with a trapped-ion quantum simulator. By measuring how correlations spread, we show that confinement can dramatically suppress information propagation and thermalization in such many-body systems. We are able to quantitatively determine the excitation energy of domain wall bound states from non-equilibrium quench dynamics. Furthermore, we study the number of domain wall excitations created for different quench parameters, in a regime that is difficult to model with classical computers. This work demonstrates the capability of quantum simulators for investigating exotic high-energy physics phenomena, such as quark collision and string breaking

}, url = {https://arxiv.org/abs/1912.11117}, author = {W. L. Tan and P. Becker and F. Liu and G. Pagano and K. S. Collins and A. De and L. Feng and H. B. Kaplan and A. Kyprianidis and R. Lundgren and W. Morong and S. Whitsitt and Alexey V. Gorshkov and C. Monroe} } @article {2362, title = {Opportunities for Nuclear Physics \& Quantum Information Science}, year = {2019}, month = {03/13/2019}, abstract = {

his whitepaper is an outcome of the workshop Intersections between Nuclear Physics and Quantum Information held at Argonne National Laboratory on 28-30 March 2018 [www.phy.anl.gov/npqi2018/]. The workshop brought together 116 national and international experts in nuclear physics and quantum information science to explore opportunities for the two fields to collaborate on topics of interest to the U.S. Department of Energy (DOE) Office of Science, Office of Nuclear Physics, and more broadly to U.S. society and industry. The workshop consisted of 22 invited and 10 contributed talks, as well as three panel discussion sessions. Topics discussed included quantum computation, quantum simulation, quantum sensing, nuclear physics detectors, nuclear many-body problem, entanglement at collider energies, and lattice gauge theories.

}, url = {https://arxiv.org/abs/1903.05453}, author = {I. C. Clo{\"e}t and Matthew R. Dietrich and John Arrington and Alexei Bazavov and Michael Bishof and Adam Freese and Alexey V. Gorshkov and Anna Grassellino and Kawtar Hafidi and Zubin Jacob and Michael McGuigan and Yannick Meurice and Zein-Eddine Meziani and Peter Mueller and Christine Muschik and James Osborn and Matthew Otten and Peter Petreczky and Tomas Polakovic and Alan Poon and Raphael Pooser and Alessandro Roggero and Mark Saffman and Brent VanDevender and Jiehang Zhang and Erez Zohar} } @article {2223, title = {Parallel Self-Testing of the GHZ State with a Proof by Diagrams}, journal = {EPTCS }, volume = {287}, year = {2019}, month = {01/29/2019}, pages = {43-66}, abstract = {

Quantum self-testing addresses the following question: is it possible to verify the existence of a multipartite state even when one\&$\#$39;s measurement devices are completely untrusted? This problem has seen abundant activity in the last few years, particularly with the advent of parallel self-testing (i.e., testing several copies of a state at once), which has applications not only to quantum cryptography but also quantum computing. In this work we give the first error-tolerant parallel self-test in a three-party (rather than two-party) scenario, by showing that an arbitrary number of copies of the GHZ state can be self-tested. In order to handle the additional complexity of a three-party setting, we use a diagrammatic proof based on categorical quantum mechanics, rather than a typical symbolic proof. The diagrammatic approach allows for manipulations of the complicated tensor networks that arise in the proof, and gives a demonstration of the importance of picture-languages in quantum information.

}, doi = {https://doi.org/10.4204/EPTCS.287.3}, url = {https://arxiv.org/abs/1806.04744}, author = {Spencer Breiner and Amir Kalev and Carl Miller} } @article {2390, title = {Photon pair condensation by engineered dissipation}, journal = {Phys. Rev. Lett. }, volume = {123}, year = {2019}, month = {04/02/2019}, abstract = {

Dissipation can usually induce detrimental decoherence in a quantum system. However, engineered dissipation can be used to prepare and stabilize coherent quantum many-body states. Here, we show that by engineering dissipators containing photon pair operators, one can stabilize an exotic dark state, which is a condensate of photon pairs with a phase-nematic order. In this system, the usual superfluid order parameter, i.e. single-photon correlation, is absent, while the photon pair correlation exhibits long-range order. Although the dark state is not unique due to multiple parity sectors, we devise an additional type of dissipators to stabilize the dark state in a particular parity sector via a diffusive annihilation process which obeys Glauber dynamics in an Ising model. Furthermore, we propose an implementation of these photon-pair dissipators in circuit-QED architecture.\ 

}, doi = {10.1103/PhysRevLett.123.063602}, url = {https://arxiv.org/abs/1904.00016}, author = {Ze-Pei Cian and Guanyu Zhu and Su-Kuan Chu and Alireza Seif and Wade DeGottardi and Liang Jiang and Mohammad Hafezi} } @article {2415, title = {Polynomial Time Algorithms for Estimating Spectra of Adiabatic Hamiltonians}, journal = {Phys. Rev. A}, volume = {100}, year = {2019}, month = {10/1/2020}, abstract = {

Much research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians with Hamming symmetric potentials, such as the well studied \"spike\" example. Due to the large amount of symmetry in these potentials such problems are readily open to analysis both analytically and computationally. However, more realistic potentials do not have such a high degree of symmetry and may have many local minima. Here we present a somewhat more realistic class of problems consisting of many individually Hamming symmetric potential wells. For two or three such wells we demonstrate that such a problem can be solved exactly in time polynomial in the number of qubits and wells. For greater than three wells, we present a tight binding approach with which to efficiently analyze the performance of such Hamiltonians in an adiabatic computation. We provide several basic examples designed to highlight the usefulness of this toy model and to give insight into using the tight binding approach to examining it, including: (1) adiabatic unstructured search with a transverse field driver and a prior guess to the marked item and (2) a scheme for adiabatically simulating the ground states of small collections of strongly interacting spins, with an explicit demonstration for an Ising model Hamiltonian.

}, doi = {https://doi.org/10.1103/PhysRevA.100.032336}, url = {https://arxiv.org/abs/1905.07461}, author = {Jacob Bringewatt and William Dorland and Stephen P. Jordan} } @article {2489, title = {A Probabilistic Framework and a Homotopy Method for Real-time Hierarchical Freight Dispatch Decisions}, year = {2019}, month = {2019/12/8}, abstract = {

We propose a real-time decision framework for multimodal freight dispatch through a system of hierarchical hubs, using a probabilistic model for transit times. Instead of assigning a fixed time to each transit, we advocate using historical records to identify characteristics of the probability density function for each transit time. We formulate a nonlinear optimization problem that defines dispatch decisions that minimize expected cost, using this probabilistic information. Finally, we propose an effective homotopy algorithm that (empirically) outperforms standard optimization algorithms on this problem by taking advantage of its structure, and we demonstrate its effectiveness on numerical examples.\ 

}, url = {https://arxiv.org/abs/1912.03733}, author = {Roozbeh Yousefzadeh and Dianne P. O{\textquoteright}Leary} } @article {2265, title = {Probing ground-state phase transitions through quench dynamics}, journal = {Phys. Rev. Lett.}, volume = {123}, year = {2019}, month = {9/11/2019}, abstract = {

The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a non-analytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal time scales. Therefore, our method can be used to approximately locate the quantum critical point. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.

}, doi = {https://doi.org/10.1103/PhysRevLett.123.115701}, url = {https://arxiv.org/abs/1809.06377}, author = {Paraj Titum and Joseph T. Iosue and James R. Garrison and Alexey V. Gorshkov and Zhe-Xuan Gong} } @article {2296, title = {Product Spectrum Ansatz and the Simplicity of Thermal States}, journal = {Phys. Rev. A }, volume = {100}, year = {2019}, month = {2019/11/18}, abstract = {

Calculating the physical properties of quantum thermal states is a difficult problem for classical computers, rendering it intractable for most quantum many-body systems. A quantum computer, by contrast, would make many of these calculations feasible in principle, but it is still non-trivial to prepare a given thermal state or sample from it. It is also not known how to prepare special simple purifications of thermal states known as thermofield doubles, which play an important role in quantum many-body physics and quantum gravity. To address this problem, we propose a variational scheme to prepare approximate thermal states on a quantum computer by applying a series of two-qubit gates to a product mixed state. We apply our method to a non-integrable region of the mixed field Ising chain and the Sachdev-Ye-Kitaev model. We also demonstrate how our method can be easily extended to large systems governed by local Hamiltonians and the preparation of thermofield double states. By comparing our results with exact solutions, we find that our construction enables the efficient preparation of approximate thermal states on quantum devices. Our results can be interpreted as implying that the details of the many-body energy spectrum are not needed to capture simple thermal observables.

}, doi = {https://doi.org/10.1103/PhysRevA.100.032107}, url = {https://arxiv.org/abs/1812.01015}, author = {John Martyn and Brian Swingle} } @article {2529, title = {Programmable Quantum Simulations of Spin Systems with Trapped Ions}, year = {2019}, month = {12/17/2019}, abstract = {

Laser-cooled and trapped atomic ions form an ideal standard for the simulation of interacting quantum spin models. Effective spins are represented by appropriate internal energy levels within each ion, and the spins can be measured with near-perfect efficiency using state-dependent fluorescence techniques. By applying optical fields that exert optical dipole forces on the ions, their Coulomb interaction can be modulated in ways that give rise to long-range and tunable spin-spin interactions that can be reconfigured by shaping the spectrum and pattern of the laser fields. Here we review the theoretical mapping of atomic ions to interacting spin systems, the experimental preparation of complex equilibrium states, and the study of dynamical processes of this many-body interacting quantum system. The use of such quantum simulators for studying spin models may inform our understanding of exotic quantum materials and shed light on interacting quantum systems that cannot be modeled with conventional computers.\ 

}, url = {https://arxiv.org/abs/1912.07845}, author = {C. Monroe and W. C. Campbell and L. -M. Duan and Z. -X. Gong and Alexey V. Gorshkov and P. Hess and R. Islam and K. Kim and G. Pagano and P. Richerme and C. Senko and N. Y. Yao} } @article {2352, title = {Quantifying the magic of quantum channels}, journal = {New Journal of Physics}, volume = {21}, year = {2019}, month = {10/8/2019}, abstract = {

To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum \"magic\" or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension d, it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise.

}, doi = {https://doi.org/10.1088/1367-2630/ab451d}, url = {https://arxiv.org/abs/1903.04483}, author = {Xin Wang and Mark M. Wilde and Yuan Su} } @article {2131, title = {Quantum Algorithm for Simulating the Wave Equation}, journal = {Phys. Rev. A }, volume = {99 }, year = {2019}, month = {03/24/2019}, abstract = {

We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for improved scaling in truncation errors and improved scaling for state preparation relative to general purpose linear differential equation algorithms. We also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell\&$\#$39;s equations.

}, doi = {https://doi.org/10.1103/PhysRevA.99.012323}, url = {https://arxiv.org/abs/1711.05394}, author = {Pedro C.S. Costa and Stephen P. Jordan and Aaron Ostrander} } @article {2410, title = {Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator}, year = {2019}, month = {06/06/2019}, abstract = {

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly solving exponentially hard problems, such as optimization and satisfiability. Here we report the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator to estimate the ground state energy of the transverse field Ising model with tunable long-range interactions. First, we exhaustively search the variational control parameters to approximate the ground state energy with up to 40 trapped-ion qubits. We then interface the quantum simulator with a classical algorithm to more efficiently find the optimal set of parameters that minimizes the resulting energy of the system. We finally sample from the full probability distribution of the QAOA output with single-shot and efficient measurements of every qubit.\ 

}, url = {https://arxiv.org/abs/1906.02700}, author = {G. Pagano and A. Bapat and P. Becker and K. S. Collins and A. De and P. W. Hess and H. B. Kaplan and A. Kyprianidis and W. L. Tan and Christopher L. Baldwin and L. T. Brady and A. Deshpande and F. Liu and S. Jordan and Alexey V. Gorshkov and C. Monroe} } @article {2413, title = {Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions}, year = {2019}, month = {05/21/2019}, abstract = {

The multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data of the corresponding conformal field theories with high accuracy. However, a rigorous understanding of its success and precise relation to the continuum is still lacking. To address this challenge, we provide an explicit construction of entanglement-renormalization quantum circuits that rigorously approximate correlation functions of the massless Dirac conformal field theory. We directly target the continuum theory: discreteness is introduced by our choice of how to probe the system, not by any underlying short-distance lattice regulator. To achieve this, we use multiresolution analysis from wavelet theory to obtain an approximation scheme and to implement entanglement renormalization in a natural way. This could be a starting point for constructing quantum circuit approximations for more general conformal field theories.\ 

}, url = {https://arxiv.org/abs/1905.08821}, author = {Freek Witteveen and Volkher Scholz and Brian Swingle and Michael Walter} } @article {2530, title = {Quantum Computer Systems for Scientific Discovery}, year = {2019}, month = {12/16/2019}, abstract = {

The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, and significant challenges for the development of quantum computers for science over the next 2-10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21-22, 2019 in Alexandria, VA.

}, url = {https://arxiv.org/abs/1912.07577}, author = {Yuri Alexeev and Dave Bacon and Kenneth R. Brown and Robert Calderbank and Lincoln D. Carr and Frederic T. Chong and Brian DeMarco and Dirk Englund and Edward Farhi and Bill Fefferman and Alexey V. Gorshkov and Andrew Houck and Jungsang Kim and Shelby Kimmel and Michael Lange and Seth Lloyd and Mikhail D. Lukin and Dmitri Maslov and Peter Maunz and Christopher Monroe and John Preskill and Martin Roetteler and Martin Savage and Jeff Thompson and Umesh Vazirani} } @article {2486, title = {Quantum Computing at the Frontiers of Biological Sciences}, year = {2019}, month = {2019/11/16}, abstract = {

The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems. Innovation in massively parallel, classical computing hardware and algorithms continues to address many of these challenges, but there is a need to simultaneously consider new paradigms to circumvent current barriers to processing speed. Accordingly, we articulate a view towards quantum computation and quantum information science, where algorithms have demonstrated potential polynomial and exponential computational speedups in certain applications, such as machine learning. The maturation of the field of quantum computing, in hardware and algorithm development, also coincides with the growth of several collaborative efforts to address questions across length and time scales, and scientific disciplines. We use this coincidence to explore the potential for quantum computing to aid in one such endeavor: the merging of insights from genetics, genomics, neuroimaging and behavioral phenotyping. By examining joint opportunities for computational innovation across fields, we highlight the need for a common language between biological data analysis and quantum computing. Ultimately, we consider current and future prospects for the employment of quantum computing algorithms in the biological sciences.\ 

}, url = {https://arxiv.org/abs/1911.07127}, author = {Prashant S. Emani and Jonathan Warrell and Alan Anticevic and Stefan Bekiranov and Michael Gandal and Michael J. McConnell and Guillermo Sapiro and Al{\'a}n Aspuru-Guzik and Justin Baker and Matteo Bastiani and Patrick McClure and John Murray and Stamatios N Sotiropoulos and J. M. Taylor and Geetha Senthil and Thomas Lehner and Mark B. Gerstein and Aram W. Harrow} } @article {2490, title = {Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes}, year = {2019}, month = {2019/11/14}, abstract = {

With the long-term goal of studying quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in recent traversable wormhole constructions: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of \"teleportation by size\" to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semi-classical holographic wormhole corresponds to a rather special property of the operator-size distribution we call \"size winding\". For more general setups (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable wormhole phenomenon. For example, a form of signalling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole, but rather to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations feasible with current technology in two experimental platforms: Rydberg atom arrays and trapped ions.\ 

}, url = {https://arxiv.org/abs/1911.06314}, author = {Adam R. Brown and Hrant Gharibyan and Stefan Leichenauer and Henry W. Lin and Sepehr Nezami and Grant Salton and Leonard Susskind and Brian Swingle and Michael Walter} } @article {2386, title = {Quantum hardness of learning shallow classical circuits}, year = {2019}, month = {03/07/2019}, abstract = {

In this paper we study the quantum learnability of constant-depth classical circuits under the uniform distribution and in the distribution-independent framework of PAC learning. In order to attain our results, we establish connections between quantum learning and quantum-secure cryptosystems. We then achieve the following results. 1) Hardness of learning AC0 and TC0 under the uniform distribution. Our first result concerns the concept class TC0 (resp. AC0), the class of constant-depth and polynomial-sized circuits with unbounded fan-in majority gates (resp. AND, OR, NOT gates). We show that if there exists no quantum polynomial-time (resp. sub-exponential time) algorithm to solve the Learning with Errors (LWE) problem, then there exists no polynomial-time quantum learning algorithm for TC0 (resp. AC0) under the uniform distribution (even with access to quantum membership queries). The main technique in this result uses explicit pseudo-random generators that are believed to be quantum-secure to construct concept classes that are hard to learn quantumly under the uniform distribution. 2) Hardness of learning TC02 in the PAC setting. Our second result shows that if there exists no quantum polynomial time algorithm for the LWE problem, then there exists no polynomial time quantum PAC learning algorithm for the class TC02, i.e., depth-2 TC0 circuits. The main technique in this result is to establish a connection between the quantum security of public-key cryptosystems and the learnability of a concept class that consists of decryption functions of the cryptosystem. This gives a strong conditional negative answer to one of the \"Ten Semi-Grand Challenges for Quantum Computing Theory\" raised by Aaronson [Aar05], who asked if AC0 and TC0 can be PAC-learned in quantum polynomial time.

}, url = {https://arxiv.org/abs/1903.02840}, author = {Srinivasan Arunachalam and Alex B. Grilo and Aarthi Sundaram} } @article {2202, title = {Quantum Lyapunov Spectrum}, journal = {JHEP04}, volume = {082}, year = {2019}, month = {04/10/2019}, abstract = {

We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is not just the fastest scrambler, but also the fastest entropy generator. We also study the statistical features of the quantum Lyapunov spectrum and find universal random matrix behavior, which resembles the recently-found universality in classical chaos. The random matrix behavior is lost when the system is deformed away from chaos, towards integrability or a many-body localized phase. We propose that quantum systems holographically dual to gravity satisfy this universality in a strong form. We further argue that the quantum Lyapunov spectrum contains important additional information beyond the largest Lyapunov exponent and hence provides us with a better characterization of chaos in quantum systems.\ 

}, doi = {https://doi.org/10.1007/JHEP04(2019)082}, url = {https://arxiv.org/abs/1809.01671}, author = {Hrant Gharibyan and Masanori Hanada and Brian Swingle and Masaki Tezuka} } @article {2371, title = {Quantum Physics Meets Music: A "Real-Time" Guitar Recording Using Rydberg-Atoms and Electromagnetically Induced Transparency}, year = {2019}, month = {04/01/2019}, abstract = {

We demonstrate how Rydberg atoms and the phenomena of electromagnetically induced transparency can be used to aid in the recording of a musical instrument in real time as it is played. Also, by using two different atomic species (cesium and rubidium) in the same vapor cell, we demonstrate the ability to record two guitars simultaneously, where each atomic species detects and allows for the recording of each guitar separately. The approach shows how audio data (the musical composition) can be detected with a quantum system, illustrating how we can control ensembles of atoms to such an extent that we can use them in this \"entertaining\" example of recording a musical instrument.

}, url = {https://arxiv.org/abs/1904.01952}, author = {Christopher L. Holloway and Matthew T. Simons and Abdulaziz H. Haddab and Carl J. Williams and Maxwell W. Holloway} } @article {2105, title = {Quantum query complexity of entropy estimation}, journal = {IEEE Transactions on Information Theory}, volume = {65}, year = {2019}, month = {10/16/2017}, pages = {2899-2921}, abstract = {

Estimation of Shannon and R\´enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on the number of samples to estimate these entropies have been established in the classical setting, while little is known about their quantum counterparts. In this paper, we give the first quantum algorithms for estimating α- R\´enyi entropies (Shannon entropy being 1-Renyi entropy). In particular, we demonstrate a quadratic quantum speedup for Shannon entropy estimation and a generic quantum speedup for α-R\´enyi entropy estimation for all α \≥ 0, including a tight bound for the collision-entropy (2-R\´enyi entropy). We also provide quantum upper bounds for extreme cases such as the Hartley entropy (i.e., the logarithm of the support size of a distribution, corresponding to α = 0) and the min-entropy case (i.e., α = +\∞), as well as the Kullback-Leibler divergence between two distributions. Moreover, we complement our results with quantum lower bounds on α-R\´enyi entropy estimation for all α \≥ 0. Our approach is inspired by the pioneering work of Bravyi, Harrow, and Hassidim (BHH) [13] on quantum algorithms for distributional property testing, however, with many new technical ingredients. For Shannon entropy and 0-R\´enyi entropy estimation, we improve the performance of the BHH framework, especially its error dependence, using Montanaro\’s approach to estimating the expected output value of a quantum subroutine with bounded variance [41] and giving a fine-tuned error analysis. For general α-R\´enyi entropy estimation, we further develop a procedure that recursively approximates α-R\´enyi entropy for a sequence of αs, which is in spirit similar to a cooling schedule in simulated annealing. For special cases such as integer α \≥ 2 and α = +\∞ (i.e., the min-entropy), we reduce the entropy estimation problem to the α-distinctness and the dlog ne-distinctness problems, respectively. We exploit various techniques to obtain our lower bounds for different ranges of α, including reductions to (variants of) existing lower bounds in quantum query complexity as well as the polynomial method inspired by the celebrated quantum lower bound for the collision problem.

}, doi = {https://doi.org/10.1109/TIT.2018.2883306}, url = {https://arxiv.org/abs/1710.06025}, author = {Tongyang Li and Xiaodi Wu} } @article {2290, title = {Quantum repeaters based on two species trapped ions}, journal = {New J. Phys. }, volume = {21}, year = {2019}, month = {05/02/2019}, abstract = {

We examine the viability of quantum repeaters based on two-species trapped ion modules for long distance quantum key distribution. Repeater nodes comprised of ion-trap modules of co-trapped ions of distinct species are considered. The species used for communication qubits has excellent optical properties while the other longer lived species serves as a memory qubit in the modules. Each module interacts with the network only via single photons emitted by the communication ions. Coherent Coulomb interaction between ions is utilized to transfer quantum information between the communication and memory ions and to achieve entanglement swapping between two memory ions. We describe simple modular quantum repeater architectures realizable with the ion-trap modules and numerically study the dependence of the quantum key distribution rate on various experimental parameters, including coupling efficiency, gate infidelity, operation time and length of the elementary links. Our analysis suggests crucial improvements necessary in a physical implementation for co-trapped two-species ions to be a competitive platform in long-distance quantum communication.\ 

}, doi = {https://doi.org/10.1088/1367-2630/ab2a45}, url = {https://arxiv.org/abs/1811.10723}, author = {Siddhartha Santra and Sreraman Muralidharan and Martin Lichtman and Liang Jiang and Christopher Monroe and Vladimir S. Malinovsky} } @article {2532, title = {Quantum Simulators: Architectures and Opportunities}, year = {2019}, month = {12/14/2019}, abstract = {

Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behaviors to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the NSF workshop on \"Programmable Quantum Simulators,\" that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multi-disciplinary collaborations with resources for quantum simulator software, hardware, and education.\ 

}, url = {https://arxiv.org/abs/1912.06938}, author = {Ehud Altman and Kenneth R. Brown and Giuseppe Carleo and Lincoln D. Carr and Eugene Demler and Cheng Chin and Brian DeMarco and Sophia E. Economou and Mark A. Eriksson and Kai-Mei C. Fu and Markus Greiner and Kaden R. A. Hazzard and Randall G. Hulet and Alicia J. Koll{\'a}r and Benjamin L. Lev and Mikhail D. Lukin and Ruichao Ma and Xiao Mi and Shashank Misra and Christopher Monroe and Kater Murch and Zaira Nazario and Kang-Kuen Ni and Andrew C. Potter and Pedram Roushan} } @article {2500, title = {Quantum Wasserstein Generative Adversarial Networks}, journal = {Advances in Neural Information Processing Systems (NIPS)}, volume = {32}, year = {2019}, month = {2019/10/31}, abstract = {

The study of quantum generative models is well-motivated, not only because of its importance in quantum machine learning and quantum chemistry but also because of the perspective of its implementation on near-term quantum machines. Inspired by previous studies on the adversarial training of classical and quantum generative models, we propose the first design of quantum Wasserstein Generative Adversarial Networks (WGANs), which has been shown to improve the robustness and the scalability of the adversarial training of quantum generative models even on noisy quantum hardware. Specifically, we propose a definition of the Wasserstein semimetric between quantum data, which inherits a few key theoretical merits of its classical counterpart. We also demonstrate how to turn the quantum Wasserstein semimetric into a concrete design of quantum WGANs that can be efficiently implemented on quantum machines. Our numerical study, via classical simulation of quantum systems, shows the more robust and scalable numerical performance of our quantum WGANs over other quantum GAN proposals. As a surprising application, our quantum WGAN has been used to generate a 3-qubit quantum circuit of ~50 gates that well approximates a 3-qubit 1-d Hamiltonian simulation circuit that requires over 10k gates using standard techniques.

}, doi = {https://papers.nips.cc/paper/8903-quantum-wasserstein-generative-adversarial-networks.pdf}, url = {https://arxiv.org/abs/1911.00111}, author = {Shouvanik Chakrabarti and Yiming Huang and Tongyang Li and Soheil Feizi and Xiaodi Wu} } @article {2338, title = {Quantum-inspired classical sublinear-time algorithm for solving low-rank semidefinite programming via sampling approaches}, year = {2019}, abstract = {

Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. Recently, quantum algorithms with superpolynomial speedups for solving SDPs have been proposed assuming access to its constraint matrices in quantum superposition. Mutually inspired by both classical and quantum SDP solvers, in this paper we present a sublinear classical algorithm for solving low-rank SDPs which is asymptotically as good as existing quantum algorithms. Specifically, given an SDP with m constraint matrices, each of dimension n and rank poly(logn), our algorithm gives a succinct description and any entry of the solution matrix in time O(m\⋅poly(logn,1/ε)) given access to a sample-based low-overhead data structure of the constraint matrices, where ε is the precision of the solution. In addition, we apply our algorithm to a quantum state learning task as an application. Technically, our approach aligns with both the SDP solvers based on the matrix multiplicative weight (MMW) framework and the recent studies of quantum-inspired machine learning algorithms. The cost of solving SDPs by MMW mainly comes from the exponentiation of Hermitian matrices, and we propose two new technical ingredients (compared to previous sample-based algorithms) for this task that may be of independent interest: . Weighted sampling: assuming sampling access to each individual constraint matrix A1,\…,Aτ, we propose a procedure that gives a good approximation of A=A1+...+Aτ. . Symmetric approximation: we propose a sampling procedure that gives low-rank spectral decomposition of a Hermitian matrix A. This improves upon previous sampling procedures that only give low-rank singular value decompositions, losing the signs of eigenvalues.

}, url = {https://arxiv.org/abs/1901.03254}, author = {Nai-Hui Chia and Tongyang Li and Han-Hsuan Lin and Chunhao Wang} } @article {2580, title = {Quenched vs Annealed: Glassiness from SK to SYK}, year = {2019}, month = {11/26/2019}, abstract = {

We show that any SYK-like model with finite-body interactions among \textit{local} degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: the former fails to be described by an annealed free energy at low temperature. In this respect, such models more closely resemble spin glasses. We demonstrate this by two means: first, a general theorem proving that the annealed free energy is divergent at low temperature in any model with a tensor product Hilbert space; and second, a replica treatment of two prominent examples which exhibit phase transitions from an \"annealed\" phase to a \"non-annealed\" phase as a function of temperature. We further show that this effect appears only at O(N)\&$\#$39;th order in a 1/N expansion, even though lower-order terms misleadingly seem to converge. Our results prove that the non-bosonic nature of the particles in SYK is an essential ingredient for its physics, highlight connections between local models and spin glasses, and raise important questions as to the role of fermions and/or glassiness in holography.

}, url = {https://arxiv.org/abs/1911.11865}, author = {Christopher L. Baldwin and Brian Swingle} } @article {2487, title = {Real-time dynamics of string breaking in quantum spin chains}, year = {2019}, month = {2019/11/26}, abstract = {

String breaking is a central dynamical process in theories featuring confinement, where a string connecting two charges decays at the expense of the creation of new particle-antiparticle pairs. Here, we show that this process can also be observed in quantum Ising chains where domain walls get confined either by a symmetry-breaking field or by long-range interactions. We find that string breaking occurs, in general, as a two-stage process: First, the initial charges remain essentially static and stable. The connecting string, however, can become a dynamical object. We develop an effective description of this motion, which we find is strongly constrained. In the second stage, which can be severely delayed due to these dynamical constraints, the string finally breaks. We observe that the associated time scale can depend crucially on the initial separation between domain walls and can grow by orders of magnitude by changing the distance by just a few lattice sites. We discuss how our results generalize to one-dimensional confining gauge theories and how they can be made accessible in quantum simulator experiments such as Rydberg atoms or trapped ions.

}, url = {https://arxiv.org/abs/1911.11382}, author = {Roberto Verdel and Fangli Liu and Seth Whitsitt and Alexey V. Gorshkov and Markus Heyl} } @article {2455, title = {Refining the Structure of Neural Networks Using Matrix Conditioning}, year = {2019}, month = {8/6/2019}, abstract = {

Deep learning models have proven to be exceptionally useful in performing many machine learning tasks. However, for each new dataset, choosing an effective size and structure of the model can be a time-consuming process of trial and error. While a small network with few neurons might not be able to capture the intricacies of a given task, having too many neurons can lead to overfitting and poor generalization. Here, we propose a practical method that employs matrix conditioning to automatically design the structure of layers of a feed-forward network, by first adjusting the proportion of neurons among the layers of a network and then scaling the size of network up or down. Results on sample image and non-image datasets demonstrate that our method results in small networks with high accuracies. Finally, guided by matrix conditioning, we provide a method to effectively squeeze models that are already trained. Our techniques reduce the human cost of designing deep learning models and can also reduce training time and the expense of using neural networks for applications.

}, url = {https://arxiv.org/abs/1908.02400}, author = {Roozbeh Yousefzadeh and Dianne P O{\textquoteright}Leary} } @article {2385, title = {ReQWIRE: Reasoning about Reversible Quantum Circuits}, journal = {EPTCS }, volume = {287}, year = {2019}, type = {In Proceedings QPL 2018, arXiv:1901.09476}, chapter = {299-312}, abstract = {

Common quantum algorithms make heavy use of ancillae: scratch qubits that are initialized at some state and later returned to that state and discarded. Existing quantum circuit languages let programmers assert that a qubit has been returned to the |0\> state before it is discarded, allowing for a range of optimizations. However, existing languages do not provide the tools to verify these assertions, introducing a potential source of errors. In this paper we present methods for verifying that ancillae are discarded in the desired state, and use these methods to implement a verified compiler from classical functions to quantum oracles.

}, doi = {https://doi.org/10.4204/EPTCS.287.17}, url = {https://arxiv.org/abs/1901.10118}, author = {Robert Rand and Jennifer Paykin and Dong-Ho Lee and Steve Zdancewic} } @article {2417, title = {Resource theory of asymmetric distinguishability for quantum channels}, year = {2019}, month = {07/15/2019}, abstract = {

This paper develops the resource theory of asymmetric distinguishability for quantum channels, generalizing the related resource theory for states [arXiv:1006.0302, arXiv:1905.11629]. The key constituents of the channel resource theory are quantum channel boxes, consisting of a pair of quantum channels, which can be manipulated for free by means of an arbitrary quantum superchannel (the most general physical transformation of a quantum channel). One main question of the resource theory is the approximate channel box transformation problem, in which the goal is to transform an initial channel box (or boxes) to a final channel box (or boxes), while allowing for an asymmetric error in the transformation. The channel resource theory is richer than its counterpart for states because there is a wider variety of ways in which this question can be framed, either in the one-shot or n-shot regimes, with the latter having parallel and sequential variants. As in [arXiv:1905.11629], we consider two special cases of the general channel box transformation problem, known as distinguishability distillation and dilution. For the one-shot case, we find that the optimal values of the various tasks are equal to the non-smooth or smooth channel min- or max-relative entropies, thus endowing all of these quantities with operational interpretations. In the asymptotic sequential setting, we prove that the exact distinguishability cost is equal to channel max-relative entropy and the distillable distinguishability is equal to the amortized channel relative entropy of [arXiv:1808.01498]. This latter result can also be understood as a solution to Stein\&$\#$39;s lemma for quantum channels in the sequential setting. Finally, the theory simplifies significantly for environment-seizable and classical--quantum channel boxes.

}, url = {https://arxiv.org/abs/1907.06306}, author = {Xin Wang and Mark M. Wilde} } @article {2418, title = {Resource theory of entanglement for bipartite quantum channels}, year = {2019}, month = {07/08/2019}, abstract = {

The traditional perspective in quantum resource theories concerns how to use free operations to convert one resourceful quantum state to another one. For example, a fundamental and well known question in entanglement theory is to determine the distillable entanglement of a bipartite state, which is equal to the maximum rate at which fresh Bell states can be distilled from many copies of a given bipartite state by employing local operations and classical communication for free. It is the aim of this paper to take this kind of question to the next level, with the main question being: What is the best way of using free channels to convert one resourceful quantum channel to another? Here we focus on the the resource theory of entanglement for bipartite channels and establish several fundamental tasks and results regarding it. In particular, we establish bounds on several pertinent information processing tasks in channel entanglement theory, and we define several entanglement measures for bipartite channels, including the logarithmic negativity and the κ-entanglement. We also show that the max-Rains information of [B{\"a}uml et al., Physical Review Letters, 121, 250504 (2018)] has a divergence interpretation, which is helpful for simplifying the results of this earlier work.\ 

}, url = {https://arxiv.org/abs/1907.04181}, author = {Stefan B{\"a}uml and Siddhartha Das and Xin Wang and Mark M. Wilde} } @article {2217, title = {Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator}, journal = {Phys. Rev. Lett}, volume = {122}, year = {2019}, month = {03/27/2019}, abstract = {

The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.122.120502}, url = {https://arxiv.org/abs/1807.11486}, author = {Su-Kuan Chu and Guanyu Zhu and James R. Garrison and Zachary Eldredge and Ana Vald{\'e}s Curiel and Przemyslaw Bienias and I. B. Spielman and Alexey V. Gorshkov} } @article {2391, title = {Simulating quantum circuits by classical circuits}, year = {2019}, month = {04/10/2019}, abstract = {

In a recent breakthrough, Bravyi, Gosset and K{\"o}nig (BGK) [Science, 2018] proved that \"simulating\" constant depth quantum circuits takes classical circuits Ω(logn) depth. In our paper, we first formalise their notion of simulation, which we call \"possibilistic simulation\". Then, from well-known results, we deduce that their circuits can be simulated in depth O(log2n). Separately, we construct explicit classical circuits that can simulate any depth-d quantum circuit with Clifford and t T-gates in depth O(d+t). Our classical circuits use {NOT, AND, OR} gates of fan-in \≤2.

}, url = {https://arxiv.org/abs/1904.05282}, author = {Daochen Wang} } @article {2492, title = {Site-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories }, year = {2019}, month = {2019/11/8}, abstract = {

Answering whether quantum computers can efficiently simulate quantum field theories has both theoretical and practical motivation. From the theoretical point of view, it answers the question of whether a hypothetical computer that utilizes quantum field theory would be more powerful than other quantum computers. From the practical point of view, when reliable quantum computers are eventually built, these algorithms can help us better understand the underlying physics that govern our world. In the best known quantum algorithms for simulating quantum field theories, the time scaling is dominated by initial state preparation. In this paper, we exclusively focus on state preparation and present a heuristic algorithm that can prepare the vacuum of fermionic systems in more general cases and more efficiently than previous methods. With our method, state preparation is no longer the bottleneck, as its runtime has the same asymptotic scaling with the desired precision as the remainder of the simulation algorithm. We numerically demonstrate the effectiveness of our proposed method for the 1+1 dimensional Gross-Neveu model.

}, url = {https://arxiv.org/abs/1911.03505}, author = {Ali Hamed Moosavian and James R. Garrison and Stephen P. Jordan} } @article {2425, title = {The Speed of Quantum Information Spreading in Chaotic Systems}, year = {2019}, month = {08/19/2019}, abstract = {

We present a general theory of quantum information propagation in chaotic quantum many-body systems. The generic expectation in such systems is that quantum information does not propagate in localized form; instead, it tends to spread out and scramble into a form that is inaccessible to local measurements. To characterize this spreading, we define an information speed via a quench-type experiment and derive a general formula for it as a function of the entanglement density of the initial state. As the entanglement density varies from zero to one, the information speed varies from the entanglement speed to the butterfly speed. We verify that the formula holds both for a quantum chaotic spin chain and in field theories with an AdS/CFT gravity dual. For the second case, we study in detail the dynamics of entanglement in two-sided Vaidya-AdS-Reissner-Nordstrom black branes. We also show that, with an appropriate decoding process, quantum information can be construed as moving at the information speed, and, in the case of AdS/CFT, we show that a locally detectable signal propagates at the information speed in a spatially local variant of the traversable wormhole setup.

}, url = {https://arxiv.org/abs/1908.06993}, author = {Josiah Couch and Stefan Eccles and Phuc Nguyen and Brian Swingle and Shenglong Xu} } @article {2367, title = {Statistical Privacy in Distributed Average Consensus on Bounded Real Inputs}, year = {2019}, month = {03/20/2019}, abstract = {

This paper proposes a privacy protocol for distributed average consensus algorithms on bounded real-valued inputs that guarantees statistical privacy of honest agents\&$\#$39; inputs against colluding (passive adversarial) agents, if the set of colluding agents is not a vertex cut in the underlying communication network. This implies that privacy of agents\&$\#$39; inputs is preserved against t number of arbitrary colluding agents if the connectivity of the communication network is at least (t+1). A similar privacy protocol has been proposed for the case of bounded integral inputs in our previous paper~\cite{gupta2018information}. However, many applications of distributed consensus concerning distributed control or state estimation deal with real-valued inputs. Thus, in this paper we propose an extension of the privacy protocol in~\cite{gupta2018information}, for bounded real-valued agents\&$\#$39; inputs, where bounds are known apriori to all the agents.\ 

}, url = {https://arxiv.org/abs/1903.09315}, author = {Nirupam Gupta and Jonathan Katz and Nikhil Chopra} } @article {2624, title = {Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process}, journal = {School: National Institute for Standards and Technology }, year = {2019}, type = {techreport}, abstract = {

The National Institute of Standards and Technology is in the process of selecting one or more
public-key cryptographic algorithms through a public competition-like process. The new publickey cryptography standards will specify one or more additional digital signature, public-key
encryption, and key-establishment algorithms to augment FIPS 186-4, Digital Signature Standard
(DSS), as well as special publications SP 800-56A Revision 2, Recommendation for Pair-Wise
Key Establishment Schemes Using Discrete Logarithm Cryptography, and SP 800-56B,
Recommendation for Pair-Wise Key-Establishment Schemes Using Integer Factorization. It is
intended that these algorithms will be capable of protecting sensitive information well into the
foreseeable future, including after the advent of quantum computers.
In November 2017, 82 candidate algorithms were submitted to NIST for consideration. Among
these, 69 met both the minimum acceptance criteria and our submission requirements, and were
accepted as First-Round Candidates on Dec. 20, 2017, marking the beginning of the First Round
of the NIST Post-Quantum Cryptography Standardization Process. This report describes the
evaluation criteria and selection process, based on public feedback and internal review of the
first-round candidates, and summarizes the 26 candidate algorithms announced on January 30,
2019 for moving forward to the second round of the competition. The 17 Second-Round
Candidate public-key encryption and key-establishment algorithms are BIKE, Classic McEliece,
CRYSTALS-KYBER, FrodoKEM, HQC, LAC, LEDAcrypt (merger of LEDAkem/LEDApkc),
NewHope, NTRU (merger of NTRUEncrypt/NTRU-HRSS-KEM), NTRU Prime, NTS-KEM,
ROLLO (merger of LAKE/LOCKER/Ouroboros-R), Round5 (merger of Hila5/Round2), RQC,
SABER, SIKE, and Three Bears. The 9 Second-Round Candidates for digital signatures are
CRYSTALS-DILITHIUM, FALCON, GeMSS, LUOV, MQDSS, Picnic, qTESLA, Rainbow,
and SPHINCS+.

}, url = {https://nvlpubs.nist.gov/nistpubs/ir/2019/NIST.IR.8240.pdf}, author = {Gorjan Alagic and J. Alperin-Sheriff and D. Apon and D. Cooper and Q. Dang and Carl Miller and D. Moody and R. Peralta and R. Perlner and A. Robinson and D. Smith-Tone and Yi-Kai Liu} } @article {2376, title = {Sublinear quantum algorithms for training linear and kernel-based classifiers}, journal = {Proceedings of the 36th International Conference on Machine Learning (ICML 2019) PMLR }, volume = {97}, year = {2019}, month = {04/03/2019}, pages = {3815-3824}, abstract = {

We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given n d-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training classifiers with constant margin runs in O~(n+d) time. We design sublinear quantum algorithms for the same task running in O~(n\−\−\√+d\−\−\√) time, a quadratic improvement in both n and d. Moreover, our algorithms use the standard quantization of the classical input and generate the same classical output, suggesting minimal overheads when used as subroutines for end-to-end applications. We also demonstrate a tight lower bound (up to poly-log factors) and discuss the possibility of implementation on near-term quantum machines. As a side result, we also give sublinear quantum algorithms for approximating the equilibria of n-dimensional matrix zero-sum games with optimal complexity Θ~(n\−\−\√).\ 

}, url = {https://arxiv.org/abs/1904.02276}, author = {Tongyang Li and Shouvanik Chakrabarti and Xiaodi Wu} } @article {2337, title = {Thermalization and chaos in QED3}, journal = {Phys. Rev. D }, volume = {99}, year = {2019}, month = {04/11/2019}, abstract = {

We study the real time dynamics of NF flavors of fermions coupled to a U(1) gauge field in 2+1 dimensions to leading order in a 1/NF expansion. For large enough NF, this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. We focus on thermalization and the onset of many-body quantum chaos which can be diagnosed from the growth of initally anti-commuting fermion field operators. We compute such anti-commutators in this gauge theory to leading order in 1/NF. We find that the anti-commutator grows exponentially in time and compute the quantum Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance.\ 

}, doi = {https://doi.org/10.1103/PhysRevD.99.076007}, url = {https://arxiv.org/abs/1901.04984}, author = {Julia Steinberg and Brian Swingle} } @article {2392, title = {Toward convergence of effective field theory simulations on digital quantum computers}, year = {2019}, month = {04/18/2019}, abstract = {

We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansaetze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of E4=\−2.220\±0.179MeV may be compared with the exact Deuteron ground-state energy \−2.224MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps for the first time. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.\ 

}, url = {https://arxiv.org/abs/1904.04338}, author = {Omar Shehab and Kevin A. Landsman and Yunseong Nam and Daiwei Zhu and Norbert M. Linke and Matthew J. Keesan and Raphael C. Pooser and Christopher R. Monroe} } @article {2401, title = {Towards Bulk Metric Reconstruction from Extremal Area Variations}, year = {2019}, month = {04/09/19}, abstract = {

The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension , knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an\textit {explicit} spacetime metric reconstruction.

}, url = {https://arxiv.org/abs/1904.04834}, author = {Ning Bao and ChunJun Cao and Sebastian Fischetti and Cynthia Keeler} } @article {2574, title = {{\textquoteleft}Two Dogmas{\textquoteright} Redux}, year = {2019}, month = {7/14/2019}, publisher = {Springer, Cham}, abstract = {

I revisit the paper \‘Two dogmas about quantum mechanics,\’ co-authored with Itamar Pitowsky, in which we outlined an information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. Following the analysis by Frauchiger and Renner of \‘encapsulated\’ measurements (where a super-observer, with unrestricted ability to measure any arbitrary observable of a complex quantum system, measures the memory of an observer system after that system measures the spin of a qubit), I show that the Everett interpretation leads to modal contradictions. In this sense, the Everett interpretation is inconsistent.

}, url = {https://arxiv.org/abs/1907.06240}, author = {Jeffrey Bub} } @article {2412, title = {Two-qubit entangling gates within arbitrarily long chains of trapped ions}, year = {2019}, month = {05/28/2019}, abstract = {

Ion trap systems are a leading platform for large scale quantum computers. Trapped ion qubit crystals are fully-connected and reconfigurable, owing to their long range Coulomb interaction that can be modulated with external optical forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals, simplifying the scaling of ion trap quantum computers. To this end, we present analytical work that determines how parallel entangling gates produce a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also show experimental work demonstrating entangling gates on a fully-connected chain of seventeen 171Yb+ ions with fidelities as high as 97(1)\%.

}, url = {https://arxiv.org/abs/1905.10421}, author = {Kevin A. Landsman and Yukai Wu and Pak Hong Leung and Daiwei Zhu and Norbert M. Linke and Kenneth R. Brown and Luming Duan and Christopher R. Monroe} } @article {2534, title = {Universal Constraints on Energy Flow and SYK Thermalization}, year = {2019}, month = {12/10/2019}, url = {https://arxiv.org/abs/1912.04912}, author = {Ahmed Almheiri and Alexey Milekhin and Brian Swingle} } @article {2208, title = {Validating and Certifying Stabilizer States}, journal = {Phys. Rev. A }, volume = {99}, year = {2019}, month = {9/16/2019}, abstract = {

We propose a measurement scheme that validates the preparation of a target n-qubit stabilizer state. The scheme involves a measurement of n Pauli observables, a priori determined from the target stabilizer and which can be realized using single-qubit gates. Based on the proposed validation scheme, we derive an explicit expression for the worse-case fidelity, i.e., the minimum fidelity between the target stabilizer state and any other state consistent with the measured data. We also show that the worse-case fidelity can be certified, with high probability, using O(n) copies of the state of the system per measured observable.

}, doi = {https://doi.org/10.1103/PhysRevA.99.042337}, url = {https://arxiv.org/abs/1808.10786}, author = {Amir Kalev and Anastasios Kyrillidis} } @article {2416, title = {Variational Quantum Computation of Excited States}, journal = {Quantum }, volume = {3}, year = {2019}, month = {06/28/2019}, abstract = {

The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum compute

}, doi = {https://doi.org/10.22331/q-2019-07-01-156}, url = {https://arxiv.org/abs/1805.08138}, author = {Oscar Higgott and Daochen Wang and Stephen Brierley} } @article {2384, title = {Verification Logics for Quantum Programs}, year = {2019}, type = {Originally submitted in March 2016 as a qualifying examination (WPE-II) for the PhD program at the University of Pennsylvania}, abstract = {

We survey the landscape of Hoare logics for quantum programs. We review three papers: \"Reasoning about imperative quantum programs\" by Chadha, Mateus and Sernadas; \"A logic for formal verification of quantum programs\" by Yoshihiko Kakutani; and \"Floyd-hoare logic for quantum programs\" by Mingsheng Ying. We compare the mathematical foundations of the logics, their underlying languages, and the expressivity of their assertions. We also use the languages to verify the Deutsch-Jozsa Algorithm, and discuss their relative usability in practice.

}, url = {https://arxiv.org/abs/1904.04304}, author = {Robert Rand} } @article {2404, title = {Verified Optimization in a Quantum Intermediate Representation}, year = {2019}, month = {04/12/2019}, abstract = {

We present sqire, a low-level language for quantum computing and verification. sqire uses a global register of quantum bits, allowing easy compilation to and from existing {\textquoteleft}quantum assembly\&$\#$39; languages and simplifying the verification process. We demonstrate the power of sqire as an intermediate representation of quantum programs by verifying a number of useful optimizations, and we demonstrate sqire\&$\#$39;s use as a tool for general verification by proving several quantum programs correct.

}, url = {https://arxiv.org/abs/1904.06319}, author = {Kesha Hietala and Robert Rand and Shih-Han Hung and Xiaodi Wu and Michael Hicks} } @article {2393, title = {α-Logarithmic negativity}, year = {2019}, month = {04/23/2019}, abstract = {

The logarithmic negativity of a bipartite quantum state is a widely employed entanglement measure in quantum information theory, due to the fact that it is easy to compute and serves as an upper bound on distillable entanglement. More recently, the κ-entanglement of a bipartite state was shown to be the first entanglement measure that is both easily computable and operationally meaningful, being equal to the exact entanglement cost of a bipartite quantum state when the free operations are those that completely preserve the positivity of the partial transpose. In this paper, we provide a non-trivial link between these two entanglement measures, by showing that they are the extremes of an ordered family of α-logarithmic negativity entanglement measures, each of which is identified by a parameter α\∈[1,\∞]. In this family, the original logarithmic negativity is recovered as the smallest with α=1, and the κ-entanglement is recovered as the largest with α=\∞. We prove that the α-logarithmic negativity satisfies the following properties: entanglement monotone, normalization, faithfulness, and subadditivity. We also prove that it is neither convex nor monogamous. Finally, we define the α-logarithmic negativity of a quantum channel as a generalization of the notion for quantum states, and we show how to generalize many of the concepts to arbitrary resource theories.\ 

}, url = {https://arxiv.org/abs/1904.10437}, author = {Xin Wang and Mark M. Wilde} } @article {2108, title = {Absence of Thermalization in Finite Isolated Interacting Floquet Systems}, journal = {Physical Review B}, volume = {97}, year = {2018}, month = {2018/01/29}, pages = {014311}, abstract = {

Conventional wisdom suggests that the long time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy non-thermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit non-thermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even with no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have non-thermal average doublon densities. We show that this non-thermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law behavior in system size.

}, doi = {10.1103/PhysRevB.97.014311}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.014311}, author = {Karthik Seetharam and Paraj Titum and Michael Kolodrubetz and Gil Refael} } @article {2211, title = {Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics}, journal = {Phys. Rev. Lett}, volume = {121}, year = {2018}, month = {2018/12/20}, abstract = {

We study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast with the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through non-equilibrium dynamics.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.250404}, url = {https://arxiv.org/abs/1809.02614}, author = {Fangli Liu and James R. Garrison and Dong-Ling Deng and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {2067, title = {Automated optimization of large quantum circuits with continuous parameters}, journal = {npj:Quantum Information}, volume = {4}, year = {2018}, month = {2017/10/19}, abstract = {

We develop and implement automated methods for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. We show how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale quantum circuits. For the suite of benchmarks considered, we obtain substantial reductions in gate counts. In particular, we provide better optimization in significantly less time than previous approaches, while making minimal structural changes so as to preserve the basic layout of the underlying quantum algorithms. Our results help bridge the gap between the computations that can be run on existing hardware and those that are expected to outperform classical computers.\ 

}, doi = {https://doi.org/10.1038/s41534-018-0072-4}, url = {https://arxiv.org/abs/1710.07345}, author = {Yunseong Nam and Neil J. Ross and Yuan Su and Andrew M. Childs and Dmitri Maslov} } @article {2145, title = {An autonomous single-piston engine with a quantum rotor}, year = {2018}, month = {2018/02/15}, abstract = {

Pistons are elementary components of a wide variety of thermal engines, converting input fuel into rotational motion. Here, we propose a single-piston engine where the rotational degree of freedom is effectively realized by the flux of a superconducting island -- a quantum rotor -- while the working volume corresponds to the effective length of a superconducting resonator. Our autonomous design implements a Carnot cycle, relies solely on standard thermal baths and can be implemented with circuit quantum electrodynamics. We demonstrate how the piston is able to extract a net positive work via its built-in synchronicity using a filter cavity as an effective valve, eliminating the need for external control.

}, doi = {https://doi.org/10.1088/2058-9565/aac40d}, url = {https://arxiv.org/abs/1802.05486}, author = {Alexandre Roulet and Stefan Nimmrichter and J. M. Taylor} } @article {2280, title = {A belief propagation algorithm based on domain decomposition}, year = {2018}, abstract = {

This note provides a detailed description and derivation of the domain decomposition algorithm that appears in previous works by the author. Given a large re-estimation problem, domain decomposition provides an iterative method for assembling Boltzmann distributions associated to small subproblems into an approximation of the Bayesian posterior of the whole problem. The algorithm is amenable to using Boltzmann sampling to approximate these Boltzmann distributions. In previous work, we have shown the capability of heuristic versions of this algorithm to solve LDPC decoding and circuit fault diagnosis problems too large to fit on quantum annealing hardware used for sampling. Here, we rigorously prove soundness of the method.

}, url = {https://arxiv.org/abs/1810.10005}, author = {Brad Lackey} } @article {2133, title = {Bell monogamy relations in arbitrary qubit networks}, year = {2018}, month = {2018/01/09}, abstract = {

Characterizing trade-offs between simultaneous violations of multiple Bell inequalities in a large network of qubits is computationally demanding. We propose a graph-theoretic approach to efficiently produce Bell monogamy relations in arbitrary arrangements of qubits. All the relations obtained for bipartite Bell inequalities are tight and leverage only a single Bell monogamy relation. This feature is unique to bipartite Bell inequalities, as we show that there is no finite set of such elementary monogamy relations for multipartite inequalities. Nevertheless, many tight monogamy relations for multipartite inequalities can be obtained with our method as shown in explicit examples.

}, doi = {https://doi.org/10.1103/PhysRevA.98.052325}, url = {https://arxiv.org/abs/1801.03071}, author = {Minh C. Tran and Ravishankar Ramanathan and Matthew McKague and Dagomir Kaszlikowski and Tomasz Paterek} } @article {2298, title = {Black Hole Microstate Cosmology}, year = {2018}, abstract = {

In this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-the-world (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems. We study in particular states defined via Euclidean evolution from conformal boundary states and give specific predictions for the behavior of the entanglement entropy in this case. We perform analogous calculations for the SYK model and find qualitative agreement with our expectations. A fascinating possibility is that for certain states, we might have gravity localized to the ETW brane as in the Randall-Sundrum II scenario for cosmology. In this case, the effective description of physics beyond the horizon could be a big bang/big crunch cosmology of the same dimensionality as the CFT. In this case, the d-dimensional CFT describing the black hole microstate would give a precise, microscopic description of the d-dimensional cosmological physics.\ 

}, url = {https://arxiv.org/abs/1810.10601}, author = {Sean Cooper and Moshe Rozali and Brian Swingle and Mark Van Raamsdonk and Christopher Waddell and David Wakeham} } @article {2132, title = {Blind quantum computation using the central spin Hamiltonian}, year = {2018}, month = {2018/01/11}, abstract = {

Blindness is a desirable feature in delegated computation. In the classical setting, blind computations protect the data or even the program run by a server. In the quantum regime, blind computing may also enable testing computational or other quantum properties of the server system. Here we propose a scheme for universal blind quantum computation using a quantum simulator capable of emulating Heisenberg-like Hamiltonians. Our scheme is inspired by the central spin Hamiltonian in which a single spin controls dynamics of a number of bath spins. We show how, by manipulating this spin, a client that only accesses the central spin can effectively perform blind computation on the bath spins. Remarkably, two-way quantum communication mediated by the central spin is sufficient to ensure security in the scheme. Finally, we provide explicit examples of how our universal blind quantum computation enables verification of the power of the server from classical to stabilizer to full BQP computation.

}, url = {https://arxiv.org/abs/1801.04006}, author = {Minh C. Tran and J. M. Taylor} } @article {2269, title = {Bose Condensation of Photons Thermalized via Laser Cooling of Atoms}, year = {2018}, abstract = {

A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number-conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. Here we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline earth atoms) inside a Fabry-Perot cavity.

}, url = {https://arxiv.org/abs/1809.07777}, author = {Chiao-Hsuan Wang and Michael Gullans and J. V. Porto and William D. Phillips and J. M. Taylor} } @article {1949, title = {BQP-completeness of Scattering in Scalar Quantum Field Theory}, journal = {Quantum}, volume = {2}, year = {2018}, month = {2018/01/08}, pages = {44}, abstract = {

Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

}, doi = {10.22331/q-2018-01-08-44}, url = {https://quantum-journal.org/papers/q-2018-01-08-44/}, author = {Stephen P. Jordan and Hari Krovi and Keith S. M. Lee and John Preskill} } @article {2509, title = {Broadband optomechanical non-reciprocity}, journal = {Nature Photon }, volume = {12}, year = {2018}, month = {2018/1/26}, pages = {60-61}, abstract = {

Implementing non-reciprocal elements with a bandwidth comparable to optical frequencies is a challenge
in integrated photonics. Now, a phonon pump has been used to achieve optical non-reciprocity over a
large bandwidth.

}, doi = {https://doi.org/10.1038/s41566-018-0091-x}, author = {Alireza Seif and Mohammad Hafezi} } @conference {2129, title = {Capacity Approaching Codes for Low Noise Interactive Quantum Communication}, booktitle = {Annual ACM Symposium on the Theory of Computing STOC 2018}, year = {2018}, month = {2018/01/01}, abstract = {
We consider the problem of implementing two-party interactive quantum
communication over noisy channels, a necessary endeavor if we wish to
fully reap quantum advantages for communication.\ \ 
For an arbitrary protocol with n messages, designed for
noiseless qudit channels, our main result is a simulation method that fails with probability less than
$2^{-\Theta(n\epsilon)}$ and uses a qudit channel $n(1 + \Theta
(\sqrt{\epsilon}))$ times, of which an $\epsilon$ fraction can be
corrupted adversarially.
The simulation is thus capacity achieving to leading order, and
we conjecture that it is optimal up to a constant factor in\ 
the $\sqrt{\epsilon}$ term.\ \ 
Furthermore, the simulation is in a model that does not require
pre-shared resources such as randomness or entanglement between the
communicating parties.
Surprisingly, this outperforms the best-known overhead of $1 +
O(\sqrt{\epsilon \log \log 1/\epsilon})$ in the corresponding
\emph{classical} model, which is also conjectured to be optimal
\  \  \ [Haeupler, FOCS\&$\#$39;14].
Our work also improves over the best previously known quantum result
where the overhead is a non-explicit large constant [Brassard \emph{et
\  \  al.}, FOCS\&$\#$39;14] for low $\epsilon$.
}, url = {http://acm-stoc.org/stoc2018/STOC-2018-Accepted.html}, author = {Debbie Leung and Ashwin Nayak and Ala Shayeghi and Dave Touchette and Penghui Yao and Nengkun Yu} } @article {2272, title = {Circuit QED-based measurement of vortex lattice order in a Josephson junction array}, journal = {Phys. Rev. B 98, 060501}, year = {2018}, month = {2018/03/12}, abstract = {

Superconductivity provides a canonical example of a quantum phase of matter. When superconducting islands are connected by Josephson junctions in a lattice, the low temperature state of the system can map to the celebrated XY model and its associated universality classes. This has been used to experimentally implement realizations of Mott insulator and Berezinskii--Kosterlitz--Thouless (BKT) transitions to vortex dynamics analogous to those in type-II superconductors. When an external magnetic field is added, the effective spins of the XY model become frustrated, leading to the formation of topological defects (vortices). Here we observe the many-body dynamics of such an array, including frustration, via its coupling to a superconducting microwave cavity. We take the design of the transmon qubit, but replace the single junction between two antenna pads with the complete array. This allows us to probe the system at 10 mK with minimal self-heating by using weak coherent states at the single (microwave) photon level to probe the resonance frequency of the cavity. We observe signatures of ordered vortex lattice at rational flux fillings of the array.\ 

}, doi = {https://doi.org/10.1103/PhysRevB.98.060501}, url = {https://arxiv.org/abs/1803.04113}, author = {R. Cosmic and Hiroki Ikegami and Zhirong Lin and Kunihiro Inomata and J. M. Taylor and Yasunobu Nakamura} } @article {2221, title = {Classical lower bounds from quantum upper bounds}, year = {2018}, abstract = {

We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the combinatorial group testing problem.\ 
We show that for any function f, the approximate degree of computing the OR of n copies of f is Omega(sqrt{n}) times the approximate degree of f, which is optimal. No such general result was known prior to our work, and even the lower bound for the OR of ANDs function was only resolved in 2013.\ 
We then prove an analogous result in communication complexity, showing that the logarithm of the approximate rank (or more precisely, the approximate gamma_2 norm) of F: X x Y -\> {0,1} grows by a factor of Omega~(sqrt{n}) when we take the OR of n copies of F, which is also essentially optimal. As a corollary, we give a new proof of Razborov\&$\#$39;s celebrated Omega(sqrt{n}) lower bound on the quantum communication complexity of the disjointness problem.\ 
Finally, we generalize both these results from composition with the OR function to composition with arbitrary symmetric functions, yielding nearly optimal lower bounds in this setting as well.

}, url = {https://arxiv.org/abs/1807.06256}, author = {Shalev Ben-David and Adam Bouland and Ankit Garg and Robin Kothari} } @article {2216, title = {Coherent optical nano-tweezers for ultra-cold atoms}, year = {2018}, abstract = {

There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultra-cold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work opens a new frontier for the subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.

}, url = {https://arxiv.org/abs/1808.02487}, author = {P. Bienias and S. Subhankar and Y. Wang and T-C Tsui and F. Jendrzejewski and T. Tiecke and G. Juzeliunas and L. Jiang and S. L. Rolston and J. V. Porto and Alexey V. Gorshkov} } @article {2283, title = {A Coherent Spin-Photon Interface in Silicon}, journal = {Nature }, volume = {555}, year = {2018}, month = {2018/03/29}, pages = {599-603}, abstract = {

Electron spins in silicon quantum dots are attractive systems for quantum computing due to their long coherence times and the promise of rapid scaling using semiconductor fabrication techniques. While nearest neighbor exchange coupling of two spins has been demonstrated, the interaction of spins via microwave frequency photons could enable long distance spin-spin coupling and \"all-to-all\" qubit connectivity. Here we demonstrate strong-coupling between a single spin in silicon and a microwave frequency photon with spin-photon coupling rates g_s/(2π) \> 10 MHz. The mechanism enabling coherent spin-photon interactions is based on spin-charge hybridization in the presence of a magnetic field gradient. In addition to spin-photon coupling, we demonstrate coherent control of a single spin in the device and quantum non-demolition spin state readout using cavity photons. These results open a direct path toward entangling single spins using microwave frequency photons.

}, doi = {https://doi.org/10.1038/nature25769}, url = {https://arxiv.org/abs/1710.03265}, author = {X. Mi and M. Benito and S. Putz and D. M. Zajac and J. M. Taylor and Guido Burkard and J. R. Petta} } @article {2148, title = {A coherent spin{\textendash}photon interface in silicon}, journal = {Nature}, year = {2018}, month = {2018/02/14}, abstract = {

Electron spins in silicon quantum dots are attractive systems for quantum computing owing to their long coherence times and the promise of rapid scaling of the number of dots in a system using semiconductor fabrication techniques. Although nearest-neighbour exchange coupling of two spins has been demonstrated, the interaction of spins via microwave-frequency photons could enable long-distance spin\–spin coupling and connections between arbitrary pairs of qubits (\‘all-to-all\’ connectivity) in a spin-based quantum processor. Realizing coherent spin\–photon coupling is challenging because of the small magnetic-dipole moment of a single spin, which limits magnetic-dipole coupling rates to less than 1 kilohertz. Here we demonstrate strong coupling between a single spin in silicon and a single microwave-frequency photon, with spin\–photon coupling rates of more than 10 megahertz. The mechanism that enables the coherent spin\–photon interactions is based on spin\–charge hybridization in the presence of a magnetic-field gradient. In addition to spin\–photon coupling, we demonstrate coherent control and dispersive readout of a single spin. These results open up a direct path to entangling single spins using microwave-frequency photons.

}, doi = {10.1038/nature25769}, url = {https://www.nature.com/articles/nature25769$\#$author-information}, author = {X. Mi and M. Benito and S. Putz and D. M. Zajac and J. M. Taylor and Guido Burkard and J. R. Petta} } @article {2289, title = {Cryogenic Trapped-Ion System for Large Scale Quantum Simulation}, year = {2018}, abstract = {

We present a cryogenic ion trapping system designed for large scale quantum simulation of spin models. Our apparatus is based on a segmented-blade ion trap enclosed in a 4 K cryostat, which enables us to routinely trap over 100 171Yb+ ions in a linear configuration for hours due to a low background gas pressure from differential cryo-pumping. We characterize the cryogenic vacuum by using trapped ion crystals as a pressure gauge, measuring both inelastic and elastic collision rates with the molecular background gas. We demonstrate nearly equidistant ion spacing for chains of up to 44 ions using anharmonic axial potentials. This reliable production and lifetime enhancement of large linear ion chains will enable quantum simulation of spin models that are intractable with classical computer modelling.

}, url = {https://arxiv.org/abs/1802.03118}, author = {G. Pagano and P. W. Hess and H. B. Kaplan and W. L. Tan and P. Richerme and P. Becker and A. Kyprianidis and J. Zhang and E. Birckelbaw and M. R. Hernandez and Y. Wu and C. Monroe} } @article {2141, title = {Dark state optical lattice with sub-wavelength spatial structure}, journal = {Phys. Rev. Lett.}, volume = {120}, year = {2018}, month = {2018/02/20}, pages = {083601}, abstract = {

We report on the experimental realization of a conservative optical lattice for cold atoms with a subwavelength spatial structure. The potential is based on the nonlinear optical response of three-level atoms in laser-dressed dark states, which is not constrained by the diffraction limit of the light generating the potential. The lattice consists of a one-dimensional array of ultranarrow barriers with widths less than 10\ nm, well below the wavelength of the lattice light, physically realizing a Kronig-Penney potential. We study the band structure and dissipation of this lattice and find good agreement with theoretical predictions. Even on resonance, the observed lifetimes of atoms trapped in the lattice are as long as 44\ ms, nearly\ 105times the excited state lifetime, and could be further improved with more laser intensity. The potential is readily generalizable to higher dimensions and different geometries, allowing, for example, nearly perfect box traps, narrow tunnel junctions for atomtronics applications, and dynamically generated lattices with subwavelength spacings.

}, doi = {10.1103/PhysRevLett.120.083601}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.120.083601}, author = {Yang Wang and Sarthak Subhankar and Przemyslaw Bienias and Mateusz Lacki and Tsz-Chun Tsui and Mikhail A. Baranov and Alexey V. Gorshkov and Peter Zoller and James V. Porto and Steven L. Rolston} } @article {2288, title = {Demonstration of Bayesian quantum game on an ion trap quantum computer}, year = {2018}, abstract = {

We demonstrate a Bayesian quantum game on an ion trap quantum computer with five qubits. The players share an entangled pair of qubits and perform rotations on their qubit as the strategy choice. Two five-qubit circuits are sufficient to run all 16 possible strategy choice sets in a game with four possible strategies. The data are then parsed into player types randomly in order to combine them classically into a Bayesian framework. We exhaustively compute the possible strategies of the game so that the experimental data can be used to solve for the Nash equilibria of the game directly. Then we compare the payoff at the Nash equilibria and location of phase-change-like transitions obtained from the experimental data to the theory, and study how it changes as a function of the amount of entanglement.

}, url = {https://arxiv.org/abs/1802.08116}, author = {Neal Solmeyer and Norbert M. Linke and Caroline Figgatt and Kevin A. Landsman and Radhakrishnan Balu and George Siopsis and Christopher Monroe} } @article {2047, title = {Diffusion Monte Carlo Versus Adiabatic Computation for Local Hamiltonians}, journal = {Physical Review A}, volume = {97}, year = {2018}, month = {2018/02/15}, pages = {022323}, abstract = {

Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real, nonnegative amplitudes. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k-SAT problems, use k-local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n-body interactions. Here we present a new 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.

}, doi = {10.1103/PhysRevA.97.022323}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022323}, author = {Jacob Bringewatt and William Dorland and Stephen P. Jordan and Alan Mink} } @article {2142, title = {Dissipation induced dipole blockade and anti-blockade in driven Rydberg systems}, journal = {Phys. Rev. A}, volume = {97}, year = {2018}, month = {2018/02/28}, pages = {023424}, abstract = {

We study theoretically and experimentally the competing blockade and antiblockade effects induced by spontaneously generated contaminant Rydberg atoms in driven Rydberg systems. These contaminant atoms provide a source of strong dipole-dipole interactions and play a crucial role in the system\&$\#$39;s behavior. We study this problem theoretically using two different approaches. The first is a cumulant expansion approximation, in which we ignore third-order and higher connected correlations. Using this approach for the case of resonant drive, a many-body blockade radius picture arises, and we find qualitative agreement with previous experimental results. We further predict that as the atomic density is increased, the Rydberg population\&$\#$39;s dependence on Rabi frequency will transition from quadratic to linear dependence at lower Rabi frequencies. We study this behavior experimentally by observing this crossover at two different atomic densities. We confirm that the larger density system has a smaller crossover Rabi frequency than the smaller density system. The second theoretical approach is a set of phenomenological inhomogeneous rate equations. We compare the results of our rate-equation model to the experimental observations [E. A. Goldschmidt\ et al.,\ Phys. Rev. Lett.116, 113001 (2016)] and find that these rate equations provide quantitatively good scaling behavior of the steady-state Rydberg population for both resonant and off-resonant drives.

}, doi = {10.1103/PhysRevA.97.023424}, url = {https://link.aps.org/doi/10.1103/PhysRevA.97.023424}, author = {Jeremy T. Young and Thomas Boulier and Eric Magnan and Elizabeth A. Goldschmidt and Ryan M. Wilson and Steven L. Rolston and James V. Porto and Alexey V. Gorshkov} } @article {2278, title = {Distributed Quantum Metrology and the Entangling Power of Linear Networks}, journal = {Phys. Rev. Lett. 121, 043604}, year = {2018}, month = {2018/07/25}, abstract = {

We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.\ 

}, doi = {https://doi.org/10.1103/PhysRevLett.121.043604}, url = {https://arxiv.org/abs/1707.06655}, author = {Wenchao Ge and Kurt Jacobs and Zachary Eldredge and Alexey V. Gorshkov and Michael Foss-Feig} } @article {2137, title = {Distributed Quantum Metrology and the Entangling Power of Linear Networks}, year = {2018}, month = {2018/07/25}, abstract = {

We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.043604}, url = {https://arxiv.org/abs/1707.06655}, author = {Wenchao Ge and Kurt Jacobs and Zachary Eldredge and Alexey V. Gorshkov and Michael Foss-Feig} } @article {2273, title = {Dynamic suppression of Rayleigh light scattering in dielectric resonators}, year = {2018}, abstract = {

The ultimate limits of performance for any classical optical system are set by sub-wavelength fluctuations within the host material, that may be frozen-in or even dynamically induced. The most common manifestation of such sub-wavelength disorder is Rayleigh light scattering, which is observed in nearly all wave-guiding technologies today and can lead to both irreversible radiative losses as well as undesirable intermodal coupling. While it has been shown that backscattering from disorder can be suppressed by breaking time-reversal symmetry in magneto-optic and topological insulator materials, common optical dielectrics possess neither of these properties. Here we demonstrate an optomechanical approach for dynamically suppressing Rayleigh backscattering within dielectric resonators. We achieve this by locally breaking time-reversal symmetry in a silica resonator through a Brillouin scattering interaction that is available in all materials. Near-complete suppression of Rayleigh backscattering is experimentally confirmed through three independent measurements -- the reduction of the back-reflections caused by scatterers, the elimination of a commonly seen normal-mode splitting effect, and by measurement of the reduction in intrinsic optical loss. More broadly, our results provide new evidence that it is possible to dynamically suppress Rayleigh backscattering within any optical dielectric medium, for achieving robust light propagation in nanophotonic devices in spite of the presence of scatterers or defects.

}, url = {https://arxiv.org/abs/1803.02366}, author = {Seunghwi Kim and J. M. Taylor and Gaurav Bahl} } @article {2210, title = {Dynamical phase transitions in sampling complexity}, journal = {Phys. Rev. Lett.}, volume = {121}, year = {2018}, pages = {12 pages, 4 figures. v3: published version}, abstract = {

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time\ t\ due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of\ t\ with the number of bosons\ n\ for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of\ t\ with\ n\ for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proc. 43rd Annu. ACM Symp. Theory Comput. STOC \&$\#$39;11]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular and optical systems.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.030501}, url = {https://arxiv.org/abs/1703.05332}, author = {Abhinav Deshpande and Bill Fefferman and Minh C. Tran and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1998, title = {Electro-mechano-optical NMR detection}, journal = {Optica}, volume = {5}, year = {2018}, month = {2018/02/01}, pages = {152-158}, abstract = {

Signal reception of nuclear magnetic resonance (NMR) usually relies on electrical amplification of the electromotive force caused by nuclear induction. Here, we report up-conversion of a radio-frequency NMR signal to an optical regime using a high-stress silicon nitride membrane that interfaces the electrical detection circuit and an optical cavity through the electro-mechanical and the opto-mechanical couplings. This enables optical NMR detection without sacrificing the versatility of the traditional nuclear induction approach. While the signal-to-noise ratio is currently limited by the Brownian motion of the membrane as well as additional technical noise, we find it can exceed that of the conventional electrical schemes by increasing the electro-mechanical coupling strength. The electro-mechano-optical NMR detection presented here can even be combined with the laser cooling technique applied to nuclear spins.

}, doi = {10.1364/OPTICA.5.000152}, url = {https://www.osapublishing.org/optica/abstract.cfm?uri=optica-5-2-152}, author = {Kazuyuki Takeda and Kentaro Nagasaka and Atsushi Noguchi and Rekishu Yamazaki and Yasunobu Nakamura and Eiji Iwase and J. M. Taylor and Koji Usami} } @article {2104, title = {Electro-optomechanical equivalent circuits for quantum transduction}, year = {2018}, month = {2018/10/15}, abstract = {

Using the techniques of optomechanics, a high-Q mechanical oscillator may serve as a link between electromagnetic modes of vastly different frequencies. This approach has successfully been exploited for the frequency conversion of classical signals and has the potential of performing quantum state transfer between superconducting circuitry and a traveling optical signal. Such transducers are often operated in a linear regime, where the hybrid system can be described using linear response theory based on the Heisenberg-Langevin equations. While mathematically straightforward to solve, this approach yields little intuition about the dynamics of the hybrid system to aid the optimization of the transducer. As an analysis and design tool for such electro-optomechanical transducers, we introduce an equivalent circuit formalism, where the entire transducer is represented by an electrical circuit. Thereby we integrate the transduction functionality of optomechanical (OM) systems into the toolbox of electrical engineering allowing the use of its well-established design techniques. This unifying impedance description can be applied both for static (DC) and harmonically varying (AC) drive fields, accommodates arbitrary linear circuits, and is not restricted to the resolved-sideband regime. Furthermore, by establishing the quantized input/output formalism for the equivalent circuit, we obtain the scattering matrix for linear transducers using circuit analysis, and thereby have a complete quantum mechanical characterization of the transducer. Hence, this mapping of the entire transducer to the language of electrical engineering both sheds light on how the transducer performs and can at the same time be used to optimize its performance by aiding the design of a suitable electrical circuit.

}, doi = {https://doi.org/10.1103/PhysRevApplied.10.044036}, url = {https://arxiv.org/abs/1710.10136}, author = {Emil Zeuthen and Albert Schliesser and J. M. Taylor and Anders S. S{\o}rensen} } @article {2315, title = {Energy-level statistics in strongly disordered systems with power-law hopping}, journal = {Phys. Rev. }, volume = {B}, year = {2018}, month = {2018/07/16}, pages = {014201}, abstract = {

Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian \∝1/rα in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function R2(ω) in a finite system in the limit of sufficiently strong disorder. At small energy differences the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by R2(ω,V)=A3ωωV for small frequencies ω<<ωV and R2(ω,V)=1\−(α\−d)A1(ωVω)dα\−A2(ωVω)2 for large frequencies ω>>ωV, where ωV\∝V\−αd is the characteristic matrix element of excitation hopping in a system of volume V, and A1, A2 and A3 are coefficient of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.

}, doi = {https://doi.org/10.1103/PhysRevB.98.014201}, url = {https://arxiv.org/abs/1803.11178}, author = {Paraj Titum and Victor L. Quito and Sergey V. Syzranov} } @article {2054, title = {Entanglement of purification: from spin chains to holography}, journal = {Journal of High Energy Physics}, year = {2018}, month = {2018/01/22}, pages = {98}, abstract = {

Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.

}, doi = {10.1007/JHEP01(2018)098}, url = {https://link.springer.com/article/10.1007\%2FJHEP01\%282018\%29098$\#$citeas}, author = {Phuc Nguyen and Trithep Devakul and Matthew G. Halbasch and Michael P. Zaletel and Brian Swingle} } @article {2318, title = {Exact entanglement cost of quantum states and channels under PPT-preserving operations}, year = {2018}, abstract = {

This paper establishes single-letter formulas for the exact entanglement cost of generating bipartite quantum states and simulating quantum channels under free quantum operations that completely preserve positivity of the partial transpose (PPT). First, we establish that the exact entanglement cost of any bipartite quantum state under PPT-preserving operations is given by a single-letter formula, here called the\ κ-entanglement of a quantum state. This formula is calculable by a semidefinite program, thus allowing for an efficiently computable solution for general quantum states. Notably, this is the first time that an entanglement measure for general bipartite states has been proven not only to possess a direct operational meaning but also to be efficiently computable, thus solving a question that has remained open since the inception of entanglement theory over two decades ago. Next, we introduce and solve the exact entanglement cost for simulating quantum channels in both the parallel and sequential settings, along with the assistance of free PPT-preserving operations. The entanglement cost in both cases is given by the same single-letter formula and is equal to the largest\ κ-entanglement that can be shared by the sender and receiver of the channel. It is also efficiently computable by a semidefinite program.\ 

}, url = {https://arxiv.org/abs/1809.09592}, author = {Xin Wang and Mark M. Wilde} } @article {2282, title = {Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals}, journal = {Nature}, volume = {556}, year = {2018}, month = {2018/04/11}, pages = {223-226}, abstract = {

From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a number of assumptions that may not be valid, thereby compromising the integrity of the device. However, it is possible to exploit the phenomenon of quantum nonlocality with a loophole-free Bell test to build a random number generator that can produce output that is unpredictable to any adversary limited only by general physical principles. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1024 random bits uniform to within 10\−12. These random bits could not have been predicted within any physical theory that prohibits superluminal signaling and allows one to make independent measurement choices. To certify and quantify the randomness, we describe a new protocol that is optimized for apparatuses characterized by a low per-trial violation of Bell inequalities. We thus enlisted an experimental result that fundamentally challenges the notion of determinism to build a system that can increase trust in random sources. In the future, random number generators based on loophole-free Bell tests may play a role in increasing the security and trust of our cryptographic systems and infrastructure.

}, doi = {https://doi.org/10.1038/s41586-018-0019-0}, url = {https://arxiv.org/abs/1803.06219}, author = {Peter Bierhorst and Emanuel Knill and Scott Glancy and Yanbao Zhang and Alan Mink and Stephen Jordan and Andrea Rommal and Yi-Kai Liu and Bradley Christensen and Sae Woo Nam and Martin J. Stevens and Lynden K. Shalm} } @article {2325, title = {Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory}, journal = {Phys. Rev. A 98, 012332 (2018)}, volume = {A}, year = {2018}, month = {2018/05/04}, pages = {012332}, abstract = {

In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum Field Theory (QFT) on a quantum computer, which is based on the matrix product state ansatz. We apply this to the massive Gross-Neveu model in one spatial dimension to illustrate the algorithm, but we believe the same algorithm with slight modifications can be used to simulate any one-dimensional massive Fermionic QFT. In the case where the number of particle species is one, our algorithm can prepare particle states using O(ε\−3.23\…) gates, which is much faster than previous known results, namely O(ε\−8\−o(1)). Furthermore, unlike previous methods which were based on adiabatic state preparation, the method given here should be able to simulate quantum phases unconnected to the free theory.

}, doi = {https://doi.org/10.1103/PhysRevA.98.012332}, url = {https://arxiv.org/abs/1711.04006}, author = {Moosavian, Ali Hamed and Stephen Jordan} } @article {2304, title = {Fractal Universality in Near-Threshold Magnetic Lanthanide Dimers}, journal = {Science Advances}, volume = {4}, year = {2018}, month = {2018/02/16}, pages = {eaap8308}, abstract = {

Ergodic quantum systems are often quite alike, whereas nonergodic, fractal systems are unique and display characteristic properties. We explore one of these fractal systems, weakly bound dysprosium lanthanide molecules, in an external magnetic field. As recently shown, colliding ultracold magnetic dysprosium atoms display a soft chaotic behavior with a small degree of disorder. We broaden this classification by investigating the generalized inverse participation ratio and fractal dimensions for large sets of molecular wave functions. Our exact close-coupling simulations reveal a dynamic phase transition from partially localized states to totally delocalized states and universality in its distribution by increasing the magnetic field strength to only a hundred Gauss (or 10 mT). Finally, we prove the existence of nonergodic delocalized phase in the system and explain the violation of ergodicity by strong coupling between near-threshold molecular states and the nearby continuum.

}, doi = {https://doi.org/10.1126/sciadv.aap8308}, url = {https://arxiv.org/abs/1802.09586}, author = {Constantinos Makrides and Ming Li and Eite Tiesinga and Svetlana Kotochigova} } @article {2256, title = {Fractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal}, year = {2018}, abstract = {

Highly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems, and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half-filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal phase, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

}, url = {https://arxiv.org/abs/1809.04493}, author = {Tobias Gra{\ss} and Przemyslaw Bienias and Michael Gullans and Rex Lundgren and Joseph Maciejko and Alexey V. Gorshkov} } @article {2109, title = {Geometry of the quantum set of correlations}, journal = {Physical Review A}, volume = {97}, year = {2018}, month = {2018/02/07}, pages = {022104}, abstract = {

It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.

}, doi = {10.1103/PhysRevA.97.022104}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022104}, author = {Koon Tong Goh and Jedrzej Kaniewski and Elie Wolfe and Tam{\'a}s V{\'e}rtesi and Xingyao Wu and Yu Cai and Yeong-Cherng Liang and Valerio Scarani} } @article {2302, title = {High Purity Single Photons Entangled with an Atomic Memory}, year = {2018}, abstract = {

Trapped atomic ions are an ideal candidate for quantum network nodes, with long-lived identical qubit memories that can be locally entangled through their Coulomb interaction and remotely entangled through photonic channels. The integrity of this photonic interface is generally reliant on purity of single photons produced by the quantum memory. Here we demonstrate a single-photon source for quantum networking based on a trapped 138Ba+ ion with a single photon purity of g2(0)=(8.1\±2.3)\×10\−5 without background subtraction. We further optimize the tradeoff between the photonic generation rate and the memory-photon entanglement fidelity for the case of polarization photonic qubits by tailoring the spatial mode of the collected light.\ 

}, url = {https://arxiv.org/abs/1812.01749}, author = {Clayton Crocker and Martin Lichtman and Ksenia Sosnova and Allison Carter and Sophia Scarano and Christopher Monroe} } @article {2147, title = {High-fidelity quantum gates in Si/SiGe double quantum dots}, journal = {Physical Review B}, volume = {97}, year = {2018}, month = {2018/02/15}, pages = {085421}, abstract = {

Motivated by recent experiments of Zajac\ et\ al.\ [Science359, 439 (2018)], we theoretically describe high-fidelity two-qubit gates using the exchange interaction between the spins in neighboring quantum dots subject to a magnetic field gradient. We use a combination of analytical calculations and numerical simulations to provide the optimal pulse sequences and parameter settings for the gate operation. We present a synchronization method which avoids detrimental spin flips during the gate operation and provide details about phase mismatches accumulated during the two-qubit gates which occur due to residual exchange interaction, nonadiabatic pulses, and off-resonant driving. By adjusting the gate times, synchronizing the resonant and off-resonant transitions, and compensating these phase mismatches by phase control, the overall gate fidelity can be increased significantly.

}, doi = {10.1103/PhysRevB.97.085421}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.085421}, author = {Maximilian Russ and D. M. Zajac and A. J. Sigillito and F. Borjans and J. M. Taylor and J. R. Petta and Guido Burkard} } @article {2300, title = {Holographic Complexity of Einstein-Maxwell-Dilaton Gravity}, journal = {J. High Energ. Phys. }, volume = {106}, year = {2018}, month = {2018}, abstract = {

We study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed \"complexity = volume\" and \"complexity = action\" dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, in the presence of violations of hyperscaling, there is a parametric enhancement of the action growth rate. We partially match this behavior to simple tensor network models which can capture aspects of hyperscaling violation. We also exhibit the switchback effect in complexity growth using shockwave geometries and comment on a subtlety of our action calculations when the metric is discontinuous at a null surface.

}, doi = {https://doi.org/10.1007/JHEP09(2018)106}, url = {https://arxiv.org/abs/1712.09826}, author = {Brian Swingle and Yixu Wang} } @article {2258, title = {Implicit regularization and solution uniqueness in over-parameterized matrix sensing}, year = {2018}, abstract = {

We consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-r positive semi-definite (PSD) matrices in Rn\×n, with a sensing mechanism that satisfies the restricted isometry property (RIP). The algorithm we study is that of \emph{factored gradient descent}, where we model the low-rankness and PSD constraints with the factorization UU⊤, where U\∈Rn\×r. Surprisingly, recent work argues that the choice of r\≤n is not pivotal: even setting U\∈Rn\×n is sufficient for factored gradient descent to find the rank-r solution, which suggests that operating over the factors leads to an implicit regularization. In this note, we provide a different perspective. We show that, in the noiseless case, under certain conditions, the PSD constraint by itself is sufficient to lead to a unique rank-r matrix recovery, without implicit or explicit low-rank regularization. \emph{I.e.}, under assumptions, the set of PSD matrices, that are consistent with the observed data, is a singleton, irrespective of the algorithm used.

}, url = {https://arxiv.org/abs/1806.02046}, author = {Anastasios Kyrillidis and Amir Kalev} } @article {2250, title = {In Defense of a "Single-World" Interpretation of Quantum Mechanics}, journal = {forthcoming in Studies in History and Philosophy of Modern Physics}, year = {2018}, pages = {15}, abstract = {

In a recent result, Frauchiger and Renner argue that if quantum theory accurately describes complex systems like observers who perform measurements, then \"we are forced to give up the view that there is one single reality.\" Following a review of the Frauchiger-Renner argument, I argue that quantum mechanics should be understood probabilistically, as a new sort of non-Boolean probability theory, rather than representationally, as a theory about the elementary constituents of the physical world and how these elements evolve dynamically over time. I show that this way of understanding quantum mechanics is not in conflict with a consistent \"single-world\" interpretation of the theory.

}, url = {https://arxiv.org/abs/1804.03267}, author = {Jeffrey Bub} } @article {2368, title = {Information-Theoretic Privacy For Distributed Average Consensus: Bounded Integral Inputs}, year = {2018}, month = {03/28/2019}, abstract = {

We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents\&$\#$39; inputs against colluding passive adversarial agents, as long as the set of colluding passive adversarial agents is not a vertex cut in the underlying communication network. This implies that a network with (t+1)-connectivity guarantees information-theoretic privacy of honest agents\&$\#$39; inputs against any t colluding agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm. The agent\&$\#$39; inputs are bounded integers, where the bounds are apriori known to all the agents.

}, url = {https://arxiv.org/abs/1809.01794}, author = {Nirupam Gupta and Jonathan Katz and Nikhil Chopra} } @article {2212, title = {Information-Theoretic Privacy in Distributed Average Consensus}, year = {2018}, abstract = {

We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents\&$\#$39; inputs against colluding semi-honest (passively adversarial) agents, as long as the set of colluding semi-honest agents is not a vertex cut in the underlying communication network. This implies that a network with\ (t+1)-connectivity guarantees information-theoretic privacy of honest agents\&$\#$39; inputs against any\ t\ colluding semi-honest agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm.\ 

}, url = {https://arxiv.org/abs/1809.01794}, author = {Nirupam Gupta and Jonathan Katz and Nikhil Chopra} } @article {1994, title = {Keyring models: an approach to steerability}, journal = {Journal of Mathematical Physics}, volume = {59}, year = {2018}, month = {2018/01/02}, pages = {022103}, abstract = {

If a measurement is made on one half of a bipartite system then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation \— that is, if shared randomness cannot produce these reduced states for all possible measurements \— the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of keyring models \— a special class of local hidden state model. When the measurements made correspond to real projectors, these allow us to study steerability beyond T-states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels. Our results imply that Werner states, which are a special case of the previous states, are unsteerable under real projective measurements if and only if their efficiency is at most 2/π.

}, doi = {10.1063/1.5006199}, url = {http://aip.scitation.org/doi/full/10.1063/1.5006199}, author = {Carl Miller and Roger Colbeck and Yaoyun Shi} } @article {2222, title = {Local randomness: Examples and application}, journal = {Phys. Rev. A}, year = {2018}, month = {03/2018}, pages = {032324}, abstract = {

When two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness\—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).

}, doi = {https://doi.org/10.1103/PhysRevA.97.032324}, url = {https://arxiv.org/abs/1708.04338}, author = {Honghao Fu and Carl Miller} } @article {2287, title = {Machine learning assisted readout of trapped-ion qubits}, journal = { J. Phys. B: At. Mol. Opt. Phys.}, volume = {51}, year = {2018}, month = {2018/05/01}, chapter = {174006}, abstract = {

We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30\% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.

}, doi = {https://doi.org/10.1088/1361-6455/aad62b}, url = {https://arxiv.org/abs/1804.07718}, author = {Alireza Seif and Kevin A. Landsman and Norbert M. Linke and Caroline Figgatt and C. Monroe and Mohammad Hafezi} } @article {2330, title = {Mathematical methods for resource-based type theories}, year = {2018}, abstract = {

With the wide range of quantum programming languages on offer now, efficient program verification and type checking for these languages presents a challenge -- especially when classical debugging techniques may affect the states in a quantum program. In this work, we make progress towards a program verification approach using the formalism of operational quantum mechanics and resource theories. We present a logical framework that captures two mathematical approaches to resource theory based on monoids (algebraic) and monoidal categories (categorical). We develop the syntax of this framework as an intuitionistic sequent calculus, and prove soundness and completeness of an algebraic and categorical semantics that recover these approaches. We also provide a cut-elimination theorem, normal form, and analogue of Lambek\&$\#$39;s lifting theorem for polynomial systems over the logics. Using these approaches along with the Curry-Howard-Lambek correspondence for programs, proofs and categories, this work lays the mathematical groundwork for a type checker for some resource theory based frameworks, with the possibility of extending it other quantum programming languages.

}, url = {https://arxiv.org/abs/1812.08726}, author = {Aarthi Sundaram and Brad Lackey} } @article {2314, title = {Measurement Contextuality and Planck{\textquoteright}s Constant}, journal = {New Journal of Physics }, volume = {20}, year = {2018}, month = {2018/07/12}, pages = {073020}, abstract = {

Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck\&$\#$39;s constant, ℏ, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of ℏ---all orders higher than ℏ0 can be interpreted as quantum corrections to the order ℏ0 term. We show that contextual measurements in finite-dimensional systems have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order ℏ0 terms to be included in order to violate the classical bounds on their expectation values. As a result, we show that contextuality as a resource is equivalent to orders of ℏ as a resource within the WWM formalism. This explains why qubits can only exhibit state-independent contextuality under Pauli observables as in the Peres-Mermin square while odd-dimensional qudits can also exhibit state-dependent contextuality. In particular, we find that qubit Pauli observables lack an order ℏ0 contribution in their Weyl symbol and so exhibit contextuality regardless of the state being measured. On the other hand, odd-dimensional qudit observables generally possess non-zero order ℏ0 terms, and higher, in their WWM formulation, and so exhibit contextuality depending on the state measured: odd-dimensional qudit states that exhibit measurement contextuality have an order ℏ1 contribution that allows for the violation of classical bounds while states that do not exhibit measurement contextuality have insufficiently large order ℏ1 contributions.

}, doi = {https://doi.org/10.1088/1367-2630/aacef2}, url = {https://arxiv.org/abs/1711.08066}, author = {Lucas Kocia and Peter Love} } @article {2214, title = {More is Less: Perfectly Secure Oblivious Algorithms in the Multi-Server Setting}, year = {2018}, abstract = {

The problem of Oblivious RAM (ORAM) has traditionally been studied in a single-server setting, but more recently the multi-server setting has also been considered. Yet it is still unclear whether the multi-server setting has any inherent advantages, e.g., whether the multi-server setting can be used to achieve stronger security goals or provably better efficiency than is possible in the single-server case. In this work, we construct a perfectly secure 3-server ORAM scheme that outperforms the best known single-server scheme by a logarithmic factor. In the process, we also show, for the first time, that there exist specific algorithms for which multiple servers can overcome known lower bounds in the single-server setting.\ 

}, url = {https://arxiv.org/abs/1809.00825}, author = {Hubert Chan and Jonathan Katz and Kartik Nayak and Antigoni Polychroniadou and Elaine Shi} } @article {2279, title = {Morphisms in categories of nonlocal games}, year = {2018}, abstract = {

Synchronous correlations provide a class of nonlocal games that behave like functions between finite sets. In this work we examine categories whose morphisms are games with synchronous classical, quantum, or general nonsignaling correlations. In particular, we characterize when morphisms in these categories are monic, epic, sections, or retractions.

}, url = {https://arxiv.org/abs/1810.10074}, author = {Brad Lackey and Nishant Rodrigues} } @article {2251, title = {Multiparty quantum data hiding with enhanced security and remote deletion}, year = {2018}, pages = {5}, abstract = {

One of the applications of quantum technology is to use quantum states and measurements to communicate which offers more reliable security promises. Quantum data hiding, which gives the source party the ability of sharing data among multiple receivers and revealing it at a later time depending on his/her will, is one of the promising information sharing schemes which may address practical security issues. In this work, we propose a novel quantum data hiding protocol. By concatenating different subprotocols which apply to rather symmetric hiding scenarios, we cover a variety of more general hiding scenarios. We provide the general requirements for constructing such protocols and give explicit examples of encoding states for five parties. We also proved the security of the protocol in sense that the achievable information by unauthorized operations asymptotically goes to zero. In addition, due to the capability of the sender to manipulate his/her subsystem, the sender is able to abort the protocol remotely at any time before he/she reveals the information.

}, url = {https://arxiv.org/abs/1804.01982}, author = {Xingyao Wu and Jianxin Chen} } @article {2312, title = {On the need for soft dressing}, journal = {High Energ. Phys. }, volume = {121}, year = {2018}, month = {2018}, abstract = {

In order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.

}, author = {Daniel Carney and Laurent Chaurette and Dominik Neuenfeld and Gordon Semenoff} } @article {2260, title = {The Non-Disjoint Ontic States of the Grassmann Ontological Model, Transformation Contextuality, and the Single Qubit Stabilizer Subtheory}, year = {2018}, abstract = {

We show that it is possible to construct a preparation non-contextual ontological model that does not exhibit \"transformation contextuality\" for single qubits in the stabilizer subtheory. In particular, we consider the \"blowtorch\" map and show that it does not exhibit transformation contextuality under the Grassmann Wigner-Weyl-Moyal (WWM) qubit formalism. Furthermore, the transformation in this formalism can be fully expressed at order ℏ0 and so does not qualify as a candidate quantum phenomenon. In particular, we find that the Grassmann WWM formalism at order ℏ0 corresponds to an ontological model governed by an additional set of constraints arising from the relations defining the Grassmann algebra. Due to this additional set of constraints, the allowed probability distributions in this model do not form a single convex set when expressed in terms of disjoint ontic states and so cannot be mapped to models whose states form a single convex set over disjoint ontic states. However, expressing the Grassmann WWM ontological model in terms of non-disjoint ontic states corresponding to the monomials of the Grassmann algebra results in a single convex set. We further show that a recent result by Lillystone et al. that proves a broad class of preparation and measurement non-contextual ontological models must exhibit transformation contextuality lacks the generality to include the ontological model considered here; Lillystone et al.\&$\#$39;s result is appropriately limited to ontological models whose states produce a single convex set when expressed in terms of disjoint ontic states. Therefore, we prove that for the qubit stabilizer subtheory to be captured by a preparation, transformation and measurement non-contextual ontological theory, it must be expressed in terms of non-disjoint ontic states, unlike the case for the odd-dimensional single-qudit stabilizer subtheory.

}, url = {https://arxiv.org/abs/1805.09514}, author = {Lucas Kocia and Peter Love} } @article {2206, title = {Observation of bound state self-interaction in a nano-eV atom collider}, journal = {Nature Communications }, volume = {9}, year = {2018}, month = {2018/11/20}, abstract = {

Quantum mechanical scattering resonances for colliding particles occur when a continuum scattering state couples to a discrete bound state between them. The coupling also causes the bound state to interact with itself via the continuum and leads to a shift in the bound state energy, but, lacking knowledge of the bare bound state energy, measuring this self-energy via the resonance position has remained elusive. Here, we report on the direct observation of self-interaction by using a nano-eV atom collider to track the position of a magnetically-tunable Feshbach resonance through a parameter space spanned by energy and magnetic field. Our system of potassium and rubidium atoms displays a strongly non-monotonic resonance trajectory with an exceptionally large self-interaction energy arising from an interplay between the Feshbach bound state and a different, virtual bound state at a fixed energy near threshold.

}, doi = {https://doi.org/10.1038/s41467-018-07375-8}, url = {https://arxiv.org/abs/1807.01174}, author = {Ryan Thomas and Matthew Chilcott and Eite Tiesinga and Amita B. Deb and Niels Kj{\ae}rgaard} } @article {2060, title = {Observation of three-photon bound states in a quantum nonlinear medium}, journal = {Science}, volume = {359}, year = {2018}, month = {2018/02/16}, pages = {783-786}, abstract = {

Bound states of massive particles, such as nuclei, atoms or molecules, are ubiquitous in nature and constitute the bulk of the visible world around us. In contrast, photons typically only weakly influence each other due to their very weak interactions and vanishing mass. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. In particular, photon correlation and conditional phase measurements reveal the distinct features associated with three-photon and two-photon bound states. Such photonic trimers and dimers can be viewed as quantum solitons with shape-preserving wavefunctions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are quantitatively described by an effective field theory (EFT) of Rydberg-induced photon-photon interactions, which demonstrates the presence of a substantial effective three-body force between the photons. These observations pave the way towards the realization, studies, and control of strongly interacting quantum many-body states of light.

}, doi = {10.1126/science.aao7293}, url = {http://science.sciencemag.org/content/359/6377/783}, author = {Qi-Yu Liang and Aditya V. Venkatramani and Sergio H. Cantu and Travis L. Nicholson and Michael Gullans and Alexey V. Gorshkov and Jeff D. Thompson and Cheng Chin and Mikhail D. Lukin and Vladan Vuletic} } @article {1836, title = {Optimal and Secure Measurement Protocols for Quantum Sensor Networks}, year = {2018}, month = {2018/03/23}, abstract = {

Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting where the quantity to be measured is a linear function of parameters coupled to each qubit individually. We first generalize the Heisenberg limit to the measurement of non-local observables in a quantum network, deriving a bound based on the multi-parameter quantum Fisher information. We then propose a protocol that can make use of GHZ states or spin-squeezed states, and show that in the case of GHZ states the procedure is optimal, i.e., it saturates our bound.

}, doi = {https://doi.org/10.1103/PhysRevA.97.042337}, url = {http://arxiv.org/abs/1607.04646}, author = {Zachary Eldredge and Michael Foss-Feig and Steven L. Rolston and Alexey V. Gorshkov} } @article {2259, title = {Optimal Pure-State Qubit Tomography via Sequential Weak Measurements}, journal = {Phys. Rev. Lett. }, volume = {121}, year = {2018}, abstract = {

The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively measuring the spin projection of an ensemble of qubits weakly and isotropically. We apply this in the context of optimal tomography of pure qubits. We show numerically that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continuous measurement with random controls, one can approach the optimal bound.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.130404}, url = {https://arxiv.org/abs/1805.01012}, author = {Ezad Shojaee and Christopher S. Jackson and Carlos A. Riofrio and Amir Kalev and Ivan H. Deutsch} } @article {2209, title = {Optimization of photon storage fidelity in ordered atomic arrays}, journal = {New Journal of Physics}, volume = {20}, year = {2018}, month = {2018/08/31}, abstract = {

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. The validity of this model can break down, however, in systems such as dense, ordered atomic arrays, where strong interference in emission can give rise to phenomena such as subradiance and \"selective\" radiance. Here, we develop a general formalism that finds the maximum storage efficiency for a collection of atoms with discrete, known positions, and a given spatial mode in which an optical field is sent. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number Na like \∼(logNa)2/N2a, and that, remarkably, an array of just 4\×4 atoms in principle allows for an efficiency comparable to a disordered ensemble with optical depth of around 600.

}, doi = {https://doi.org/10.1088/1367-2630/aadb74}, url = {https://arxiv.org/abs/1710.06312}, author = {M. T. Manzoni and M. Moreno-Cardoner and A. Asenjo-Garcia and J. V. Porto and Alexey V. Gorshkov and D. E. Chang} } @article {1997, title = {Optomechanical approach to controlling the temperature and chemical potential of light}, journal = {Phys. Rev. A 97, 033850}, year = {2018}, month = {2018/05/18}, abstract = {

Massless particles, including photons, are not conserved even at low energies and thus have no chemical potential. However, in driven systems, near equilibrium dynamics can lead to equilibration of photons with a finite number, describable using an effective chemical potential. Here we build upon this general concept with an implementation appropriate for a nonlinear photon-based quantum simulator. We consider how laser cooling of a well-isolated mechanical mode can provide an effective low-frequency bath for the quantum simulator system. We show that the use of auxiliary photon modes, coupled by the mechanical system, enables control of both the chemical potential, by drive frequency, and temperature, by drive amplitude, of the resulting photonic quantum simulator\&$\#$39;s grand canonical ensemble.

}, doi = {https://doi.org/10.1103/PhysRevA.97.033850}, url = {https://arxiv.org/abs/1706.00789}, author = {Chiao-Hsuan Wang and J. M. Taylor} } @article {2255, title = {Orbital quantum magnetism in spin dynamics of strongly interacting magnetic lanthanide atoms}, year = {2018}, abstract = {

Laser cooled lanthanide atoms are ideal candidates with which to study strong and unconventional quantum magnetism with exotic phases. Here, we use state-of-the-art closed-coupling simulations to model quantum magnetism for pairs of ultracold spin-6 erbium lanthanide atoms placed in a deep optical lattice. In contrast to the widely used single-channel Hubbard model description of atoms and molecules in an optical lattice, we focus on the single-site multi-channel spin evolution due to spin-dependent contact, anisotropic van der Waals, and dipolar forces. This has allowed us to identify the leading mechanism, orbital anisotropy, that governs molecular spin dynamics among erbium atoms. The large magnetic moment and combined orbital angular momentum of the 4f-shell electrons are responsible for these strong anisotropic interactions and unconventional quantum magnetism. Multi-channel simulations of magnetic Cr atoms under similar trapping conditions show that their spin-evolution is controlled by spin-dependent contact interactions that are distinct in nature from the orbital anisotropy in Er. The role of an external magnetic field and the aspect ratio of the lattice site on spin dynamics is also investigated.

}, url = {https://arxiv.org/abs/1804.10102}, author = {Ming Li and Eite Tiesinga and Svetlana Kotochigova} } @article {2286, title = {Parallel Entangling Operations on a Universal Ion Trap Quantum Computer}, year = {2018}, abstract = {

The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor\&$\#$39;s factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.

}, url = {https://arxiv.org/abs/1810.11948}, author = {C. Figgatt and A. Ostrander and N. M. Linke and K. A. Landsman and D. Zhu and D. Maslov and C. Monroe} } @article {2139, title = {Phase Retrieval Without Small-Ball Probability Assumptions}, journal = {IEEE Transactions on Information Theory }, volume = {64}, year = {2018}, month = {2018/01/01}, pages = {485-500}, abstract = {

In the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even in combination with certain practically feasible random masks. To avoid this difficulty, the analysis is often restricted to measurement ensembles (or masks) that satisfy a small-ball probability condition, in order to ensure that the reconstruction is unique. This paper shows a complementary result: for random Bernoulli measurements, there is still a large class of signals that can be reconstructed uniquely, namely, those signals that are non-peaky. In fact, this result is much more general: it holds for random measurements sampled from any subgaussian distribution 2), without any small-ball conditions. This is demonstrated in two ways: 1) a proof of stability and uniqueness and 2) a uniform recovery guarantee for the PhaseLift algorithm. In all of these cases, the number of measurements m approaches the information-theoretic lower bound. Finally, for random Bernoulli measurements with erasures, it is shown that PhaseLift achieves uniform recovery of all signals (including peaky ones).

}, doi = {10.1109/TIT.2017.2757520}, url = {http://ieeexplore.ieee.org/document/8052535/}, author = {Felix Krahmer and Yi-Kai Liu} } @article {2218, title = {Photon propagation through dissipative Rydberg media at large input rates}, year = {2018}, abstract = {

We study the dissipative propagation of quantized light in interacting Rydberg media under the conditions of electromagnetically induced transparency (EIT). Rydberg blockade physics in optically dense atomic media leads to strong dissipative interactions between single photons. The regime of high incoming photon flux constitutes a challenging many-body dissipative problem. We experimentally study in detail for the first time the pulse shapes and the second-order correlation function of the outgoing field and compare our data with simulations based on two novel theoretical approaches well-suited to treat this many-photon limit. At low incoming flux, we report good agreement between both theories and the experiment. For higher input flux, the intensity of the outgoing light is lower than that obtained from theoretical predictions. We explain this discrepancy using a simple phenomenological model taking into account pollutants, which are nearly-stationary Rydberg excitations coming from the reabsorption of scattered probe photons. At high incoming photon rates, the blockade physics results in unconventional shapes of measured correlation functions.\ 

}, url = {https://arxiv.org/abs/1807.07586}, author = {Przemyslaw Bienias and James Douglas and Asaf Paris-Mandoki and Paraj Titum and Ivan Mirgorodskiy and Christoph Tresp and Emil Zeuthen and Michael Gullans and Marco Manzoni and Sebastian Hofferberth and Darrick Chang and Alexey V. Gorshkov} } @article {2144, title = {Photon Subtraction by Many-Body Decoherence}, year = {2018}, month = {2018/03/13}, abstract = {

We present an experimental and theoretical investigation of the scattering-induced decoherence of multiple photons stored in a strongly interacting atomic ensemble. We derive an exact solution to this many-body problem, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis demonstrates a correlated coherence-protection process, in which the induced decoherence of one photon can preserve the spatial coherence of all others. We discuss how this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability.

}, doi = {https://doi.org/10.1103/PhysRevLett.120.113601}, url = {https://arxiv.org/abs/1710.10047}, author = {Callum R. Murray and Ivan Mirgorodskiy and Christoph Tresp and Christoph Braun and Asaf Paris-Mandoki and Alexey V. Gorshkov and Sebastian Hofferberth and Thomas Pohl} } @article {2135, title = {Photon thermalization via laser cooling of atoms}, journal = {Phys. Rev. A 98, 013834}, year = {2018}, month = {2018}, abstract = {

Laser cooling of atomic motion enables a wide variety of technological and scientific explorations using cold atoms. Here we focus on the effect of laser cooling on the photons instead of on the atoms. Specifically, we show that non-interacting photons can thermalize with the atoms to a grand canonical ensemble with a non-zero chemical potential. This thermalization is accomplished via scattering of light between different optical modes, mediated by the laser cooling process. While optically thin modes lead to traditional laser cooling of the atoms, the dynamics of multiple scattering in optically thick modes has been more challenging to describe. We find that in an appropriate set of limits, multiple scattering leads to thermalization of the light with the atomic motion in a manner that approximately conserves total photon number between the laser beams and optically thick modes. In this regime, the subsystem corresponding to the thermalized modes is describable by a grand canonical ensemble with a chemical potential set by the energy of a single laser photon. We consider realization of this regime using two-level atoms in Doppler cooling, and find physically realistic conditions for rare earth atoms. With the addition of photon-photon interactions, this system could provide a new platform for exploring many-body physics.

}, doi = {https://doi.org/10.1103/PhysRevA.98.013834}, url = {https://arxiv.org/abs/1712.08643}, author = {Chiao-Hsuan Wang and Michael Gullans and J. V. Porto and William D. Phillips and J. M. Taylor} } @article {2319, title = {Practitioner{\textquoteright}s guide to social network analysis: Examining physics anxiety in an active-learning setting}, year = {2018}, abstract = {

The application of social network analysis (SNA) has recently grown prevalent in science, technology, engineering, and mathematics education research. Research on classroom networks has led to greater understandings of student persistence in physics majors, changes in their career-related beliefs (e.g., physics interest), and their academic success. In this paper, we aim to provide a practitioner\&$\#$39;s guide to carrying out research using SNA, including how to develop data collection instruments, set up protocols for gathering data, as well as identify network methodologies relevant to a wide range of research questions beyond what one might find in a typical primer. We illustrate these techniques using student anxiety data from active-learning physics classrooms. We explore the relationship between students\&$\#$39; physics anxiety and the social networks they participate in throughout the course of a semester. We find that students\&$\#$39; with greater numbers of outgoing interactions are more likely to experience negative anxiety shifts even while we control for {\it pre} anxiety, gender, and final course grade. We also explore the evolution of student networks and find that the second half of the semester is a critical period for participating in interactions associated with decreased physics anxiety. Our study further supports the benefits of dynamic group formation strategies that give students an opportunity to interact with as many peers as possible throughout a semester. To complement our guide to SNA in education research, we also provide a set of tools for letting other researchers use this approach in their work -- the {\it SNA toolbox} -- that can be accessed on GitHub.\ 

}, url = {https://arxiv.org/abs/1809.00337}, author = {Remy Dou and Justyna P. Zwolak} } @article {2146, title = {Probing electron-phonon interactions in the charge-photon dynamics of cavity-coupled double quantum dots}, journal = {Physical Review B}, volume = {97}, year = {2018}, month = {2018/01/16}, pages = {035305}, abstract = {

Electron-phonon coupling is known to play an important role in the charge dynamics of semiconductor quantum dots. Here we explore its role in the combined charge-photon dynamics of cavity-coupled double quantum dots. Previous work on these systems has shown that strong electron-phonon coupling leads to a large contribution to photoemission and gain from phonon-assisted emission and absorption processes. We compare the effects of this phonon sideband in three commonly investigated gate-defined quantum dot material systems: InAs nanowires and GaAs and Si two-dimensional electron gases (2DEGs). We compare our theory with existing experimental data from cavity-coupled InAs nanowire and GaAs 2DEG double quantum dots and find quantitative agreement only when the phonon sideband and photoemission processes during lead tunneling are taken into account. Finally, we show that the phonon sideband also leads to a sizable renormalization of the cavity frequency, which allows for direct spectroscopic probes of the electron-phonon coupling in these systems.

}, doi = {10.1103/PhysRevB.97.035305}, url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.035305}, author = {Michael Gullans and J. M. Taylor and J. R. Petta} } @article {2098, title = {Pseudorandom States, Non-Cloning Theorems and Quantum Money}, journal = {In: Shacham H., Boldyreva A. (eds) Advances in Cryptology {\textendash} CRYPTO 2018. CRYPTO 2018. Lecture Notes in Computer Science.}, volume = {10993}, year = {2018}, month = {2017/11/01}, abstract = {

We propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study\—it motivates the proper definition and characterizes one of the important properties of pseudorandom quantum states. Namely, there is no efficient quantum algorithm that can create more copies of the state from a given number of pseudorandom states. As the main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.

}, doi = {https://doi.org/10.1007/978-3-319-96878-0_5}, url = {https://arxiv.org/abs/1711.00385}, author = {Zhengfeng Ji and Yi-Kai Liu and Fang Song} } @article {2268, title = {QFlow lite dataset: A machine-learning approach to the charge states in quantum dot experiments}, journal = {PLOS ONE}, volume = {13}, year = {2018}, month = {2018}, pages = {e0205844}, type = {2018/10/17}, abstract = {

Over the past decade, machine learning techniques have revolutionized how research is done, from designing new materials and predicting their properties to assisting drug discovery to advancing cybersecurity. Recently, we added to this list by showing how a machine learning algorithm (a so-called learner) combined with an optimization routine can assist experimental efforts in the realm of tuning semiconductor quantum dot (QD) devices. Among other applications, semiconductor QDs are a candidate system for building quantum computers. The present-day tuning techniques for bringing the QD devices into a desirable configuration suitable for quantum computing that rely on heuristics do not scale with the increasing size of the quantum dot arrays required for even near-term quantum computing demonstrations. Establishing a reliable protocol for tuning that does not rely on the gross-scale heuristics developed by experimentalists is thus of great importance. To implement the machine learning-based approach, we constructed a dataset of simulated QD device characteristics, such as the conductance and the charge sensor response versus the applied electrostatic gate voltages. Here, we describe the methodology for generating the dataset, as well as its validation in training convolutional neural networks. We show that the learner\&$\#$39;s accuracy in recognizing the state of a device is ~96.5 \% in both current- and charge-sensor-based training. We also introduce a tool that enables other researchers to use this approach for further research: QFlow lite - a Python-based mini-software suite that uses the dataset to train neural networks to recognize the state of a device and differentiate between states in experimental data. This work gives the definitive reference for the new dataset that will help enable researchers to use it in their experiments or to develop new machine learning approaches and concepts

}, doi = {https://doi.org/10.1371/journal.pone.0205844}, url = {https://arxiv.org/abs/1809.10018}, author = {Justyna P. Zwolak and Sandesh S. Kalantre and Xingyao Wu and Stephen Ragole and J. M. Taylor} } @article {2306, title = {Quantitative Robustness Analysis of Quantum Programs (Extended Version)}, journal = {Proc. ACM Program. Lang.}, volume = {3}, year = {2018}, month = {2018/12/1}, pages = {Article 31}, abstract = {

Quantum computation is a topic of significant recent interest, with practical advances coming from both research and industry. A major challenge in quantum programming is dealing with errors (quantum noise) during execution. Because quantum resources (e.g., qubits) are scarce, classical error correction techniques applied at the level of the architecture are currently cost-prohibitive. But while this reality means that quantum programs are almost certain to have errors, there as yet exists no principled means to reason about erroneous behavior. This paper attempts to fill this gap by developing a semantics for erroneous quantum while-programs, as well as a logic for reasoning about them. This logic permits proving a property we have identified, called ε-robustness, which characterizes possible \"distance\" between an ideal program and an erroneous one. We have proved the logic sound, and showed its utility on several case studies, notably: (1) analyzing the robustness of noisy versions of the quantum Bernoulli factory (QBF) and quantum walk (QW); (2) demonstrating the (in)effectiveness of different error correction schemes on single-qubit errors; and (3) analyzing the robustness of a fault-tolerant version of QBF.

}, doi = {https://doi.org/10.1145/3290344}, url = {https://arxiv.org/abs/1811.03585}, author = {Shih-Han Hung and Kesha Hietala and Shaopeng Zhu and Mingsheng Ying and Michael Hicks and Xiaodi Wu} } @article {2281, title = {Quantum adiabatic optimization without heuristics}, year = {2018}, abstract = {

Quantum adiabatic optimization (QAO) is performed using a time-dependent Hamiltonian H(s) with spectral gap γ(s). Assuming the existence of an oracle Γ such that γ(s)=Θ(Γ(s)), we provide an algorithm that reliably performs QAO in time Oγ\−1minlog(γ\−1min) with Olog(γ\−1min) oracle queries, where γmin=minsγ(s). Our strategy is not heuristic and does not require guessing time parameters or annealing paths. Rather, our algorithm naturally produces an annealing path such that dH/ds\≈γ(s) and chooses its own runtime T to be as close as possible to optimal while promising convergence to the ground state. We then demonstrate the feasibility of this approach in practice by explicitly constructing a gap oracle Γ for the problem of finding a vertex m=argminuW(u) of the cost function W:V⟶[0,1], restricting ourselves to computational basis measurements and driving Hamiltonian H(0)=I\−V\−1\∑u,v\∈V|u\⟩\⟨v|, with V=|V|. Requiring only that W have a constant lower bound on its spectral gap and upper bound κ on its spectral ratio, our QAO algorithm returns m using Γ with probability (1\−ε)(1\−e\−1/ε) in time O\˜(ε\−1[V\−\−\√+(κ\−1)2/3V2/3]). This achieves a quantum advantage for all κ, and when κ\≈1, recovers Grover scaling up to logarithmic factors. We implement the algorithm as a subroutine in an optimization procedure that produces m with exponentially small failure probability and expected runtime O\˜(ε\−1[V\−\−\√+(κ\−1)2/3V2/3]), even when κ is not known beforehand.

}, url = {https://arxiv.org/abs/1810.04686}, author = {Michael Jarret and Brad Lackey and Aike Liu and Kianna Wan} } @article {1922, title = {Quantum algorithm for multivariate polynomial interpolation}, journal = {Proceedings of The Royal Society A}, volume = {474}, year = {2018}, month = {2018/01/17}, abstract = {

How many quantum queries are required to determine the coefficients of a degree-d polynomial in n variables? We present and analyze quantum algorithms for this multivariate polynomial interpolation problem over the fields Fq, R, and C. We show that kC and 2kC queries suffice to achieve probability 1 for C and R, respectively, where kC = \⌈ 1 n+1 ( n+d d )\⌉ except for d = 2 and four other special cases. For Fq, we show that \⌈ d n+d ( n+d d )\⌉ queries suffice to achieve probability approaching 1 for large field order q. The classical query complexity of this problem is ( n+d d ), so our result provides a speedup by a factor of n + 1, n+1 2 , and n+d d for C, R, and Fq, respectively. Thus we find a much larger gap between classical and quantum algorithms than the univariate case, where the speedup is by a factor of 2. For the case of Fq, we conjecture that 2kC queries also suffice to achieve probability approaching 1 for large field order q, although we leave this as an open problem.

}, doi = {10.1098/rspa.2017.0480}, url = {http://rspa.royalsocietypublishing.org/content/474/2209/20170480}, author = {Jianxin Chen and Andrew M. Childs and Shih-Han Hung} } @article {2317, title = {Quantum Channel Simulation and the Channel{\textquoteright}s Smooth Max-Information}, year = {2018}, abstract = {

We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the channel\&$\#$39;s smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel\&$\#$39;s smooth max-information as the one-shot quantum simulation cost under no-signalling assisted codes. Third, we derive the asymptotic equipartition property of the channel\&$\#$39;s smooth max-information, i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various quantum channels.

}, url = {https://arxiv.org/abs/1807.05354}, author = {Kun Fang and Xin Wang and Marco Tomamichel and Mario Berta} } @article {2326, title = {Quantum Cryptanalysis: Shor, Grover, and Beyond}, journal = {IEEE Security \& Privacy }, volume = {16}, year = {2018}, month = {2018/09}, pages = {14-21}, doi = {10.1109/MSP.2018.3761719}, author = {Stephen P. Jordan and Yi-Kai Liu} } @article {2316, title = {Quantum field theory for the chiral clock transition in one spatial dimension}, journal = {Phys. Rev. }, volume = {B }, year = {2018}, month = {2018/11/09}, pages = {205118 }, abstract = {

We describe the quantum phase transition in the N-state chiral clock model in spatial dimension d=1. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and N=3, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ZN symmetry, to a gapped phase with the ZN symmetry restored. The transition has dynamical critical exponent z\≠1, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in d=1, involving the onset of a single boson condensate in the background of a higher-dimensional N-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in 2\−d, with 4\−N chosen to be of order 2\−d. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for N=3, finding good evidence for a direct phase transition, and obtain estimates for z and the correlation length exponent ν.

}, doi = {https://doi.org/10.1103/PhysRevB.98.205118}, url = {https://arxiv.org/abs/1808.07056}, author = {Seth Whitsitt and Rhine Samajdar and Subir Sachdev} } @article {2261, title = {Quantum generalizations of the polynomial hierarchy with applications to QMA(2)}, journal = {Proceedings of 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, year = {2018}, abstract = {

The polynomial-time hierarchy (PH) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as PH does not collapse). Here, we study whether two quantum generalizations of PH can similarly prove separations in the quantum setting. The first generalization, QCPH, uses classical proofs, and the second, QPH, uses quantum proofs. For the former, we show quantum variants of the Karp-Lipton theorem and Toda\&$\#$39;s theorem. For the latter, we place its third level, QΣ3, into NEXP {using the Ellipsoid Method for efficiently solving semidefinite programs}. These results yield two implications for QMA(2), the variant of Quantum Merlin-Arthur (QMA) with two unentangled proofs, a complexity class whose characterization has proven difficult. First, if QCPH=QPH (i.e., alternating quantifiers are sufficiently powerful so as to make classical and quantum proofs \"equivalent\"), then QMA(2) is in the Counting Hierarchy (specifically, in PPPPP). Second, unless QMA(2)=QΣ3 (i.e., alternating quantifiers do not help in the presence of \"unentanglement\"), QMA(2) is strictly contained in NEXP.

}, doi = {https://doi.org/10.4230/LIPIcs.MFCS.2018.58}, url = {https://arxiv.org/abs/1805.11139}, author = {Sevag Gharibian and Miklos Santha and Jamie Sikora and Aarthi Sundaram and Justin Yirka} } @article {2309, title = {Quantum SDP Solvers: Large Speed-ups, Optimality, and Applications to Quantum Learning}, journal = {To appear at the 46th International Colloquium on Automata, Languages and Programming (ICALP 2019)}, year = {2018}, abstract = {

We give two new quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with m constraint matrices, each of dimension n, rank r, and sparsity s. The first algorithm assumes an input model where one is given access to entries of the matrices at unit cost. We show that it has run time O~(s2(m\−\−\√ε\−10+n\−\−\√ε\−12)), where ε is the error. This gives an optimal dependence in terms of m,n and quadratic improvement over previous quantum algorithms when m\≈n. The second algorithm assumes a fully quantum input model in which the matrices are given as quantum states. We show that its run time is O~(m\−\−\√+poly(r))\⋅poly(logm,logn,B,ε\−1), with B an upper bound on the trace-norm of all input matrices. In particular the complexity depends only poly-logarithmically in n and polynomially in r. We apply the second SDP solver to the problem of learning a good description of a quantum state with respect to a set of measurements: Given m measurements and copies of an unknown state ρ, we show we can find in time m\−\−\√\⋅poly(logm,logn,r,ε\−1) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as ρ on the m measurements, up to error ε. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes\&$\#$39; principle from statistical mechanics. As in previous work, we obtain our algorithm by \"quantizing\" classical SDP solvers based on the matrix multiplicative weight method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians with a poly-logarithmic dependence on its dimension, which could be of independent interest.

}, url = {https://arxiv.org/abs/1710.02581}, author = {Fernando G. S. L. Brand{\~a}o and Amir Kalev and Tongyang Li and Cedric Yen-Yu Lin and Krysta M. Svore and Xiaodi Wu} } @article {2175, title = {Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics}, journal = {Proceedings of the 51st ACM Symposium on Theory of Computing }, year = {2018}, month = {2018/06/05}, pages = {193-204}, abstract = {

Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new \"Singular value transformation\" algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang. The proposed quantum circuits have a very simple structure, often give rise to optimal algorithms and have appealing constant factors, while usually only use a constant number of ancilla qubits. We show that singular value transformation leads to novel algorithms. We give an efficient solution to a certain \"non-commutative\" measurement problem and propose a new method for singular value estimation. We also show how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum. Finally, as a quantum machine learning application we show how to efficiently implement principal component regression. \"Singular value transformation\" is conceptually simple and efficient, and leads to a unified framework of quantum algorithms incorporating a variety of quantum speed-ups. We illustrate this by showing how it generalizes a number of prominent quantum algorithms, including: optimal Hamiltonian simulation, implementing the Moore-Penrose pseudoinverse with exponential precision, fixed-point amplitude amplification, robust oblivious amplitude amplification, fast QMA amplification, fast quantum OR lemma, certain quantum walk results and several quantum machine learning algorithms. In order to exploit the strengths of the presented method it is useful to know its limitations too, therefore we also prove a lower bound on the efficiency of singular value transformation, which often gives optimal bounds.

}, doi = {https://doi.org/10.1145/3313276.3316366}, url = {https://arxiv.org/abs/1806.01838}, author = {Andras Gilyen and Yuan Su and Guang Hao Low and Nathan Wiebe} } @article {2311, title = {Quantum Supremacy and the Complexity of Random Circuit Sampling}, year = {2018}, abstract = {

A critical milestone on the path to useful quantum computers is quantum supremacy - a demonstration of a quantum computation that is prohibitively hard for classical computers. A leading near-term candidate, put forth by the Google/UCSB team, is sampling from the probability distributions of randomly chosen quantum circuits, which we call Random Circuit Sampling (RCS). In this paper we study both the hardness and verification of RCS. While RCS was defined with experimental realization in mind, we show complexity theoretic evidence of hardness that is on par with the strongest theoretical proposals for supremacy. Specifically, we show that RCS satisfies an average-case hardness condition - computing output probabilities of typical quantum circuits is as hard as computing them in the worst-case, and therefore $\#$P-hard. Our reduction exploits the polynomial structure in the output amplitudes of random quantum circuits, enabled by the Feynman path integral. In addition, it follows from known results that RCS satisfies an anti-concentration property, making it the first supremacy proposal with both average-case hardness and anti-concentration.\ 

}, url = {https://arxiv.org/abs/1803.04402}, author = {Adam Bouland and Bill Fefferman and Chinmay Nirkhe and Umesh Vazirani} } @article {2308, title = {Quantum-secure message authentication via blind-unforgeability}, year = {2018}, abstract = {

Formulating and designing unforgeable authentication of classical messages in the presence of quantum adversaries has been a challenge, as the familiar classical notions of unforgeability do not directly translate into meaningful notions in the quantum setting. A particular difficulty is how to fairly capture the notion of \"predicting an unqueried value\" when the adversary can query in quantum superposition. In this work, we uncover serious shortcomings in existing approaches, and propose a new definition. We then support its viability by a number of constructions and characterizations. Specifically, we demonstrate a function which is secure according to the existing definition by Boneh and Zhandry, but is clearly vulnerable to a quantum forgery attack, whereby a query supported only on inputs that start with 0 divulges the value of the function on an input that starts with 1. We then propose a new definition, which we call \"blind-unforgeability\" (or BU.) This notion matches \"intuitive unpredictability\" in all examples studied thus far. It defines a function to be predictable if there exists an adversary which can use \"partially blinded\" oracle access to predict values in the blinded region. Our definition (BU) coincides with standard unpredictability (EUF-CMA) in the classical-query setting. We show that quantum-secure pseudorandom functions are BU-secure MACs. In addition, we show that BU satisfies a composition property (Hash-and-MAC) using \"Bernoulli-preserving\" hash functions, a new notion which may be of independent interest. Finally, we show that BU is amenable to security reductions by giving a precise bound on the extent to which quantum algorithms can deviate from their usual behavior due to the blinding in the BU security experiment.\ 

}, url = {https://arxiv.org/abs/1803.03761}, author = {Gorjan Alagic and Christian Majenz and Alexander Russell and Fang Song} } @article {2248, title = {The quasiprobability behind the out-of-time-ordered correlator}, journal = {Phys. Rev. }, volume = {A}, year = {2018}, month = {04/2018}, chapter = {042105}, abstract = {

Two topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC has been shown to equal a moment of a summed quasiprobability. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability\&$\#$39;s structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze the weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse-graining) numerically and analytically: We simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors: The quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC\&$\#$39;s underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.

}, doi = {https://doi.org/10.1103/PhysRevA.97.042105}, url = {https://arxiv.org/abs/1704.01971}, author = {Nicole Yunger Halpern and Brian Swingle and Justin Dressel} } @article {2138, title = {Recovering quantum gates from few average gate fidelities}, journal = {Phys. Rev. Lett. }, volume = {121}, year = {2018}, month = {2018/03/01}, pages = {170502}, abstract = {

Characterising quantum processes is a key task in and constitutes a challenge for the development of quantum technologies, especially at the noisy intermediate scale of today\&$\#$39;s devices. One method for characterising processes is randomised benchmarking, which is robust against state preparation and measurement (SPAM) errors, and can be used to benchmark Clifford gates. A complementing approach asks for full tomographic knowledge. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency. So far, guarantees for compressed sensing protocols rely on unstructured random measurements and can not be applied to the data acquired from randomised benchmarking experiments. It has been an open question whether or not the favourable features of both worlds can be combined. In this work, we give a positive answer to this question. For the important case of characterising multi-qubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured respect to random Clifford unitaries. Moreover, for general unital quantum channels we provide an explicit expansion into a unitary 2-design, allowing for a practical and guaranteed reconstruction also in that case. As a side result, we obtain a new statistical interpretation of the unitarity -- a figure of merit that characterises the coherence of a process. In our proofs we exploit recent representation theoretic insights on the Clifford group, develop a version of Collins\&$\#$39; calculus with Weingarten functions for integration over the Clifford group, and combine this with proof techniques from compressed sensing.

}, doi = {https://doi.org/10.1103/PhysRevLett.121.170502}, url = {https://arxiv.org/abs/1803.00572}, author = {Ingo Roth and Richard Kueng and Shelby Kimmel and Yi-Kai Liu and David Gross and Jens Eisert and Martin Kliesch} } @article {2297, title = {Recovery Map for Fermionic Gaussian Channels}, year = {2018}, abstract = {

A recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices.

}, url = {https://arxiv.org/abs/1811.04956}, author = {Brian Swingle and Yixu Wang} } @article {2247, title = {Resilience of scrambling measurements}, journal = {Phys. Rev.}, volume = {A}, year = {2018}, month = {2018/06/18}, chapter = {062113}, abstract = {

Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian\&$\#$39;s negative counterpart (backwards time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum-chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol\&$\#$39;s effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

}, doi = {https://doi.org/10.1103/PhysRevA.97.062113}, url = {https://arxiv.org/abs/1802.01587}, author = {Brian Swingle and Nicole Yunger Halpern} } @article {2150, title = {Resonantly driven CNOT gate for electron spins}, journal = {Science}, volume = {359}, year = {2018}, month = {2018/01/26}, pages = {439-442}, abstract = {

Single-qubit rotations and two-qubit CNOT operations are crucial ingredients for universal quantum computing. Although high-fidelity single-qubit operations have been achieved using the electron spin degree of freedom, realizing a robust CNOT gate has been challenging because of rapid nuclear spin dephasing and charge noise. We demonstrate an efficient resonantly driven CNOT gate for electron spins in silicon. Our platform achieves single-qubit rotations with fidelities greater than 99\%, as verified by randomized benchmarking. Gate control of the exchange coupling allows a quantum CNOT gate to be implemented with resonant driving in ~200 nanoseconds. We used the CNOT gate to generate a Bell state with 78\% fidelity (corrected for errors in state preparation and measurement). Our quantum dot device architecture enables multi-qubit algorithms in silicon.

}, doi = {10.1126/science.aao5965}, url = {http://science.sciencemag.org/content/359/6374/439}, author = {D. M. Zajac and A. J. Sigillito and M. Russ and F. Borjans and J. M. Taylor and Guido Burkard and J. R. Petta} } @article {2052, title = {Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force}, journal = {Physical Review Letters}, volume = {120}, year = {2018}, month = {2018/01/09}, pages = {020501}, abstract = {

In an ion trap quantum computer, collective motional modes are used to entangle two or more qubits in order to execute multi-qubit logical gates. Any residual entanglement between the internal and motional states of the ions will result in decoherence errors, especially when there are many spectator ions in the crystal. We propose using a frequency-modulated (FM) driving force to minimize such errors and implement it experimentally. In simulation, we obtained an optimized FM gate that can suppress decoherence to less than 10\−4 and is robust against a frequency drift of more than \±1 kHz. The two-qubit gate was tested in a five-qubit trapped ion crystal, with 98.3(4)\% fidelity for a M{\o}lmer-S{\o}rensen entangling gate and 98.6(7)\% for a controlled-not (CNOT) gate. We also show an optimized FM two-qubit gate for 17 ions, proving the scalability of our method.

}, doi = {10.1103/PhysRevLett.120.020501}, url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.020501}, author = {Pak Hong Leung and Kevin A. Landsman and Caroline Figgatt and Norbert M. Linke and Christopher Monroe and Kenneth R. Brown} } @article {2203, title = {Scrambling dynamics across a thermalization-localization quantum phase transition}, year = {2018}, abstract = {

We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with sub-ballistic operator spreading. The critical disorder strength for the ballistic to sub-ballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the operator dynamics is not very sensitive to the actual eigenstate localization transition. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.

}, url = {https://arxiv.org/abs/1807.06086}, author = {Subhayan Sahu and Shenglong Xu and Brian Swingle} } @article {2303, title = {A semiclassical theory of phase-space dynamics of interacting bosons}, year = {2018}, abstract = {

We study the phase-space representation of dynamics of bosons in the semiclassical regime where the occupation number of the modes is large. To this end, we employ the van Vleck-Gutzwiller propagator to obtain an approximation for the Green\&$\#$39;s function of the Wigner distribution. The semiclassical analysis incorporates interference of classical paths and reduces to the truncated Wigner approximation (TWA) when the interference is ignored. Furthermore, we identify the Ehrenfest time after which the TWA fails. As a case study, we consider a single-mode quantum nonlinear oscillator, which displays collapse and revival of observables. We analytically show that the interference of classical paths leads to revivals, an effect that is not reproduced by the TWA or a perturbative analysis.

}, url = {https://arxiv.org/abs/1803.05122}, author = {Ranchu Mathew and Eite Tiesinga} } @article {2213, title = {Single-photon bound states in atomic ensembles}, year = {2018}, abstract = {

We illustrate the existence of single-excitation bound states for propagating photons interacting with N two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson\&$\#$39;s theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.

}, url = {https://arxiv.org/abs/1809.01147}, author = {Yidan Wang and Michael Gullans and Antoine Browaeys and J. V. Porto and Darrick E. Chang and Alexey V. Gorshkov} } @article {1837, title = {Spectrum estimation of density operators with alkaline-earth atoms}, volume = {120}, year = {2018}, month = {2018/01/09}, abstract = {

We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing, quantum simulation, and time-keeping with alkalineearth atoms are discussed.

}, doi = {https://doi.org/10.1103/PhysRevLett.120.025301}, url = {http://arxiv.org/abs/1608.02045}, author = {Michael E. Beverland and Jeongwan Haah and Gorjan Alagic and Gretchen K. Campbell and Ana Maria Rey and Alexey V. Gorshkov} } @article {2205, title = {A spinor Bose-Einstein condensate phase-sensitive amplifier for SU(1,1) interferometry}, journal = {Phys. Rev}, volume = {A 98}, year = {2018}, abstract = {

The SU(1,1) interferometer was originally conceived as a Mach-Zehnder interferometer with the beam-splitters replaced by parametric amplifiers. The parametric amplifiers produce states with correlations that result in enhanced phase sensitivity. F=1 spinor Bose-Einstein condensates (BECs) can serve as the parametric amplifiers for an atomic version of such an interferometer by collisionally producing entangled pairs of \⟨F=1,m=\±1| atoms. We simulate the effect of single and double-sided seeding of the inputs to the amplifier using the truncated-Wigner approximation. We find that single-sided seeding degrades the performance of the interferometer exactly at the phase the unseeded interferometer should operate the best. Double-sided seeding results in a phase-sensitive amplifier, where the maximal sensitivity is a function of the phase relationship between the input states of the amplifier. In both single and double-sided seeding we find there exists an optimal phase shift that achieves sensitivity beyond the standard quantum limit. Experimentally, we demonstrate a spinor phase-sensitive amplifier using a BEC of 23Na in an optical dipole trap. This configuration could be used as an input to such an interferometer. We are able to control the initial phase of the double-seeded amplifier, and demonstrate sensitivity to initial population fractions as small as 0.1\%.\ 

}, url = {https://arxiv.org/abs/1807.06676}, author = {J. P. Wrubel and A. Schwettmann and D. P. Fahey and Z. Glassman and H. K. Pechkis and P. F. Griffin and R. Barnett and E. Tiesinga and P. D. Lett} } @article {2313, title = {Stationary Phase Method in Discrete Wigner Functions and Classical Simulation of Quantum Circuits}, year = {2018}, abstract = {

We apply the periodized stationary phase method to discrete Wigner functions of systems with odd prime dimension using results from p-adic number theory. We derive the Wigner-Weyl-Moyal (WWM) formalism with higher order ℏ corrections representing contextual corrections to non-contextual Clifford operations. We apply this formalism to a subset of unitaries that include diagonal gates such as the π8 gates. We characterize the stationary phase critical points as a quantum resource injecting contextuality and show that this resource allows for the replacement of the p2t points that represent t magic state Wigner functions on p-dimensional qudits by \≤pt points. We find that the π8 gate introduces the smallest higher order ℏ correction possible, requiring the lowest number of additional critical points compared to the Clifford gates. We then establish a relationship between the stabilizer rank of states and the number of critical points necessary to treat them in the WWM formalism. This allows us to exploit the stabilizer rank decomposition of two qutrit π8 gates to develop a classical strong simulation of a single qutrit marginal on t qutrit π8 gates that are followed by Clifford evolution, and show that this only requires calculating 3t2+1 critical points corresponding to Gauss sums. This outperforms the best alternative qutrit algorithm (based on Wigner negativity and scaling as \∼30.8t for 10\−2 precision) for any number of π8 gates to full precision.

}, url = {https://arxiv.org/abs/1810.03622}, author = {Lucas Kocia and Peter Love} } @article {2257, title = {Structure of Correlated Worldline Theories of Quantum Gravity}, journal = {Phys. Rev.}, volume = {D}, year = {2018}, month = {2018/06/21}, pages = {084052}, abstract = {

We consider the general form of \"Correlated Worldline\" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple copies of the coupled matter and gravitational fields. In both versions, the paths in a functional formulation are correlated via gravity itself, causing a breakdown of the superposition principle; however, the product form survives consistency tests not satisfied by the summed form. To better understand the structure of these two theories, we show how to perform diagrammatic expansions in the gravitational coupling for each version of CWL theory, using particle propagation and scalar fields as examples. We explicitly calculate contributions to 2-point and 4-point functions, again for each version of the theory, up to 2nd-order in the gravitational coupling.

}, doi = {https://doi.org/10.1103/PhysRevD.98.084052}, url = {https://arxiv.org/abs/1806.08043}, author = {Andrei O. Barvinsky and Daniel Carney and Philip C. E. Stamp} } @article {2322, title = {Study of radon reduction in gases for rare event search experiments}, year = {2018}, abstract = {

The noble elements, argon and xenon, are frequently employed as the target and event detector for weakly interacting particles such as neutrinos and Dark Matter. For such rare processes, background radiation must be carefully minimized. Radon provides one of the most significant contaminants since it is an inevitable product of trace amounts of natural uranium. To design a purification system for reducing such contamination, the adsorption characteristics of radon in nitrogen, argon, and xenon carrier gases on various types of charcoals with different adsorbing properties and intrinsic radioactive purities have been studied in the temperature range of 190-295 K at flow rates of 0.5 and 2 standard liters per minute. Essential performance parameters for the various charcoals include the average breakthrough times (τ), dynamic adsorption coefficients (ka) and the number of theoretical stages (n). It is shown that the ka-values for radon in nitrogen, argon, and xenon increase as the temperature of the charcoal traps decreases, and that they are significantly larger in nitrogen and argon than in xenon gas due to adsorption saturation effects. It is found that, unlike in xenon, the dynamic adsorption coefficients for radon in nitrogen and argon strictly obey the Arrhenius law. The experimental results strongly indicate that nitric acid etched Saratech is the best candidate among all used charcoal brands. It allows reducing total radon concentration in the LZ liquid Xe detector to meet the ultimate goal in the search for Dark Matter.

}, doi = {https://doi.org/10.1016/j.nima.2018.06.076}, url = {https://arxiv.org/abs/1805.11306}, author = {K. Pushkin and C. Akerlof and D. Anbajagane and J. Armstrong and M. Arthurs and Jacob Bringewatt and T. Edberg and C. Hall and M. Lei and R. Raymond and M. Reh and D. Saini and A. Sander and J. Schaefer and D. Seymour and N. Swanson and Y. Wang and W. Lorenzon} } @article {2320, title = {Studying community development: a network analytical approach}, year = {2018}, abstract = {

Research shows that community plays a central role in learning, and strong community engages students and aids in student persistence. Thus, understanding the function and structure of communities in learning environments is essential to education. We use social network analysis to explore the community dynamics of students in a pre-matriculation, two-week summer program. Unlike previous network analysis studies in PER, we build our networks from classroom video that has been coded for student interactions using labeled, directed ties. We define 3 types of interaction: on task interactions (regarding the assigned task), on topic interactions (having to do with science, technology, engineering, and mathematics (STEM)), and off topic interactions (unrelated to the assignment or STEM). To study the development of community in this program, we analyze the shift in conversation topicality over the course of the program. Conversations are more on-task toward the end of the program and we propose that this conversational shift represents a change in student membership within their forming community.\ 

}, url = {https://arxiv.org/abs/1808.08193}, author = {C. A. Hass and Florian Genz and Mary Bridget Kustusch and Pierre-P. A. Ouime and Katarzyna Pomian and Eleanor C. Sayre and Justyna P. Zwolak} } @article {2254, title = {Subsystem Complexity and Holography}, year = {2018}, abstract = {

We study circuit complexity for spatial regions in holographic field theories. We study analogues based on the entanglement wedge of the bulk quantities appearing in the \"complexity = volume\" and \"complexity = action\" conjectures. We calculate these quantities for one exterior region of an eternal static neutral or charged black hole in general dimensions, dual to a thermal state on one boundary with or without chemical potential respectively, as well as for a shock wave geometry. We then define several analogues of circuit complexity for mixed states, and use tensor networks to gain intuition about them. We find a promising qualitative match between the holographic action and what we call the purification complexity, the minimum number of gates required to prepare an arbitrary purification of the given mixed state. On the other hand, the holographic volume does not appear to match any of our definitions of mixed-state complexity.

}, url = {https://arxiv.org/abs/1804.01561}, author = {Cesar A. Ag{\'o}n and Matthew Headrick and Brian Swingle} } @article {2204, title = {Tabletop experiments for quantum gravity: a user{\textquoteright}s manual}, year = {2018}, abstract = {

Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

}, url = {https://arxiv.org/abs/1807.11494}, author = {Daniel Carney and Philip C. E. Stamp and J. M. Taylor} } @article {2270, title = {Tabletop experiments for quantum gravity: a user{\textquoteright}s manual}, year = {2018}, abstract = {

Recent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

}, url = {https://arxiv.org/abs/1807.11494}, author = {Daniel Carney and Philip C. E. Stamp and J. M. Taylor} } @article {2507, title = {Thermal management and non-reciprocal control of phonon flow via optomechanics}, journal = {Nat. Commun.}, volume = {9(1)}, year = {2018}, month = {2018/3/23}, abstract = {

Engineering phonon transport in physical systems is a subject of interest in the study of materials and plays a crucial role in controlling energy and heat transfer. Of particular interest are non-reciprocal phononic systems, which in direct analogy to electric diodes, provide a directional flow of energy. Here, we propose an engineered nanostructured material, in which tunable non-reciprocal phonon transport is achieved through optomechanical coupling. Our scheme relies on breaking time-reversal symmetry by a spatially varying laser drive, which manipulates low-energy acoustic phonons. Furthermore, we take advantage of recent developments in the manipulation of high-energy phonons through controlled scattering mechanisms, such as using alloys and introducing disorder. These combined approaches allow us to design an acoustic isolator and a thermal diode. Our proposed device will have potential impact in phonon-based information processing, and heat management in low temperatures.\ 

}, doi = {https://doi.org/10.1038/s41467-018-03624-y}, url = {https://arxiv.org/abs/1710.08967}, author = {Alireza Seif and Wade DeGottardi and Keivan Esfarjani and Mohammad Hafezi} } @article {2118, title = {Time-reversal of rank-one quantum strategy functions}, journal = {Quantum }, volume = {2}, year = {2018}, month = {2018/01/25}, abstract = {

The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to the set of rank-one positive semidefinite operators on a certain space. This time-reversal property states that the maximum value obtained by such a function over all valid quantum strategies is also obtained when the direction of time for the function is reversed, despite the fact that the strategies themselves are generally not time reversible. An application of this fact is an alternative proof of a known relationship between the conditional min- and max-entropy of bipartite quantum states, along with generalizations of this relationship.

}, doi = {https://doi.org/10.22331/q-2018-10-04-98}, url = {https://arxiv.org/abs/1801.08491}, author = {Yuan Su and John Watrous} } @book {2249, title = {Totally random: why nobody understands quantum mechanics (a serious comic on entanglement)}, year = {2018}, publisher = {Princeton University Press}, organization = {Princeton University Press}, author = {Jeffrey Bub and Tanya Bub} } @article {2220, title = {Toward the first quantum simulation with quantum speedup}, journal = {Proceedings of the National Academy of Sciences}, volume = {115 }, year = {2018}, pages = {9456-9461}, abstract = {

With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.

}, doi = {https://doi.org/10.1073/pnas.1801723115}, url = {https://arxiv.org/abs/1711.10980}, author = {Andrew M. Childs and Dmitri Maslov and Yunseong Nam and Neil J. Ross and Yuan Su} } @article {2463, title = {Two-Dimensional Dilaton Gravity Theory and Lattice Schwarzian Theory}, year = {2018}, abstract = {
We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of non-vanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of non-vanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term R2, where R is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cut-off ε2 under a constant boundary dilaton field and the non-vanishing cosmological constant by identifying the lattice spacing a of a lattice Schwarzian theory with the boundary cut-off ε of the two-dimensional dilaton gravity theory.\ 
}, url = {https://arxiv.org/abs/1802.04599}, author = {Su-Kuan Chu and Chen-Te Ma and Chih-Hung Wu} } @article {2622, title = {Unforgeable Quantum Encryption}, journal = {In: Nielsen J., Rijmen V. (eds) Advances in Cryptology {\textendash} EUROCRYPT 2018. Lecture Notes in Computer Science, Springer, Cham}, volume = {10822}, year = {2018}, abstract = {

We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i) ciphertext unforgeability, (ii) indistinguishability under adaptive chosen-ciphertext attack, and (iii) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies\ \  INT-CTXT , (ii) implies\ \  IND-CCA2 , and (iii) implies\ \  AE . All of our new notions also imply\ \  QIND-CPA\  privacy. Combining one-time authentication and classical pseudorandomness, we construct symmetric-key quantum encryption schemes for each of these new security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.

}, doi = {https://doi.org/10.1007/978-3-319-78372-7_16}, author = {Gorjan Alagic and Tommaso Gagliardoni and Christian Majenz} } @article {2215, title = {Unitary Entanglement Construction in Hierarchical Networks}, year = {2018}, abstract = {

The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

}, url = {https://arxiv.org/abs/1808.07876}, author = {Aniruddha Bapat and Zachary Eldredge and James R. Garrison and Abhinav Desphande and Frederic T. Chong and Alexey V. Gorshkov} } @article {2252, title = {Verified Quantum Information Scrambling}, year = {2018}, abstract = {

Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and more recently has emerged as a powerful tool for characterizing chaos in black holes. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, since scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here, we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous litmus test for scrambling while projecting potential circuit errors into an ancillary observable. We engineer quantum scrambling processes through a tunable 3-qubit unitary operation as part of a 7-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically \∼80\%, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

}, url = {https://arxiv.org/abs/1806.02807}, author = {Kevin A. Landsman and Caroline Figgatt and Thomas Schuster and Norbert M. Linke and Beni Yoshida and Norman Y. Yao and Christopher Monroe} } @article {2619, title = {3-manifold diagrams and NP vs P}, journal = {Quantum Information \& Computation }, volume = {17}, year = {2017}, pages = {125-141 }, abstract = {

The computational complexity class $\#$P captures the di_culty of counting the satisfying assignments to a boolean formula. In this work, we use basic tools from quantum computation to give a proof that the SO(3) Witten-Reshetikhin-Turaev (WRT) invariant of 3-manifolds is $\#$P-hard to calculate. We then apply this result to a question about the combinatorics of Heegaard splittings, motivated by analogous work on link diagrams by M. Freedman. We show that, if $\#$P \⊆ FPNP, then there exist infinitely many Heegaard splittings which cannot be made logarithmically thin by local WRT-preserving moves, except perhaps via a superpolynomial number of steps. We also outline two extensions of the above results. First, adapting a result of Kuperberg, we show that any presentation-independent approximation of WRT is also $\#$P-hard. Second, we sketch out how all of our results can be translated to the setting of triangulations and Turaev-Viro invariants.

}, url = {https://dl.acm.org/doi/abs/10.5555/3179483.3179491}, author = {Gorjan Alagic and C. Lo} } @article {2000, title = {Above threshold scattering about a Feshbach resonance for ultracold atoms in an optical collider}, journal = {Nature Communications}, volume = {8}, year = {2017}, month = {2017/09/06}, abstract = {

Studies of magnetically tunable Feshbach resonances in ultracold atomic gases have predominantly been carried out in the zero collision-energy limit. Here, we explore above threshold collisions at well-defined energies in the vicinity of a narrow magnetic Feshbach resonance by means of a laser-based collider. Our experiment focuses on collisions between ground-state 87Rb atoms in the |F = 2,mF = 0i and |F = 1,mF = 1i hyperfine states, which have a known s-wave resonance at 9.040(7) G at threshold that strongly couples to inelastic channels, where 1 G = 10\−4 T. Using our collider we can track the magnetic field shift in resonance position as the energy is tuned. This presents a challenge due to the narrow width of the resonance in conjunction with inherent broadening mechanisms of the collider. We find, however, that the narrow Feshbach scattering feature becomes imprinted on the spatial distribution of atoms in a fashion that allows for an accurate determination of resonance position as a function of collision energy through a shift in center-of-mass position of the outgoing clouds. This shift has a dispersive line shape with a zero value at the resonance position. We obtain excellent agreement with theory on the resonance position.

}, doi = {10.1038/s41467-017-00458-y}, url = {https://arxiv.org/abs/1704.07109}, author = {Milena S. J. Horvath and Ryan Thomas and Eite Tiesinga and Amita B. Deb and Niels Kj{\ae}rgaard} } @article {2267, title = {Advances in Quantum Reinforcement Learning}, journal = {IEEE SMC, Banff, AB}, year = {2017}, month = {2017}, pages = {282-287}, abstract = {

In recent times, there has been much interest in quantum enhancements of machine learning, specifically in the context of data mining and analysis. Reinforcement learning, an interactive form of learning, is, in turn, vital in artificial intelligence-type applications. Also in this case, quantum mechanics was shown to be useful, in certain instances. Here, we elucidate these results, and show that quantum enhancements can be achieved in a new setting: the setting of learning models which learn how to improve themselves -- that is, those that meta-learn. While not all learning models meta-learn, all non-trivial models have the potential of being \"lifted\", enhanced, to meta-learning models. Our results show that also such models can be quantum-enhanced to make even better learners. In parallel, we address one of the bottlenecks of current quantum reinforcement learning approaches: the need for so-called oracularized variants of task environments. Here we elaborate on a method which realizes these variants, with minimal changes in the setting, and with no corruption of the operative specification of the environments. This result may be important in near-term experimental demonstrations of quantum reinforcement learning.

}, doi = {https://doi.org/10.1109/SMC.2017.8122616}, url = {https://arxiv.org/abs/1811.08676}, author = {Vedran Dunjko and J. M. Taylor and Hans J. Briegel} } @article {1732, title = {Basic circuit compilation techniques for an ion-trap quantum machine}, journal = {New Journal of Physics}, volume = {19}, year = {2017}, month = {2016/02/20}, pages = {023035}, abstract = {

We study the problem of compilation of quantum algorithms into optimized physical-level circuits executable in a quantum information processing (QIP) experiment based on trapped atomic ions. We report a complete strategy: starting with an algorithm in the form of a quantum computer program, we compile it into a high-level logical circuit that goes through multiple stages of decomposition into progressively lower-level circuits until we reach the physical execution-level specification. We skip the fault-tolerance layer, as it is not necessary in this work. The different stages are structured so as to best assist with the overall optimization while taking into account numerous optimization criteria, including minimizing the number of expensive two-qubit gates, minimizing the number of less expensive single-qubit gates, optimizing the runtime, minimizing the overall circuit error, and optimizing classical control sequences. Our approach allows a trade-off between circuit runtime and quantum error, as well as to accommodate future changes in the optimization criteria that may likely arise as a result of the anticipated improvements in the physical-level control of the experiment.

}, doi = {10.1088/1367-2630/aa5e47}, url = {http://iopscience.iop.org/article/10.1088/1367-2630/aa5e47/meta;jsessionid=55CC235A0B106081E825099310586F07.c3.iopscience.cld.iop.org}, author = {Dmitri Maslov} } @article {1971, title = {Complete 3-Qubit Grover Search on a Programmable Quantum Computer}, journal = {Nature Communications, accepted}, year = {2017}, month = {2017/03/30}, abstract = {

Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state-marking scheme required to perform a classical search. All quantum solutions are shown to outperform their classical counterparts. We also report the first implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5\% and 89.6\%, respectively.

}, url = {https://arxiv.org/abs/1703.10535}, author = {C. Figgatt and Dmitri Maslov and K. A. Landsman and N. M. Linke and S. Debnath and Christopher Monroe} } @article {1952, title = {Complexity of sampling as an order parameter}, year = {2017}, month = {2017/03/15}, abstract = {

We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time\ t. We obtain upper and lower bounds on the scaling of\ twith the number of bosons,\ n, for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian and conjecture a link to dynamical phase transitions. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter systems.

}, url = {https://arxiv.org/abs/1703.05332}, author = {Abhinav Deshpande and Bill Fefferman and Michael Foss-Feig and Alexey V. Gorshkov} } @article {2056, title = {Computational Notions of Quantum Min-Entropy}, year = {2017}, month = {2017/09/09}, abstract = {

We initiate the study of computational entropy in the quantum setting. We investigate to what extent the classical notions of computational entropy generalize to the quantum setting, and whether quantum analogues of classical theorems hold. Our main results are as follows. (1) The classical Leakage Chain Rule for pseudoentropy can be extended to the case that the leakage information is quantum (while the source remains classical). Specifically, if the source has pseudoentropy at least k, then it has pseudoentropy at least k \− l conditioned on an l- qubit leakage. (2) As an application of the Leakage Chain Rule, we construct the first quantum leakage-resilient stream-cipher in the bounded-quantum-storage model, assuming the existence of a quantum-secure pseudorandom generator. (3) We show that the general form of the classical Dense Model Theorem (interpreted as the equivalence between two definitions of pseudo-relativemin-entropy) does not extend to quantum states. Along the way, we develop quantum analogues of some classical techniques (e.g., the Leakage Simulation Lemma, which is proven by a Nonuniform Min-Max Theorem or Boosting). On the other hand, we also identify some classical techniques (e.g., Gap Amplification) that do not work in the quantum setting. Moreover, we introduce a variety of notions that combine quantum information and quantum complexity, and this raises several directions for future work.

}, url = {https://arxiv.org/abs/1704.07309}, author = {Yi-Hsiu Chen and Kai-Min Chung and Ching-Yi Lai and Salil P. Vadhan and Xiaodi Wu} } @article {1820, title = {Cooling a harmonic oscillator by optomechanical modification of its bath}, journal = {Physical Review Letters}, volume = {118}, year = {2017}, month = {2017/05/31}, pages = {223602}, abstract = {

Optomechanical systems show tremendous promise for high sensitivity sensing of forces and modification of mechanical properties via light. For example, similar to neutral atoms and trapped ions, laser cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an approach for simultaneously reducing the thermal load on a mechanical resonator while improving its quality factor. In essence, we use the optical interaction to dynamically modify the dominant damping mechanism, providing an optomechanically-induced effect analogous to a phononic band gap. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme.

}, doi = {doi.org/10.1103/PhysRevLett.118.223602}, url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.223602}, author = {Xunnong Xu and Thomas Purdy and J. M. Taylor} } @article {1814, title = {Correlated Photon Dynamics in Dissipative Rydberg Media}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/07/26}, pages = {043602}, abstract = {

Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of non-perturbative dissipative interactions relevant to current experiments. Our model is in good agreement with experimental data. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.

}, doi = {10.1103/PhysRevLett.119.043602}, url = {https://arxiv.org/abs/1608.06068}, author = {Emil Zeuthen and Michael Gullans and Mohammad F. Maghrebi and Alexey V. Gorshkov} } @article {2305, title = {Development of a new UHV/XHV pressure standard (cold atom vacuum standard)}, journal = {Metrologia}, volume = {54}, year = {2017}, month = {2017/11/3}, abstract = {

The National Institute of Standards and Technology has recently begun a program to develop a primary pressure standard that is based on ultra-cold atoms, covering a pressure range of 1 x 10-6 to 1 x 10-10 Pa and possibly lower. These pressures correspond to the entire ultra-high vacuum range and extend into the extreme-high vacuum. This cold-atom vacuum standard (CAVS) is both a primary standard and absolute sensor of vacuum. The CAVS is based on the loss of cold, sensor atoms (such as the alkali-metal lithium) from a magnetic trap due to collisions with the background gas (primarily H2) in the vacuum. The pressure is determined from a thermally-averaged collision cross section, which is a fundamental atomic property, and the measured loss rate. The CAVS is primary because it will use collision cross sections determined from ab initio calculations for the Li + H2 system. Primary traceability is transferred to other systems of interest using sensitivity coefficients.

}, doi = {https://doi.org/10.1088/1681-7575/aa8a7b}, url = {https://arxiv.org/abs/1801.10120}, author = {Julia Scherschligt and James A Fedchak and Daniel S Barker and Stephen Eckel and Nikolai Klimov and Constantinos Makrides and Eite Tiesinga} } @article {2062, title = {Disorder induced transitions in resonantly driven Floquet Topological Insulators}, journal = {Physical Review B}, volume = {96}, year = {2017}, month = {2017/08/16}, pages = {054207}, abstract = {

We investigate the effects of disorder in Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are induced by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a mobility gap at the resonant quasi-energy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator. Interestingly, the effects of disorder are not necessarily adverse: we show that in the same quantum well, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). We identify the conditions on the driving field necessary for observing such a transition.

}, doi = {10.1103/PhysRevB.96.054207}, url = {https://arxiv.org/abs/1702.02956}, author = {Paraj Titum and Netanel H. Lindner and Gil Refael} } @article {1959, title = {Dispersive optical detection of magnetic Feshbach resonances in ultracold gases}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/08/18}, pages = {022705}, abstract = {

Magnetically tunable Feshbach resonances in ultracold atomic systems are chiefly identified and characterized through time consuming atom loss spectroscopy. We describe an off-resonant dispersive optical probing technique to rapidly locate Feshbach resonances and demonstrate the method by locating four resonances of\ 87Rb, between the\ |F=1,mF=1\⟩\ and\ |F=2,mF=0\⟩\ states. Despite the loss features being\ 100\ mG wide, we require only 21 experimental runs to explore a magnetic field range \>18 G. The resonances consist of two known s-wave features in the vicinity of 9 G and 18 G and two previously unobserved p-wave features near 5 G and 10 G. We further utilize the dispersive approach to directly characterize the two-body loss dynamics for each Feshbach resonance.

}, doi = {10.1103/PhysRevA.96.022705}, url = {https://arxiv.org/abs/1702.02216}, author = {Bianca J. Sawyer and Milena S. J. Horvath and Eite Tiesinga and Amita B. Deb and Niels Kj{\ae}rgaard} } @article {1985, title = {Domination with decay in triangular matchstick arrangement graphs}, journal = {Involve, a Journal of Mathematics}, volume = {10}, year = {2017}, month = {2017/05/14}, pages = {749 - 766}, abstract = {

We provide results for the exponential dominating numbers and total exponential dominating numbers of a family of triangular grid graphs. We then prove inequalities for these numbers and compare them with inequalities that hold more generally for exponential dominating numbers of graphs.

}, issn = {1944-4176}, doi = {10.2140/involve10.2140/involve.2017.10-510.2140/involve.2017.10.749}, url = {http://msp.org/involve/http://msp.org/involve/2017/10-5/index.xhtmlhttp://msp.org/involve/2017/10-5/p03.xhtmlhttp://msp.org/involve/2017/10-5/involve-v10-n5-p03-s.pdf}, author = {Jill Cochran and Terry Henderson and Aaron Ostrander and Ron Taylor} } @article {1913, title = {Dynamically induced robust phonon transport and chiral cooling in an optomechanical system}, journal = {Nature Communications}, volume = {8}, year = {2017}, month = {2017/06/19}, pages = {205}, abstract = {

The transport of sound and heat, in the form of phonons, has a fundamental material limit: disorder-induced scattering. In electronic and optical settings, introduction of chiral transport - in which carrier propagation exhibits broken parity symmetry - provides robustness against such disorder by preventing elastic backscattering. Here we experimentally demonstrate a path for achieving robust phonon transport even in the presence of material disorder, by dynamically inducing chirality through traveling-wave optomechanical coupling. Using this approach, we demonstrate dramatic optically-induced chiral transport for clockwise and counterclockwise phonons in a symmetric resonator. This induced chirality also enhances isolation from the thermal bath and leads to gain-free reduction of the intrinsic damping of the phonons. Surprisingly, this passive mechanism is also accompanied by a chiral reduction in heat load leading to a novel optical cooling of the mechanics. This technique has the potential to improve upon the fundamental thermal limits of resonant mechanical sensor, which cannot be otherwise attained through conventional optomechanical cooling.

}, doi = {10.1038/s41467-017-00247-7}, url = {https://arxiv.org/abs/1609.08674}, author = {Seunghwi Kim and Xunnong Xu and J. M. Taylor and Gaurav Bahl} } @article {2001, title = {{E}ntanglement area laws for long-range interacting systems}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/07/31}, pages = {050501}, abstract = {

We prove that the entanglement entropy of any state evolved under an arbitrary 1/rα long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any α \> D + 1. We also prove that for any α \> 2D + 2, the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.

}, doi = {10.1103/PhysRevLett.119.050501}, url = {https://arxiv.org/abs/1702.05368}, author = {Zhe-Xuan Gong and Michael Foss-Feig and Fernando G. S. L. Brand{\~a}o and Alexey V. Gorshkov} } @article {2021, title = {Efficient quantum algorithms for analyzing large sparse electrical networks}, journal = {Quantum Information \& Computation}, volume = {17}, year = {2017}, month = {2017/07/21}, pages = {987-1026}, abstract = {

Analyzing large sparse electrical networks is a fundamental task in physics, electrical engineering and computer science. We propose two classes of quantum algorithms for this task. The first class is based on solving linear systems, and the second class is based on using quantum walks. These algorithms compute various electrical quantities, including voltages, currents, dissipated powers and effective resistances, in time poly(d, c,log(N),1/λ,1/ε), where N is the number of vertices in the network, d is the maximum unweighted degree of the vertices, c is the ratio of largest to smallest edge resistance, λ is the spectral gap of the normalized Laplacian of the network, and ε is the accuracy. Furthermore, we show that the polynomial dependence on 1/λ is necessary. This implies that our algorithms are optimal up to polynomial factors and cannot be signficantly improved.

}, url = {https://arxiv.org/abs/1311.1851}, author = {Guoming Wang} } @article {1902, title = {Efficient simulation of sparse Markovian quantum dynamics}, journal = {Quantum Information and Computation}, volume = {17}, year = {2017}, month = {2017/09/01}, pages = {901-947}, abstract = {

Quantum algorithms for simulating Hamiltonian dynamics have been extensively developed, but there has been much less work on quantum algorithms for simulating the dynamics of open quantum systems. We give the first efficient quantum algorithms for simulating Markovian quantum dynamics generated by Lindbladians that are not necessarily local. We introduce two approaches to simulating sparse Lindbladians. First, we show how to simulate Lindbladians that act within small invariant subspaces using a quantum algorithm to implement sparse Stinespring isometries. Second, we develop a method for simulating sparse Lindblad operators by concatenating a sequence of short-time evolutions. We also show limitations on Lindbladian simulation by proving a no-fast-forwarding theorem for simulating sparse Lindbladians in a black-box model.

}, doi = {10.26421/QIC17.11-12}, url = {https://arxiv.org/abs/1611.05543}, author = {Andrew M. Childs and Tongyang Li} } @article {2059, title = {Efimov States of Strongly Interacting Photons}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/12/04}, pages = {233601}, abstract = {

We demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that in suitably rescaled coordinates the effective interactions become dominated by s-wave scattering near threshold and, as a result, give rise to an Efimov effect near unitarity, but with spatially anisotropic wavefunctions in the original coordinates. We show that the three-body loss of these Efimov trimers can be strongly suppressed and determine conditions under which these states are observable in current experiments. These effects can be naturally extended to probe few-body universality beyond three bodies, as well as the role of Efimov physics in the non-equilbrium, many-body regime.

}, doi = {10.1103/PhysRevLett.119.233601}, url = {https://arxiv.org/abs/1709.01955}, author = {Michael Gullans and S. Diehl and S. T. Rittenhouse and B. P. Ruzic and J. P. D{\textquoteright}Incao and P. Julienne and Alexey V. Gorshkov and J. M. Taylor} } @article {2051, title = {An Elementary Proof of Private Random Number Generation from Bell Inequalities}, year = {2017}, month = {2017/07/20}, abstract = {

The field of device-independent quantum cryptography has seen enormous success in the past several years, including security proofs for key distribution and random number generation that account for arbitrary imperfections in the devices used. Full security proofs in the field so far are long and technically deep. In this paper we show that the concept of the mirror adversary can be used to simplify device-independent proofs. We give a short proof that any bipartite Bell violation can be used to generate private random numbers. The proof is based on elementary techniques and is self-contained.

}, url = {https://arxiv.org/abs/1707.06597}, author = {Carl Miller} } @article {1906, title = {Emergent equilibrium in many-body optical bistability}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/04/17}, pages = {043826}, abstract = {

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.

}, doi = {doi.org/10.1103/PhysRevA.95.043826}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.043826}, author = {Michael Foss-Feig and Pradeep Niroula and Jeremy T. Young and Mohammad Hafezi and Alexey V. Gorshkov and Ryan M. Wilson and Mohammad F. Maghrebi} } @article {2301, title = {Entanglement Wedge Reconstruction via Universal Recovery Channels}, year = {2017}, abstract = {

We apply and extend the theory of universal recovery channels from quantum information theory to address the problem of entanglement wedge reconstruction in AdS/CFT. It has recently been proposed that any low-energy local bulk operators in a CFT boundary region\&$\#$39;s entanglement wedge can be reconstructed on that boundary region itself. Existing work arguing for this proposal relies on algebraic consequences of the exact equivalence between bulk and boundary relative entropies, namely the theory of operator algebra quantum error correction. However, bulk and boundary relative entropies are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. The framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture in addition to new physical insights. Most notably, we find that a bulk operator acting in a given boundary region\&$\#$39;s entanglement wedge can be expressed as the response of the boundary region\&$\#$39;s modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes\&$\#$39; rule that attempts to undo the noise induced by restricting to only a portion of the boundary, and has an integral representation in terms of modular flows. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra

}, url = {https://arxiv.org/abs/1704.05839}, author = {Jordan Cotler and Patrick Hayden and Geoffrey Penington and Grant Salton and Brian Swingle and Michael Walter} } @article {1921, title = {Exact sampling hardness of Ising spin models}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/09/14}, pages = {032324}, abstract = {

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of\ exact\ classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in\ Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl\–Leibniz-Zentrum f{\"u}r Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

}, doi = {10.1103/PhysRevA.96.032324}, url = {https://arxiv.org/abs/1701.03167}, author = {Bill Fefferman and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1780, title = {Exactly soluble model of boundary degeneracy}, journal = {Physical Review B}, volume = {95}, year = {2017}, month = {2017/01/25}, chapter = {045309}, abstract = {

We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as \"boundary degeneracy\") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.

}, doi = {10.1103/PhysRevB.95.045309}, url = {http://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.045309}, author = {Sriram Ganeshan and Alexey V. Gorshkov and Victor Gurarie and Victor M. Galitski} } @proceedings {1935, title = {Experimental Comparison of Two Quantum Computing Architectures}, volume = {114}, year = {2017}, month = {2017/03/21}, pages = {3305-3310}, edition = {13}, abstract = {

We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device [1] with limited connectivity, and the other is a fully connected trapped-ion system [2]. Even though the two systems have different native quantum interactions, both can be programmed in a way that is blind to the underlying hardware, thus allowing the first comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that employ more connectivity clearly benefit from a better connected system of qubits. While the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that co-designing particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.

}, doi = {10.1073/pnas.1618020114}, url = {http://www.pnas.org/content/114/13/3305}, author = {N.M. Linke and Dmitri Maslov and Martin Roetteler and S. Debnath and C. Figgatt and K. A. Landsman and K. Wright and Christopher Monroe} } @article {1944, title = {Experimental demonstration of cheap and accurate phase estimation}, journal = {Physical Review Letters}, volume = {118}, year = {2017}, month = {2017/05/12}, pages = {190502}, abstract = {

We demonstrate experimental implementation of robust phase estimation (RPE) to learn the phases of X and Y rotations on a trapped Yb+ ion qubit. We estimate these phases with uncertainties less than 4 \· 10\−4 radians using as few as 176 total experimental samples per phase, and our estimates exhibit Heisenberg scaling. Unlike standard phase estimation protocols, RPE neither assumes perfect state preparation and measurement, nor requires access to ancillae. We cross-validate the results of RPE with the more resource-intensive protocol of gate set tomography.

}, doi = {doi.org/10.1103/PhysRevLett.118.190502}, url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.190502}, author = {Kenneth Rudinger and Shelby Kimmel and Daniel Lobser and Peter Maunz} } @article {2130, title = {Experimental Study of Optimal Measurements for Quantum State Tomography}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/10/13}, pages = {150401}, abstract = {

Quantum tomography is a critically important tool to evaluate quantum hardware, making it essential to develop optimized measurement strategies that are both accurate and efficient. We compare a variety of strategies using nearly pure test states. Those that are informationally complete for all states are found to be accurate and reliable even in the presence of errors in the measurements themselves, while those designed to be complete only for pure states are far more efficient but highly sensitive to such errors. Our results highlight the unavoidable trade-offs inherent in quantum tomography.

}, doi = {10.1103/PhysRevLett.119.150401}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.150401}, author = {Sosa-Martinez, H. and Lysne, N. K. and Baldwin, C. H. and Kalev, A. and Deutsch, I. H. and Jessen, P. S.} } @article {1945, title = {Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling}, year = {2017}, month = {2017/02/16}, abstract = {

Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.

}, url = {https://arxiv.org/abs/1702.05178$\#$}, author = {Peter Bierhorst and Emanuel Knill and Scott Glancy and Alan Mink and Stephen P. Jordan and Andrea Rommal and Yi-Kai Liu and Bradley Christensen and Sae Woo Nam and Lynden K. Shalm} } @article {2201, title = {Exponential improvements for quantum-accessible reinforcement learning}, year = {2017}, abstract = {

Quantum computers can offer dramatic improvements over classical devices for data analysis tasks such as prediction and classification. However, less is known about the advantages that quantum computers may bring in the setting of reinforcement learning, where learning is achieved via interaction with a task environment. Here, we consider a special case of reinforcement learning, where the task environment allows quantum access. In addition, we impose certain \"naturalness\" conditions on the task environment, which rule out the kinds of oracle problems that are studied in quantum query complexity (and for which quantum speedups are well-known). Within this framework of quantum-accessible reinforcement learning environments, we demonstrate that quantum agents can achieve exponential improvements in learning efficiency, surpassing previous results that showed only quadratic improvements. A key step in the proof is to construct task environments that encode well-known oracle problems, such as Simon\&$\#$39;s problem and Recursive Fourier Sampling, while satisfying the above \"naturalness\" conditions for reinforcement learning. Our results suggest that quantum agents may perform well in certain game-playing scenarios, where the game has recursive structure, and the agent can learn by playing against itself

}, url = {https://arxiv.org/abs/1710.11160}, author = {Vedran Dunjko and Yi-Kai Liu and Xingyao Wu and J. M. Taylor} } @article {2106, title = {Exponential Quantum Speed-ups for Semidefinite Programming with Applications to Quantum Learning}, year = {2017}, month = {2017/10/06}, abstract = {

We give semidefinite program (SDP) quantum solvers with an exponential speed-up over classical ones. Specifically, we consider SDP instances with m constraint matrices of dimension n, each of rank at most r, and assume that the input matrices of the SDP are given as quantum states (after a suitable normalization). Then we show there is a quantum algorithm that solves the SDP feasibility problem with accuracy ǫ by using \√ m log m \· poly(log n,r, ǫ \−1 ) quantum gates. The dependence on n provides an exponential improvement over the work of Brand \˜ao and Svore [6] and the work of van Apeldoorn et al. [23], and demonstrates an exponential quantum speed-up when m and r are small. We apply the SDP solver to the problem of learning a good description of a quantum state with respect to a set of measurements: Given m measurements and a supply of copies of an unknown state ρ, we show we can find in time \√ m log m \· poly(log n,r, ǫ \−1 ) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as ρ on the m measurements up to error ǫ. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes\’ principle. As in previous work, we obtain our algorithm by \“quantizing\” classical SDP solvers based on the matrix multiplicative weight update method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians with a poly-logarithmic dependence on its dimension based on the techniques developed in quantum principal component analysis, which could be of independent interest. Our quantum SDP solver is different from previous ones in the following two aspects: (1) it follows from a zero-sum game approach of Hazan [11] of solving SDPs rather than the primal-dual approach by Arora and Kale [5]; and (2) it does not rely on any sparsity assumption of the input matrices.

}, url = {https://arxiv.org/abs/1710.02581}, author = {Fernando G. S. L. Brand{\~a}o and Amir Kalev and Tongyang Li and Cedric Yen-Yu Lin and Krysta M. Svore and Xiaodi Wu} } @article {1986, title = {Extracting entanglement geometry from quantum states}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/10/06}, abstract = {

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network - and hence the geometry - is largely fixed a priori by the choice of tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of non-interacting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.

}, doi = {10.1103/PhysRevLett.119.140502}, url = {https://arxiv.org/abs/1704.01974}, author = {Katharine Hyatt and James R. Garrison and Bela Bauer} } @article {2009, title = {Extreme learning machines for regression based on V-matrix method}, journal = {Cognitive Neurodynamics}, year = {2017}, month = {2017/06/10}, abstract = {

This paper studies the joint effect of V-matrix, a recently proposed framework for statistical inferences, and extreme learning machine (ELM) on regression problems. First of all, a novel algorithm is proposed to efficiently evaluate the V-matrix. Secondly, a novel weighted ELM algorithm called V-ELM is proposed based on the explicit kernel mapping of ELM and the V-matrix method. Though V-matrix method could capture the geometrical structure of training data, it tends to assign a higher weight to instance with smaller input value. In order to avoid this bias, a novel method called VI-ELM is proposed by minimizing both the regression error and the V-matrix weighted error simultaneously. Finally, experiment results on 12 real world benchmark datasets show the effectiveness of our proposed methods.

}, issn = {1871-4099}, doi = {10.1007/s11571-017-9444-2}, url = {http://dx.doi.org/10.1007/s11571-017-9444-2}, author = {Yang, Zhiyong and Zhang, Taohong and Lu, Jingcheng and Yuan Su and Zhang, Dezheng and Duan, Yaowu} } @article {1991, title = {Fast optimization algorithms and the cosmological constant}, journal = {Physical Review D}, volume = {96}, year = {2017}, month = {2017/11/13}, pages = {103512}, abstract = {

Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of an NP-hard problem. The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10\−120 in a randomly generated 109 -dimensional ADK landscape.

}, doi = {10.1103/PhysRevD.96.103512}, url = {https://arxiv.org/abs/1706.08503}, author = {Ning Bao and Raphael Bousso and Stephen P. Jordan and Brad Lackey} } @article {1948, title = {Fast quantum computation at arbitrarily low energy}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/03/06}, pages = {032305}, abstract = {

One version of the energy-time uncertainty principle states that the minimum time\ T\⊥\ for a quantum system to evolve from a given state to any orthogonal state is\ h/(4ΔE), where\ ΔE\ is the energy uncertainty. A related bound called the Margolus-Levitin theorem states that\ T\⊥\≥h/(2\⟨E\⟩), where\ \⟨E\⟩\ is the expectation value of energy and the ground energy is taken to be zero. Many subsequent works have interpreted\ T\⊥\ as defining a minimal time for an elementary computational operation and correspondingly a fundamental limit on clock speed determined by a system\&$\#$39;s energy. Here we present local time-independent Hamiltonians in which computational clock speed becomes arbitrarily large relative to\ \⟨E\⟩\ and\ ΔE\ as the number of computational steps goes to infinity. We argue that energy considerations alone are not sufficient to obtain an upper bound on computational speed, and that additional physical assumptions such as limits to information density and information transmission speed are necessary to obtain such a bound.

}, doi = {10.1103/PhysRevA.95.032305}, url = {http://link.aps.org/doi/10.1103/PhysRevA.95.032305}, author = {Stephen P. Jordan} } @article {1908, title = {Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/10/25}, pages = {170503}, abstract = {

In short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speed-up possible is an open question. In this paper, we present a protocol capable of transferring a quantum state across a distance\ L\ in\ d\ dimensions using long-range interactions with strength bounded by\ 1/rα. If\ α\<d, the state transfer time is asymptotically independent of\ L; if\ α=d, the time is logarithmic in distance\ L; if\ d\<α\<d+1, transfer occurs in time proportional to\ Lα\−d; and if\ α\≥d+1, it occurs in time proportional to\ L. We then use this protocol to upper bound the time required to create a state specified by a MERA (multiscale entanglement renormalization ansatz) tensor network, and show that, if the linear size of the MERA state is\ L, then it can be created in time that scales with\ L\ identically to state transfer up to multiplicative logarithmic corrections.

}, doi = {10.1103/PhysRevLett.119.170503}, url = {https://arxiv.org/abs/1612.02442}, author = {Zachary Eldredge and Zhe-Xuan Gong and Ali Hamed Moosavian and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1990, title = {Genuine N -partite entanglement without N -partite correlation functions}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/06/26}, pages = {062331}, abstract = {

A genuinely\ N-partite entangled state may display vanishing\ N-partite correlations measured for arbitrary local observables. In such states the genuine entanglement is noticeable solely in correlations between subsets of particles. A straightforward way to obtain such states for odd\ N\ is to design an \“antistate\” in which all correlations between an odd number of observers are exactly opposite. Evenly mixing a state with its antistate then produces a mixed state with no\ N-partite correlations, with many of them genuinely multiparty entangled. Intriguingly, all known examples of \“entanglement without correlations\” involve an\ odd\ number of particles. Here we further develop the idea of antistates, thereby shedding light on the different properties of even and odd particle systems. We conjecture that there is no antistate to any pure even-N-party entangled state making the simple construction scheme unfeasible. However, as we prove by construction, higher-rank examples of entanglement without correlations for arbitrary even\ N\ indeed exist. These classes of states exhibit genuine entanglement and even violate an\ N-partite Bell inequality, clearly demonstrating the nonclassical features of these states as well as showing their applicability for quantum information processing.

}, doi = {doi.org/10.1103/PhysRevA.95.062331}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.062331}, author = {Minh C. Tran and Margherita Zuppardo and Anna de Rosier and Lukas Knips and Wieslaw Laskowski and Tomasz Paterek and Harald Weinfurter} } @article {1812, title = {Hamiltonian Simulation with Optimal Sample Complexity}, journal = {npj Quantum Information}, volume = {13}, year = {2017}, month = {2017/03/31}, abstract = {
We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd, Mohseni, and Rebentrost [Nat. Phys., 10(9):631--633, 2014] is optimal for this task. We further extend their method to the case of multiple input states, showing how to simulate any Hermitian polynomial of the states provided. As applications, we derive optimal algorithms for commutator simulation and orthogonality testing, and we give a protocol for creating a coherent superposition of pure states, when given sample access to those states. We also show that this sample-based Hamiltonian simulation can be used as the basis of a universal model of quantum computation that requires only partial swap operations and simple single-qubit states.
}, doi = {10.1038/s41534-017-0013-7}, url = {https://www.nature.com/articles/s41534-017-0013-7}, author = {Shelby Kimmel and Cedric Yen-Yu Lin and Guang Hao Low and Maris Ozols and Theodore J. Yoder} } @article {1955, title = {High-Order Multipole Radiation from Quantum Hall States in Dirac Materials}, journal = {Physical Review B}, volume = {95}, year = {2017}, month = {2017/06/30}, pages = {235439}, abstract = {

Topological states can exhibit electronic coherence on macroscopic length scales. When the coherence length exceeds the wavelength of light, one can expect new phenomena to occur in the optical response of these states. We theoretically characterize this limit for integer quantum Hall states in two-dimensional Dirac materials. We find that the radiation from the bulk is dominated by dipole emission, whose spectral properties vary with the local disorder potential. On the other hand, the radiation from the edge is characterized by large multipole moments in the far-field associated with the efficient transfer of angular momentum from the electrons into the scattered light. These results demonstrate that high-order multipole transitions are a necessary component for the optical spectroscopy and control of quantum Hall and related topological states in electronic systems.

}, doi = {10.1103/PhysRevB.95.235439}, url = {https://arxiv.org/abs/1701.03464}, author = {Michael Gullans and J. M. Taylor and Atac Imamoglu and Pouyan Ghaemi and Mohammad Hafezi} } @article {2149, title = {Input-output theory for spin-photon coupling in Si double quantum dots}, journal = {Physical Review B}, volume = {96}, year = {2017}, month = {2017/12/22}, pages = {235434}, abstract = {

The interaction of qubits via microwave frequency photons enables long-distance qubit-qubit coupling and facilitates the realization of a large-scale quantum processor. However, qubits based on electron spins in semiconductor quantum dots have proven challenging to couple to microwave photons. In this theoretical work we show that a sizable coupling for a single electron spin is possible via spin-charge hybridization using a magnetic field gradient in a silicon double quantum dot. Based on parameters already shown in recent experiments, we predict optimal working points to achieve a coherent spin-photon coupling, an essential ingredient for the generation of long-range entanglement. Furthermore, we employ input-output theory to identify observable signatures of spin-photon coupling in the cavity output field, which may provide guidance to the experimental search for strong coupling in such spin-photon systems and opens the way to cavity-based readout of the spin qubit.

}, doi = {10.1103/PhysRevB.96.235434}, url = {https://link.aps.org/doi/10.1103/PhysRevB.96.235434}, author = {Benito, M. and Mi, X. and J. M. Taylor and Petta, J. R. and Burkard, Guido} } @article {2277, title = {Lieb-Robinson bounds on n-partite connected correlation functions}, journal = {Phys. Rev. A 96, 052334}, year = {2017}, abstract = {

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

}, doi = {https://doi.org/10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1987, title = {Lieb-Robinson bounds on n-partite connected correlations}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/11/27}, abstract = {

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an\ n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an\ n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

}, doi = {10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {2061, title = {Light-induced fractional quantum Hall phases in graphene}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/12/15}, pages = {247403}, abstract = {

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν = 1/2 and ν = 2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

}, doi = {10.1103/PhysRevLett.119.247403}, url = {https://arxiv.org/abs/1612.08748}, author = {Areg Ghazaryan and Tobias Gra{\ss} and Michael Gullans and Pouyan Ghaemi and Mohammad Hafezi} } @article {2103, title = {Machine Learning techniques for state recognition and auto-tuning in quantum dots}, year = {2017}, month = {2017/12/13}, abstract = {

Recent progress in building large-scale quantum devices for exploring quantum computing and simulation paradigms has relied upon effective tools for achieving and maintaining good experimental parameters, i.e. tuning up devices. In many cases, including in quantum-dot based architectures, the parameter space grows substantially with the number of qubits, and may become a limit to scalability. Fortunately, machine learning techniques for pattern recognition and image classification using so-called deep neural networks have shown surprising successes for computer-aided understanding of complex systems. In this work, we use deep and convolutional neural networks to characterize states and charge configurations of semiconductor quantum dot arrays when one can only measure a current-voltage characteristic of transport (here conductance) through such a device. For simplicity, we model a semiconductor nanowire connected to leads and capacitively coupled to depletion gates using the Thomas-Fermi approximation and Coulomb blockade physics. We then generate labeled training data for the neural networks, and find at least 90 \% accuracy for charge and state identification for single and double dots purely from the dependence of the nanowire\’s conductance upon gate voltages. Using these characterization networks, we can then optimize the parameter space to achieve a desired configuration of the array, a technique we call \‘auto-tuning\’. Finally, we show how such techniques can be implemented in an experimental setting by applying our approach to an experimental data set, and outline further problems in this domain, from using charge sensing data to extensions to full one and two-dimensional arrays, that can be tackled with machine learning.

}, url = {https://arxiv.org/abs/1712.04914}, author = {Sandesh S. Kalantre and Justyna P. Zwolak and Stephen Ragole and Xingyao Wu and Neil M. Zimmerman and M. D. Stewart and J. M. Taylor} } @article {1392, title = {Modulus of continuity eigenvalue bounds for homogeneous graphs and convex subgraphs with applications to quantum Hamiltonians}, journal = {Journal of Mathematical Analysis and Applications}, volume = {452}, year = {2017}, month = {2017/03/03}, pages = {1269-1290}, abstract = {

We adapt modulus of continuity estimates to the study of spectra of combinatorial graph Laplacians, as well as the Dirichlet spectra of certain weighted Laplacians. The latter case is equivalent to stoquastic Hamiltonians and is of current interest in both condensed matter physics and quantum computing. In particular, we introduce a new technique which bounds the spectral gap of such Laplacians (Hamiltonians) by studying the limiting behavior of the oscillations of their eigenvectors when introduced into the heat equation. Our approach is based on recent advances in the PDE literature, which include a proof of the fundamental gap theorem by Andrews and Clutterbuck.

}, doi = {10.1016/j.jmaa.2017.03.030}, url = {http://www.sciencedirect.com/science/article/pii/S0022247X1730272X}, author = {Michael Jarret and Stephen P. Jordan} } @article {1835, title = {Multicritical behavior in dissipative {I}sing models}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/04/26}, pages = {042133}, abstract = {

We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.

}, doi = {doi.org/10.1103/PhysRevA.95.042133}, url = {https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.042133}, author = {Vincent R. Overbeck and Mohammad F. Maghrebi and Alexey V. Gorshkov and Hendrik Weimer} } @article {2049, title = {Nonlocal games, synchronous correlations, and Bell inequalities}, year = {2017}, month = {2017/09/21}, abstract = {

A nonlocal game with a synchronous correlation is a natural generalization of a function between two finite sets, and has recently appeared in the context of quantum graph homomorphisms. In this work we examine analogues of Bell\&$\#$39;s inequalities for synchronous correlations. We show that, unlike general correlations and the CHSH inequality, there can be no quantum Bell violation among synchronous correlations with two measurement settings. However we exhibit explicit analogues of Bell\&$\#$39;s inequalities for synchronous correlations with three measurement settings and two outputs, provide an analogue of Tsirl\&$\#$39;son\&$\#$39;s bound in this setting, and give explicit quantum correlations that saturate this bound.

}, url = {https://arxiv.org/abs/1707.06200}, author = {Brad Lackey and Nishant Rodrigues} } @article {2053, title = {Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator}, journal = {Nature}, volume = {551}, year = {2017}, month = {2017/11/29}, pages = {601-604}, abstract = {

A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical mechanics does not apply. The qubits are represented by trapped ion spins that can be prepared in a variety of initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with near 99\% efficiency. This allows the single-shot measurement of arbitrary many-body correlations for the direct probing of the dynamical phase transition and the uncovering of computationally intractable features that rely on the long-range interactions and high connectivity between the qubits.

}, doi = {10.1038/nature24654}, url = {https://www.nature.com/articles/nature24654}, author = {J. Zhang and G. Pagano and P. W. Hess and A. Kyprianidis and P. Becker and H. Kaplan and Alexey V. Gorshkov and Z. -X. Gong and C. Monroe} } @article {1965, title = {Optimal length of decomposition sequences composed of imperfect gates}, journal = {Quantum Information Processing}, volume = {16}, year = {2017}, month = {2017/03/24}, pages = {123}, abstract = {

Quantum error correcting circuitry is both a resource for correcting errors and a source for generating errors. A balance has to be struck between these two aspects. Perfect quantum gates do not exist in nature. Therefore, it is important to investigate how flaws in the quantum hardware affect quantum computing performance. We do this in two steps. First, in the presence of realistic, faulty quantum hardware, we establish how quantum error correction circuitry achieves reduction in the extent of quantum information corruption. Then, we investigate fault-tolerant gate sequence techniques that result in an approximate phase rotation gate, and establish the existence of an optimal length\ Lopt\ of the length\ L\ of the decomposition sequence. The existence of\ Lopt\ is due to the competition between the increase in gate accuracy with increasing\ L, but the decrease in gate performance due to the diffusive proliferation of gate errors due to faulty basis gates. We present an analytical formula for the gate fidelity as a function of\ L\ that is in satisfactory agreement with the results of our simulations and allows the determination of\ Lopt\ via the solution of a transcendental equation. Our result is universally applicable since gate sequence approximations also play an important role, e.g., in atomic and molecular physics and in nuclear magnetic resonance.

}, issn = {1573-1332}, doi = {10.1007/s11128-017-1571-5}, url = {https://link.springer.com/article/10.1007/s11128-017-1571-5}, author = {Yunseong Nam and R. Bl{\"u}mel} } @article {2151, title = {Optomechanical Analogy for Toy Cosmology with Quantized Scale Factor}, journal = {Entropy}, volume = {19}, year = {2017}, month = {2017/09/12}, chapter = {485}, abstract = {

The simplest cosmology{\^a}\€\”the Friedmann{\^a}\€\“Robertson{\^a}\€\“Walker{\^a}\€\“Lema{\~A}\®tre (FRW) model{\^a}\€\” describes a spatially homogeneous and isotropic universe where the scale factor is the only dynamical parameter. Here we consider how quantized electromagnetic fields become entangled with the scale factor in a toy version of the FRW model. A system consisting of a photon, source, and detector is described in such a universe, and we find that the detection of a redshifted photon by the detector system constrains possible scale factor superpositions. Thus, measuring the redshift of the photon is equivalent to a weak measurement of the underlying cosmology. We also consider a potential optomechanical analogy system that would enable experimental exploration of these concepts. The analogy focuses on the effects of photon redshift measurement as a quantum back-action on metric variables, where the position of a movable mirror plays the role of the scale factor. By working in the rotating frame, an effective Hubble equation can be simulated with a simple free moving mirror.

}, issn = {1099-4300}, doi = {10.3390/e19090485}, url = {http://www.mdpi.com/1099-4300/19/9/485}, author = {Smiga, Joseph A. and J. M. Taylor} } @article {1956, title = {Optomechanically-induced chiral transport of phonons in one dimension}, year = {2017}, month = {2017/01/10}, abstract = {

Non-reciprocal devices, with one-way transport properties, form a key component for isolating and controlling light in photonic systems. Optomechanical systems have emerged as a potential platform for optical non-reciprocity, due to ability of a pump laser to break time and parity symmetry in the system. Here we consider how the non-reciprocal behavior of light can also impact the transport of sound in optomechanical devices. We focus on the case of a quasi one dimensional optical ring resonator with many mechanical modes coupled to light via the acousto-optic effect. The addition of disorder leads to finite diffusion for phonon transport in the material, largely due to elastic backscattering between clockwise and counter-clockwise phonons. We show that a laser pump field, along with the assumption of high quality-factor, sideband-resolved optical resonances, suppresses the effects of disorder and leads to the emergence of chiral diffusion, with direction-dependent diffusion emerging in a bandwidth similar to the phase-matching bandwidth for Brillouin scattering. A simple diagrammatic theory connects the observation of reduced mechanical linewidths directly to the associated phonon diffusion properties, and helps explain recent experimental results.

}, url = {https://arxiv.org/abs/1701.02699}, author = {Xunnong Xu and J. M. Taylor} } @article {2002, title = {Out-of-time-order correlators in finite open systems}, year = {2017}, month = {2017/04/27}, abstract = {

We study out-of-time order correlators (OTOCs) of the form hA\ˆ(t)B\ˆ(0)C\ˆ(t)D\ˆ(0)i for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially \∝ Paie \−t/τi + const to a constant value at t \→ \∞, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focussing on the case of a two-level system, we calculate microscopically the decay times τi and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.

}, doi = {https://doi.org/10.1103/PhysRevB.97.161114}, url = {https://arxiv.org/abs/1704.08442}, author = {S. V. Syzranov and Alexey V. Gorshkov and V. Galitski} } @article {1954, title = {Partial breakdown of quantum thermalization in a Hubbard-like model}, journal = {Physical Review B}, volume = {95}, year = {2017}, month = {2017/02/17}, pages = {054204}, abstract = {

We study the possible breakdown of quantum thermalization in a model of itinerant electrons on a one-dimensional chain without disorder, with both spin and charge degrees of freedom. The eigenstates of this model exhibit peculiar properties in the entanglement entropy, the apparent scaling of which is modified from a \“volume law\” to an \“area law\” after performing a partial, site-wise measurement on the system. These properties and others suggest that this model realizes a new, nonthermal phase of matter, known as a quantum disentangled liquid (QDL). The putative existence of this phase has striking implications for the foundations of quantum statistical mechanics.

}, doi = {10.1103/PhysRevB.95.054204}, url = {http://link.aps.org/doi/10.1103/PhysRevB.95.054204}, author = {James R. Garrison and Ryan V. Mishmash and Matthew P. A. Fisher} } @article {1993, title = {Penalty models for bitstrings of constant Hamming weight}, year = {2017}, month = {2017/04/24}, abstract = {

To program a quantum annealer, one must construct objective functions whose minima encode hard constraints imposed by the underlying problem. For such \"penalty models,\" one desires the additional property that the gap in the objective value between such minima and states that fail the constraints is maximized amongst the allowable objective functions. In this short note, we prove the standard penalty model for the constraint that a bitstring has given Hamming weight is optimal with respect to objective value gap.

}, url = {https://arxiv.org/abs/1704.07290}, author = {Brad Lackey} } @article {1958, title = {Pendular trapping conditions for ultracold polar molecules enforced by external electric fields}, journal = {Physical Review A}, volume = {95}, year = {2017}, month = {2017/06/26}, pages = {063422}, abstract = {

We theoretically investigate trapping conditions for ultracold polar molecules in optical lattices, when external magnetic and electric fields are simultaneously applied. Our results are based on an accurate electronic-structure calculation of the polar\ 23Na40K polar molecule in its absolute ground state combined with a calculation of its rovibrational-hyperfine motion. We find that an electric field strength of\ 5.26(15)\ kV/cm and an angle of\ 54.7o\ between this field and the polarization of the optical laser lead to a trapping design for\ 23Na40K molecules where decoherences due laser-intensity fluctuations and fluctuations in the direction of its polarization are kept to a minimum. One standard deviation systematic and statistical uncertainties are given in parenthesis. Under such conditions pairs of hyperfine-rotational states of\ v=0\ molecules, used to induce tunable dipole-dipole interactions between them, experience ultrastable, matching trapping forces.

}, doi = {10.1103/PhysRevA.95.063422}, url = {https://arxiv.org/abs/1703.03839}, author = {Ming Li and Alexander Petrov and Constantinos Makrides and Eite Tiesinga and Svetlanta Kotochigova} } @conference {2140, title = {Phase retrieval using unitary 2-designs}, booktitle = {SampTA 2017}, year = {2017}, month = {2017/07}, abstract = {

We consider a variant of the phase retrieval problem, where vectors are replaced by unitary matrices, i.e., the unknown signal is a unitary matrix U, and the measurements consist of squared inner products |tr(C\†U)|2\ with unitary matrices C that are chosen by the observer. This problem has applications to quantum process tomography, when the unknown process is a unitary operation. We show that PhaseLift, a convex programming algorithm for phase retrieval, can be adapted to this matrix setting, using measurements that are sampled from unitary 4- and 2-designs. In the case of unitary 4-design measurements, we show that PhaseLift can reconstruct all unitary matrices, using a nearoptimal number of measurements. This extends previous work on PhaseLift using spherical 4-designs. In the case of unitary 2-design measurements, we show that PhaseLift still works pretty well on average: it recovers almost all signals, up to a constant additive error, using a near-optimal number of measurements. These 2-design measurements are convenient for quantum process tomography, as they can be implemented via randomized benchmarking techniques. This is the first positive result on PhaseLift using 2-designs.

}, doi = {10.1109/SAMPTA.2017.8024414}, url = {http://ieeexplore.ieee.org/document/8024414/}, author = {Shelby Kimmel and Yi-Kai Liu} } @article {1999, title = {Phase-space mixing in dynamically unstable, integrable few-mode quantum systems}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/07/05}, pages = {013604}, abstract = {

Quenches in isolated quantum systems are currently a subject of intense study. Here, we consider quantum few-mode systems that are integrable in their classical mean-field limit and become dynamically unstable after a quench of a system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a double-well potential and an antiferromagnetic spinor BEC constrained to a single spatial mode. We study the time dynamics after the quench within the truncated Wigner approximation (TWA) and find that system relaxes to a steady state due to phase-space mixing. Using the action-angle formalism and a pendulum as an illustration, we derive general analytical expressions for the time evolution of expectation values of observables and their long-time limits. We find that the deviation of the long-time expectation value from its classical value scales as 1/O(ln N), where N is the number of atoms in the condensate. Furthermore, the relaxation of an observable to its steady state value is a damped oscillation and the damping is Gaussian in time. We confirm our results with numerical TWA simulations.

}, doi = {10.1103/PhysRevA.96.013604}, url = {https://arxiv.org/abs/1705.01702}, author = {Ranchu Mathew and Eite Tiesinga} } @article {2107, title = {Provable quantum state tomography via non-convex methods}, year = {2017}, month = {2017/11/19}, abstract = {

With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from non-convex optimization. The algorithm excels in the compressed-sensing-like setting, where only a few data points are measured from a lowrank or highly-pure quantum state of a high-dimensional system. We show that the algorithm can practically be used in quantum tomography problems that are beyond the reach of convex solvers, and, moreover, is faster than other state-of-the-art non-convex approaches. Crucially, we prove that, despite being a non-convex program, under mild conditions, the algorithm is guaranteed to converge to the global minimum of the problem; thus, it constitutes a provable quantum state tomography protocol.

}, url = {https://arxiv.org/abs/1711.02524}, author = {Anastasios Kyrillidis and Amir Kalev and Dohuyng Park and Srinadh Bhojanapalli and Constantine Caramanis and Sujay Sanghavi} } @article {1923, title = {Quantum algorithm for linear differential equations with exponentially improved dependence on precision}, journal = {Communications in Mathematical Physics}, volume = {356}, year = {2017}, month = {2017/12/01}, pages = {1057-1081}, abstract = {

We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time. The complexity of the algorithm is polynomial in the logarithm of the inverse error, an exponential improvement over previous quantum algorithms for this problem. Our result builds upon recent advances in quantum linear systems algorithms by encoding the simulation into a sparse, well-conditioned linear system that approximates evolution according to the propagator using a Taylor series. Unlike with finite difference methods, our approach does not require additional hypotheses to ensure numerical stability.

}, url = {https://arxiv.org/abs/1701.03684}, author = {Dominic W. Berry and Andrew M. Childs and Aaron Ostrander and Guoming Wang} } @article {2020, title = {Quantum Algorithm for Linear Regression}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/07/31}, pages = {012335}, abstract = {

We present a quantum algorithm for fitting a linear regression model to a given data set using the least squares approach. Different from previous algorithms which only yield a quantum state encoding the optimal parameters, our algorithm outputs these numbers in the classical form. So by running it once, one completely determines the fitted model and then can use it to make predictions on new data at negligible cost. Moreover, our algorithm does not require the design matrix to be sparse or need any help from additional state preparation procedures. It runs in time poly(log(N), d, κ, 1/), where N is the size of the data set, d is the number of adjustable parameters, κ is the condition number of the design matrix, and  is the desired precision in the output. We also show that the polynomial dependence on d and κ is necessary. Thus, our algorithm cannot be significantly improved. Furthermore, we also give a quantum algorithm that estimates the quality of the least-squares fit without computing its parameters explicitly. This algorithm runs faster than the one for finding this fit, and can be used to check whether the given data set qualifies for linear regression in the first place.

}, url = {https://arxiv.org/abs/1402.0660}, author = {Guoming Wang} } @article {1605, title = {Quantum algorithm for systems of linear equations with exponentially improved dependence on precision}, journal = {SIAM Journal on Computing}, volume = {46}, year = {2017}, month = {2017/12/21}, pages = {1920-1950}, abstract = {

Harrow, Hassidim, and Lloyd showed that for a suitably specified N\×N matrix A and N-dimensional vector b⃗ , there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of equations Ax⃗ =b⃗ . If A is sparse and well-conditioned, their algorithm runs in time poly(logN,1/ϵ), where ϵ is the desired precision in the output state. We improve this to an algorithm whose running time is polynomial in log(1/ϵ), exponentially improving the dependence on precision while keeping essentially the same dependence on other parameters. Our algorithm is based on a general technique for implementing any operator with a suitable Fourier or Chebyshev series representation. This allows us to bypass the quantum phase estimation algorithm, whose dependence on ϵ is prohibitive.

}, doi = {10.1137/16M1087072}, url = {http://epubs.siam.org/doi/10.1137/16M1087072}, author = {Andrew M. Childs and Robin Kothari and Rolando D. Somma} } @article {1989, title = {Quantum Algorithms for Graph Connectivity and Formula Evaluation}, year = {2017}, month = {2017/04/03}, abstract = {

We give a new upper bound on the quantum query complexity of deciding st-connectivity on certain classes of planar graphs, and show the bound is sometimes exponentially better than previous results. We then show Boolean formula evaluation reduces to deciding connectivity on just such a class of graphs. Applying the algorithm for st-connectivity to Boolean formula evaluation problems, we match the O( \√ N) bound on the quantum query complexity of evaluating formulas on N variables, give a quadratic speed-up over the classical query complexity of a certain class of promise Boolean formulas, and show this approach can yield superpolynomial quantum/classical separations. These results indicate that this st-connectivity-based approach may be the \“right\” way of looking at quantum algorithms for formula evaluation.

}, url = {https://arxiv.org/abs/1704.00765}, author = {Stacey Jeffery and Shelby Kimmel} } @article {2058, title = {Quantum Fully Homomorphic Encryption With Verification}, journal = {Proceedings of ASIACRYPT 2017}, year = {2017}, month = {2017/11/30}, pages = {438-467}, abstract = {

Fully-homomorphic encryption (FHE) enables computation on encrypted data while maintaining secrecy. Recent research has shown that such schemes exist even for quantum computation. Given the numerous applications of classical FHE (zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is reasonable to hope that quantum FHE (or QFHE) will lead to many new results in the quantum setting. However, a crucial ingredient in almost all applications of FHE is circuit verification. Classically, verification is performed by checking a transcript of the homomorphic computation. Quantumly, this strategy is impossible due to no-cloning. This leads to an important open question: can quantum computations be delegated and verified in a non-interactive manner? In this work, we answer this question in the affirmative, by constructing a scheme for QFHE with verification (vQFHE). Our scheme provides authenticated encryption, and enables arbitrary polynomial-time quantum computations without the need of interaction between client and server. Verification is almost entirely classical; for computations that start and end with classical states, it is completely classical. As a first application, we show how to construct quantum one-time programs from classical one-time programs and vQFHE.

}, doi = {10.1007/978-3-319-70694-8_16}, url = {https://arxiv.org/abs/1708.09156}, author = {Gorjan Alagic and Yfke Dulek and Christian Schaffner and Florian Speelman} } @article {2620, title = {Quantum Non-malleability and Authentication}, journal = {In: Katz J., Shacham H. (eds) Advances in Cryptology {\textendash} CRYPTO 2017. Lecture Notes in Computer Science. Springer, Cham}, volume = {10402}, year = {2017}, abstract = {

In encryption, non-malleability is a highly desirable property: it ensures that adversaries cannot manipulate the plaintext by acting on the ciphertext. In [6], Ambainis et al. gave a definition of non-malleability for the encryption of quantum data. In this work, we show that this definition is too weak, as it allows adversaries to \“inject\” plaintexts of their choice into the ciphertext. We give a new definition of quantum non-malleability which resolves this problem. Our definition is expressed in terms of entropic quantities, considers stronger adversaries, and does not assume secrecy. Rather, we prove that quantum non-malleability implies secrecy; this is in stark contrast to the classical setting, where the two properties are completely independent. For unitary schemes, our notion of non-malleability is equivalent to encryption with a two-design (and hence also to the definition of [6]).

Our techniques also yield new results regarding the closely-related task of quantum authentication. We show that \“total authentication\” (a notion recently proposed by Garg et al. [18]) can be satisfied with two-designs, a significant improvement over the eight-design construction of [18]. We also show that, under a mild adaptation of the rejection procedure, both total authentication and our notion of non-malleability yield quantum authentication as defined by Dupuis et al. [16].

}, doi = {https://doi.org/10.1007/978-3-319-63715-0_11}, author = {Gorjan Alagic and Christian Majenz} } @article {2102, title = {Quantum simulation of ferromagnetic Heisenberg model}, year = {2017}, month = {2017/12/14}, abstract = {

Large quantum simulators, with sufficiently many qubits to be impossible to simulate classically, become hard to experimentally validate. We propose two tests of a quantum simulator with Heisenberg interaction in a linear chain of spins. In the first, we propagate half of a singlet state through a chain of spin with a ferromagnetic interaction and subsequently recover the state with an antiferromagnetic interaction. The antiferromagnetic interaction is intrinsic to the system while the ferromagnetic one can be simulated by a sequence of time-dependent controls of the antiferromagnetic interaction and Suzuki-Trotter approximations. In the second test, we use the same technique to transfer a spin singlet state from one end of a spin chain to the other. We show that the tests are robust against parametric errors in operation of the simulator and may be applicable even without error correction.

}, url = {https://arxiv.org/abs/1712.05282}, author = {Yiping Wang and Minh C. Tran and J. M. Taylor} } @article {1787, title = {Quantum state tomography via reduced density matrices}, journal = {Physical Review Letters}, volume = {118}, year = {2017}, month = {2017/01/09}, pages = {020401}, abstract = {

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.

}, doi = {10.1103/PhysRevLett.118.020401}, url = {http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.020401}, author = {Tao Xin and Dawei Lu and Joel Klassen and Nengkun Yu and Zhengfeng Ji and Jianxin Chen and Xian Ma and Guilu Long and Bei Zeng and Raymond Laflamme} } @article {2621, title = {Quantum-Secure Symmetric-Key Cryptography Based on Hidden Shifts}, journal = {In: Coron JS., Nielsen J. (eds) Advances in Cryptology {\textendash} EUROCRYPT 2017. Lecture Notes in Computer Science, Springer, Cham}, volume = {10212}, year = {2017}, abstract = {

Recent results of Kaplan et al., building on work by Kuwakado and Morii, have shown that a wide variety of classically-secure symmetric-key cryptosystems can be completely broken by quantum chosen-plaintext attacks (qCPA). In such an attack, the quantum adversary has the ability to query the cryptographic functionality in superposition. The vulnerable cryptosystems include the Even-Mansour block cipher, the three-round Feistel network, the Encrypted-CBC-MAC, and many others.

In this article, we study simple algebraic adaptations of such schemes that replace\ \  (Z/2)n\  addition with operations over alternate finite groups\—such as\ \  Z/2n \—and provide evidence that these adaptations are qCPA-secure. These adaptations furthermore retain the classical security properties and basic structural features enjoyed by the original schemes.

We establish security by treating the (quantum) hardness of the well-studied Hidden Shift problem as a cryptographic assumption. We observe that this problem has a number of attractive features in this cryptographic context, including random self-reducibility, hardness amplification, and\—in many cases of interest\—a reduction from the \“search version\” to the \“decisional version.\” We then establish, under this assumption, the qCPA-security of several such Hidden Shift adaptations of symmetric-key constructions. We show that a Hidden Shift version of the Even-Mansour block cipher yields a quantum-secure pseudorandom function, and that a Hidden Shift version of the Encrypted CBC-MAC yields a collision-resistant hash function. Finally, we observe that such adaptations frustrate the direct Simon\’s algorithm-based attacks in more general circumstances, e.g., Feistel networks and slide attacks.

}, doi = {https://doi.org/10.1007/978-3-319-56617-7_3}, author = {Gorjan Alagic and Alexander Russell} } @article {1982, title = {Randomness in nonlocal games between mistrustful players}, journal = {Quantum Information and Computation}, volume = {17}, year = {2017}, month = {2017/06/15}, pages = {0595-0610}, abstract = {

If two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of the other player? We show that for complete-support games, the answer is yes: even if the second player is given the first player\&$\#$39;s input at the conclusion of the game, he cannot perfectly recover her output. Thus some amount of local randomness (i.e., randomness possessed by only one player) is always obtained when randomness is certified from nonlocal games with quantum strategies. This is in contrast to non-signaling game strategies, which may produce global randomness without any local randomness. We discuss potential implications for cryptographic protocols between mistrustful parties.

}, url = {https://arxiv.org/abs/1706.04984}, author = {Carl Miller and Yaoyun Shi} } @article {1934, title = {Raz-McKenzie simulation with the inner product gadget}, journal = {Electronic Colloquium on Computational Complexity (ECCC)}, year = {2017}, month = {2017/01/28}, abstract = {

In this note we show that the Raz-McKenzie simulation algorithm which lifts deterministic query lower bounds to deterministic communication lower bounds can be implemented for functions f composed with the Inner Product gadget 1ip(x, y) = P i xiyi mod 2 of logarithmic size. In other words, given a function f : {0, 1} n \→ {0, 1} with deterministic query complexity D(f), we show that the deterministic communication complexity of the composed function f {\textopenbullet} 1 n ip is Θ(D(f) log n), where f {\textopenbullet} 1 n ip(x, y) = f(1ip(x 1 , y 1 ), . . . , 1ip(x n , y n )) where x = (x 1 , . . . , x n ), y = (y 1 , . . . , y n ) and each x i and y i are O(log n) bit strings. In [RM97] and [GPW15], the simulation algorithm is implemented for functions composed with the Indexing gadget, where the size of the gadget is polynomial in the input length of the outer function f.

}, url = {https://eccc.weizmann.ac.il/report/2017/010/}, author = {Xiaodi Wu and Penghui Yao and Henry Yuen} } @article {2048, title = {On the readiness of quantum optimization machines for industrial applications}, year = {2017}, month = {2017/08/31}, abstract = {

There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for near-term quantum annealers.

}, url = {https://arxiv.org/abs/1708.09780}, author = {Alejandro Perdomo-Ortiz and Alexander Feldman and Asier Ozaeta and Sergei V. Isakov and Zheng Zhu and Bryan O{\textquoteright}Gorman and Helmut G. Katzgraber and Alexander Diedrich and Hartmut Neven and Johan de Kleer and Brad Lackey and Rupak Biswas} } @article {1996, title = {Rigidity of the magic pentagram game}, journal = {Quantum Science and Technology}, volume = {3}, year = {2017}, month = {2017/11/02}, pages = {015002}, abstract = {

A game is rigid if a near-optimal score guarantees, under the sole assumption of the validity of quantum mechanics, that the players are using an approximately unique quantum strategy. Rigidity has a vital role in quantum cryptography as it permits a strictly classical user to trust behavior in the quantum realm. This property can be traced back as far as 1998 (Mayers and Yao) and has been proved for multiple classes of games. In this paper we prove ridigity for the magic pentagram game, a simple binary constraint satisfaction game involving two players, five clauses and ten variables. We show that all near-optimal strategies for the pentagram game are approximately equivalent to a unique strategy involving real Pauli measurements on three maximally-entangled qubit pairs.

}, url = {http://iopscience.iop.org/article/10.1088/2058-9565/aa931d/meta}, author = {Amir Kalev and Carl Miller} } @article {2101, title = {Robust entanglement renormalization on a noisy quantum computer}, year = {2017}, month = {2017/11/20}, abstract = {

A method to study strongly interacting quantum many-body systems at and away from criticality is proposed. The method is based on a MERA-like tensor network that can be efficiently and reliably contracted on a noisy quantum computer using a number of qubits that is much smaller than the system size. We prove that the outcome of the contraction is stable to noise and that the estimated energy upper bounds the ground state energy. The stability, which we numerically substantiate, follows from the positivity of operator scaling dimensions under renormalization group flow. The variational upper bound follows from a particular assignment of physical qubits to different locations of the tensor network plus the assumption that the noise model is local. We postulate a scaling law for how well the tensor network can approximate ground states of lattice regulated conformal field theories in d spatial dimensions and provide evidence for the postulate. Under this postulate, a O(logd (1/δ))-qubit quantum computer can prepare a valid quantum-mechanical state with energy density δ above the ground state. In the presence of noise, δ = O( logd+1(1/)) can be achieved, where  is the noise strength.

}, url = {https://arxiv.org/abs/1711.07500}, author = {Isaac H. Kim and Brian Swingle} } @proceedings {1882, title = {Sequential measurements, disturbance and property testing}, year = {2017}, month = {2017/01/01}, pages = {1598-1611}, abstract = {

We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and the case that all of the measurements have low probability of acceptance. The measurements cannot simply be tried in sequence, because early measurements may disturb the state being tested. One procedure is based on a variant of Marriott-Watrous amplification. The other procedure is based on the use of a test for this disturbance, which is applied with low probability. We find a number of applications. First, quantum query complexity separations in the property testing model for testing isomorphism of functions under group actions. We give quantum algorithms for testing isomorphism, linear isomorphism and affine isomorphism of boolean functions which use exponentially fewer queries than is possible classically, and a quantum algorithm for testing graph isomorphism which uses polynomially fewer queries than the best algorithm known. Second, testing properties of quantum states and operations. We show that any finite property of quantum states can be tested using a number of copies of the state which is logarithmic in the size of the property, and give a test for genuine multipartite entanglement of states of n qubits that uses O(n) copies of the state. Third, correcting an error in a result of Aaronson on de-Merlinizing quantum protocols. This result claimed that, in any one-way quantum communication protocol where two parties are assisted by an all-powerful but untrusted third party, the third party can be removed with only a modest increase in the communication cost. We give a corrected proof of a key technical lemma required for Aaronson\&$\#$39;s result.

}, doi = {10.1137/1.9781611974782.105}, url = {http://epubs.siam.org/doi/10.1137/1.9781611974782.105}, author = {Aram W. Harrow and Cedric Yen-Yu Lin and Ashley Montanaro} } @article {1970, title = {Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations}, year = {2017}, month = {2017/05/25}, abstract = {

In this paper we improve the layered implementation of arbitrary stabilizer circuits introduced by Aaronson and Gottesman in Phys. Rev. A 70(052328), 2004: to implement a general stabilizer circuit, we reduce their 11-stage computation -HC-P-C-P-C-H-P-C-P-C- over the gate set consisting of Hadamard, Controlled-NOT, and Phase gates, into a 7-stage computation of the form -C-CZ-P-H-P-CZ-C-. We show arguments in support of using -CZ- stages over the -C- stages: not only the use of -CZ- stages allows a shorter layered expression, but -CZ- stages are simpler and appear to be easier to implement compared to the -C- stages. Based on this decomposition, we develop a twoqubit gate depth-(14n\−4) implementation of stabilizer circuits over the gate library {H, P, CNOT}, executable in the LNN architecture, improving best previously known depth-25n circuit, also executable in the LNN architecture. Our constructions rely on Bruhat decomposition of the symplectic group and on folding arbitrarily long sequences of the form (-P-C-) m into a 3-stage computation -P-CZ-C-. Our results include the reduction of the 11-stage decomposition -H-C-P-C-P-C-H-P-C-P-C- into a 9-stage decomposition of the form -C-P-C-P-H-C-P-C-P-. This reduction is based on the Bruhat decomposition of the symplectic group. This result also implies a new normal form for stabilizer circuits. We show that a circuit in this normal form is optimal in the number of Hadamard gates used. We also show that the normal form has an asymptotically optimal number of parameters.

}, url = {https://arxiv.org/abs/1705.09176}, author = {Dmitri Maslov and Martin Roetteler} } @article {2136, title = {Simultaneous, Full Characterization of a Single-Photon State}, journal = {Physical Review X}, volume = {7}, year = {2017}, month = {2017/11/15}, pages = {041036}, abstract = {

As single-photon sources become more mature and are used more often in quantum information, communications, and measurement applications, their characterization becomes more important. Singlephoton-like light is often characterized by its brightness, as well as two quantum properties: the suppression of multiphoton content and the photon indistinguishability. While it is desirable to obtain these quantities from a single measurement, currently two or more measurements are required. Here, we show that using two-photon (n \¼ 2) number-resolving detectors, one can completely characterize single-photon-like states in a single measurement, where previously two or more measurements were necessary. We simultaneously determine the brightness, the suppression of multiphoton states, the indistinguishability, and the statistical distribution of Fock states to third order for a quantum light source. We find n \≥ 3 number-resolving detectors provide no additional advantage in the single-photon characterization. The new method extracts more information per experimental trial than a conventional measurement for all input states and is particularly more efficient for statistical mixtures of photon states. Thus, using this n \¼ 2, number-resolving detector scheme will provide advantages in a variety of quantum optics measurements and systems.

}, doi = {10.1103/PhysRevX.7.041036}, url = {https://link.aps.org/doi/10.1103/PhysRevX.7.041036}, author = {Thomay, Tim and Polyakov, Sergey V. and Gazzano, Olivier and Goldschmidt, Elizabeth and Eldredge, Zachary D. and Huber, Tobias and Loo, Vivien and Solomon, Glenn S.} } @article {2003, title = {A solvable family of driven-dissipative many-body systems}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/11/10}, abstract = {

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. And conversely, the relative scarcity of solutions for non-equilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently in any number of spatial dimensions. We leverage these solutions to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions, and to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture.

}, doi = {10.1103/PhysRevLett.119.190402}, url = {https://arxiv.org/abs/1703.04626}, author = {Michael Foss-Feig and Jeremy T. Young and Victor V. Albert and Alexey V. Gorshkov and Mohammad F. Maghrebi} } @article {1992, title = {Substochastic Monte Carlo Algorithms}, year = {2017}, month = {2017/04/28}, abstract = {

In this paper we introduce and formalize Substochastic Monte Carlo (SSMC) algorithms. These algorithms, originally intended to be a better classical foil to quantum annealing than simulated annealing, prove to be worthy optimization algorithms in their own right. In SSMC, a population of walkers is initialized according to a known distribution on an arbitrary search space and varied into the solution of some optimization problem of interest. The first argument of this paper shows how an existing classical algorithm, \"Go-With-The-Winners\" (GWW), is a limiting case of SSMC when restricted to binary search and particular driving dynamics.\ 
Although limiting to GWW, SSMC is more general. We show that (1) GWW can be efficiently simulated within the SSMC framework, (2) SSMC can be exponentially faster than GWW, (3) by naturally incorporating structural information, SSMC can exponentially outperform the quantum algorithm that first inspired it, and (4) SSMC exhibits desirable search features in general spaces. Our approach combines ideas from genetic algorithms (GWW), theoretical probability (Fleming-Viot processes), and quantum computing. Not only do we demonstrate that SSMC is often more efficient than competing algorithms, but we also hope that our results connecting these disciplines will impact each independently. An implemented version of SSMC has previously enjoyed some success as a competitive optimization algorithm for Max-k-SAT.

}, url = {https://arxiv.org/abs/1704.09014}, author = {Michael Jarret and Brad Lackey} } @article {2099, title = {Super-polynomial and exponential improvements for quantum-enhanced reinforcement learning}, year = {2017}, month = {2017/12/12}, abstract = {

Recent work on quantum machine learning has demonstrated that quantum computers can offer dramatic improvements over classical devices for data mining, prediction and classification. However, less is known about the advantages using quantum computers may bring in the more general setting of reinforcement learning, where learning is achieved via interaction with a task environment that provides occasional rewards. Reinforcement learning can incorporate data-analysis-oriented learning settings as special cases, but also includes more complex situations where, e.g., reinforcing feedback is delayed. In a few recent works, Grover-type amplification has been utilized to construct quantum agents that achieve up-to-quadratic improvements in learning efficiency. These encouraging results have left open the key question of whether super-polynomial improvements in learning times are possible for genuine reinforcement learning problems, that is problems that go beyond the other more restricted learning paradigms. In this work, we provide a family of such genuine reinforcement learning tasks. We construct quantum-enhanced learners which learn super-polynomially, and even exponentially faster than any classical reinforcement learning model, and we discuss the potential impact our results may have on future technologies.

}, url = {https://arxiv.org/abs/1710.11160}, author = {Vedran Dunjko and Yi-Kai Liu and Xingyao Wu and J. M. Taylor} } @article {2100, title = {Thermodynamic Analysis of Classical and Quantum Search Algorithms}, year = {2017}, month = {2017/09/29}, abstract = {

We analyze the performance of classical and quantum search algorithms from a thermodynamic perspective, focusing on resources such as time, energy, and memory size. We consider two examples that are relevant to post-quantum cryptography: Grover\’s search algorithm, and the quantum algorithm for collisionfinding. Using Bennett\’s \“Brownian\” model of low-power reversible computation, we show classical algorithms that have the same asymptotic energy consumption as these quantum algorithms. Thus, the quantum advantage in query complexity does not imply a reduction in these thermodynamic resource costs. In addition, we present realistic estimates of the resource costs of quantum and classical search, for near-future computing technologies. We find that, if memory is cheap, classical exhaustive search can be surprisingly competitive with Grover\’s algorithm.

}, url = {https://arxiv.org/abs/1709.10510}, author = {Ray Perlner and Yi-Kai Liu} } @article {2055, title = {Thermodynamic limits for optomechanical systems with conservative potentials}, journal = {Physical Review B}, volume = {96}, year = {2017}, month = {2017/11/13}, pages = {184106}, abstract = {

The mechanical force from light \– radiation pressure \– provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a function of external parameters. This non-analyticity, a key feature of thermodynamic phase transitions, suggests that there could be an effective thermodynamic description of optomechanical systems. Here we explicitly define the thermodynamic limit for optomechanical systems and derive a set of sufficient constraints on the system parameters as the mechanical system grows large. As an example, we show how these constraints can be satisfied in a system with Z2 symmetry and derive a free energy, allowing us to characterize this as an equilibrium phase transition.

}, doi = {10.1103/PhysRevB.96.184106}, url = {https://arxiv.org/abs/1707.05771}, author = {Stephen Ragole and Haitan Xu and John Lawall and J. M. Taylor} } @article {2152, title = {Threshold Dynamics of a Semiconductor Single Atom Maser}, journal = {Physical Review Letters}, volume = {119}, year = {2017}, month = {2017/08/31}, pages = {097702}, abstract = {

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

}, doi = {10.1103/PhysRevLett.119.097702}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.097702}, author = {Liu, Y.-Y. and Stehlik, J. and Eichler, C. and Mi, X. and Hartke, T. R. and Michael Gullans and J. M. Taylor and Petta, J. R.} } @article {2057, title = {Unforgeable Quantum Encryption}, year = {2017}, month = {2017/09/19}, abstract = {

We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i.) ciphertext unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext attack, and (iii.) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All of our new notions also imply QIND-CPA privacy. Combining one-time authentication and classical pseudorandomness, we construct schemes for each of these new quantum security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.

}, url = {https://arxiv.org/abs/1709.06539}, author = {Gorjan Alagic and Tommaso Gagliardoni and Christian Majenz} } @article {2036, title = {Universal Security for Randomness Expansion from the Spot-Checking Protocol}, journal = {SIAM Journal on Computing}, volume = {46}, year = {2017}, month = {2017/08/01}, abstract = {

Colbeck (Thesis, 2006) proposed using Bell inequality violations to generate certified random numbers. While full quantum-security proofs have been given, it remains a major open problem to identify the broadest class of Bell inequalities and lowest performance requirements to achieve such security. In this paper, working within the broad class of spot-checking protocols, we prove exactly which Bell inequality violations can be used to achieve full security. Our result greatly improves the known noise tolerance for secure randomness expansion: for the commonly used CHSH game, full security was only known with a noise tolerance of 1.5\%, and we improve this to 10.3\%. We also generalize our results beyond Bell inequalities and give the first security proof for randomness expansion based on Kochen-Specker inequalities. The central technical contribution of the paper is a new uncertainty principle for the Schatten norm, which is based on the uniform convexity inequality of Ball, Carlen, and Lieb (Inventiones mathematicae, 115:463-482, 1994).

}, doi = {10.1137/15M1044333}, url = {http://epubs.siam.org/doi/10.1137/15M1044333}, author = {Carl Miller and Yaoyun Shi} } @article {2069, title = {Use of global interactions in efficient quantum circuit constructions}, journal = {New Journal of Physics}, year = {2017}, month = {2017/12/21}, abstract = {

In this paper we study the ways to use a global entangling operator to efficiently implement circuitry common to a selection of important quantum algorithms. In particular, we focus on the circuits composed with global Ising entangling gates and arbitrary addressable single-qubit gates. We show that under certain circumstances the use of global operations can substantially improve the entangling gate count.

}, doi = {10.1088/1367-2630/aaa398}, url = {http://iopscience.iop.org/article/10.1088/1367-2630/aaa398}, author = {Dmitri Maslov and Yunseong Nam} } @article {1816, title = {Valley Blockade in a Silicon Double Quantum Dot}, journal = {Physical Review B}, volume = {96}, year = {2017}, month = {2017/11/13}, pages = {205302}, abstract = {

Electrical transport in double quantum dots (DQDs) illuminates many interesting features of the dots\&$\#$39; carrier states. Recent advances in silicon quantum information technologies have renewed interest in the valley states of electrons confined in silicon. Here we show measurements of DC transport through a mesa-etched silicon double quantum dot. Comparing bias triangles (i.e., regions of allowed current in DQDs) at positive and negative bias voltages we find a systematic asymmetry in the size of the bias triangles at the two bias polarities. Asymmetries of this nature are associated with blocking of tunneling events due to the occupation of a metastable state. Several features of our data lead us to conclude that the states involved are not simple spin states. Rather, we develop a model based on selective filling of valley states in the DQD that is consistent with all of the qualitative features of our data.

}, doi = {10.1103/PhysRevB.96.205302}, url = {https://arxiv.org/abs/1607.06107}, author = {Justin K. Perron and Michael Gullans and J. M. Taylor and M. D. Stewart, Jr. and Neil M. Zimmerman} } @article {2097, title = {Why Bohr was (Mostly) Right}, year = {2017}, month = {2017/11/05}, abstract = {

After a discussion of the Frauchiger-Renner argument that no \“singleworld\” interpretation of quantum mechanics can be self-consistent, I propose a \“Bohrian\” alternative to many-worlds or QBism as the rational option.

}, url = {https://arxiv.org/abs/1711.01604}, author = {Jeffrey Bub} } @article {1813, title = {Adiabatic optimization versus diffusion Monte Carlo}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/07/12}, pages = {042318}, abstract = {

Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate stoquastic adiabatic algorithms with polynomial overhead. Here, we analyze diffusion Monte Carlo algorithms. We argue that, based on differences between L1 and L2 normalized states, these algorithms suffer from certain obstructions preventing them from efficiently simulating stoquastic adiabatic evolution in generality. In practice however, we obtain good performance by introducing a method that we call Substochastic Monte Carlo. In fact, our simulations are good classical optimization algorithms in their own right, competitive with the best previously known heuristic solvers for MAX-k-SAT at k=2,3,4.

}, url = {https://arxiv.org/abs/1607.03389}, author = {Michael Jarret and Stephen P. Jordan and Brad Lackey} } @article {1714, title = {On the advantages of using relative phase Toffolis with an application to multiple control Toffoli optimization}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/02/10}, pages = {022311}, abstract = {Various implementations of the Toffoli gate up to a relative phase have been known for years. The advantage over regular Toffoli gate is their smaller circuit size. However, their use has been often limited to a demonstration of quantum control in designs such as those where the Toffoli gate is being applied last or otherwise for some specific reasons the relative phase does not matter. It was commonly believed that the relative phase deviations would prevent the relative phase Toffolis from being very helpful in practical large-scale designs. In this paper, we report three circuit identities that provide the means for replacing certain configurations of the multiple control Toffoli gates with their simpler relative phase implementations, up to a selectable unitary on certain qubits, and without changing the overall functionality. We illustrate the advantage via applying those identities to the optimization of the known circuits implementing multiple control Toffoli gates, and report the reductions in the CNOT-count, T-count, as well as the number of ancillae used. We suggest that a further study of the relative phase Toffoli implementations and their use may yield other optimizations.}, doi = {10.1103/PhysRevA.93.022311}, url = {http://arxiv.org/abs/1508.03273}, author = {Dmitri Maslov} } @article {1678, title = {Anomalous broadening in driven dissipative Rydberg systems}, journal = {Physical Review Letters}, volume = {116}, year = {2016}, month = {2016/03/16}, pages = {113001}, abstract = {We observe interaction-induced broadening of the two-photon 5s-18s transition in 87Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly two orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with spontaneously created populations of nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms.}, doi = {10.1103/PhysRevLett.116.113001}, url = {http://arxiv.org/abs/1510.08710}, author = {E. A. Goldschmidt and T. Boulier and R. C. Brown and S. B. Koller and J. T. Young and Alexey V. Gorshkov and S. L. Rolston and J. V. Porto} } @book {1318, title = {Bananaworld: Quantum Mechanics for Primates}, year = {2016}, month = {2012/11/13}, publisher = {Oxford University Press}, organization = {Oxford University Press}, abstract = {

This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The \&$\#$39;no go\&$\#$39; theorems tell us that we can\&$\#$39;t shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.

}, url = {http://arxiv.org/abs/1211.3062v2}, author = {Jeffrey Bub} } @article {1950, title = {Black Holes, Quantum Mechanics, and the Limits of Polynomial-time Computability}, journal = {XRDS}, volume = {23}, year = {2016}, month = {2016/09/20}, pages = {30{\textendash}33}, abstract = {

Which computational problems can be solved in polynomial-time and which cannot? Though seemingly technical, this question has wide-ranging implications and brings us to the heart of both theoretical computer science and modern physics.

}, issn = {1528-4972}, doi = {10.1145/2983539}, url = {http://doi.acm.org/10.1145/2983539}, author = {Stephen P. Jordan} } @article {1960, title = {Causality and quantum criticality in long-range lattice models}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/03/17}, pages = {125128}, doi = {10.1103/PhysRevB.93.125128}, url = {http://link.aps.org/doi/10.1103/PhysRevB.93.125128}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1179, title = {Causality and quantum criticality with long-range interactions}, journal = {Physical Review B}, volume = {92}, year = {2016}, month = {2016/03/17}, pages = {125128}, abstract = { Quantum lattice systems with long-range interactions often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model and a fermionic model with long-range interactions, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of long-range interactions, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent. }, doi = {10.1103/PhysRevB.93.125128}, url = {http://arxiv.org/abs/1508.00906}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1716, title = {Co-Designing a Scalable Quantum Computer with Trapped Atomic Ions}, year = {2016}, month = {2016/02/09}, abstract = {The first generation of quantum computers are on the horizon, fabricated from quantum hardware platforms that may soon be able to tackle certain tasks that cannot be performed or modelled with conventional computers. These quantum devices will not likely be universal or fully programmable, but special-purpose processors whose hardware will be tightly co-designed with particular target applications. Trapped atomic ions are a leading platform for first generation quantum computers, but are also fundamentally scalable to more powerful general purpose devices in future generations. This is because trapped ion qubits are atomic clock standards that can be made identical to a part in 10^15, and their quantum circuit connectivity can be reconfigured through the use of external fields, without modifying the arrangement or architecture of the qubits themselves. In this article we show how a modular quantum computer of any size can be engineered from ion crystals, and how the wiring between ion trap qubits can be tailored to a variety of applications and quantum computing protocols.}, url = {http://arxiv.org/abs/1602.02840}, author = {Kenneth R. Brown and Jaewan Kim and Christopher Monroe} } @article {1737, title = {Collective phases of strongly interacting cavity photons}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/09/01}, pages = {033801}, abstract = {

We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-12 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

}, doi = {http://dx.doi.org/10.1103/PhysRevA.94.033801}, url = {http://arxiv.org/abs/1601.06857}, author = {Ryan M. Wilson and Khan W. Mahmud and Anzi Hu and Alexey V. Gorshkov and Mohammad Hafezi and Michael Foss-Feig} } @article {1760, title = {A Complete Characterization of Unitary Quantum Space}, year = {2016}, month = {2016/04/05}, abstract = {We give two complete characterizations of unitary quantum space-bounded classes. The first is based on the Matrix Inversion problem for well-conditioned matrices. We show that given the size-n efficient encoding of a 2O(k(n)){\texttimes}2O(k(n)) well-conditioned matrix H, approximating a particular entry of H-1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation. In particular, the problem of computing entries of H-1 for an explicit well-conditioned n{\texttimes}n matrix H is complete for unitary quantum logspace. We then show that the problem of approximating to high precision the least eigenvalue of a positive semidefinite matrix H, encoded as a circuit, gives a second characterization of unitary quantum space complexity. In the process we also establish an equivalence between unitary quantum space-bounded classes and certain QMA proof systems. As consequences, we establish that QMA with exponentially small completeness-soundness gap is equal to PSPACE, that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian.}, url = {http://arxiv.org/abs/1604.01384}, author = {Bill Fefferman and Cedric Yen-Yu Lin} } @article {1234, title = {Complexity of the XY antiferromagnet at fixed magnetization}, journal = {Quantum Information and Computation}, volume = {16}, year = {2016}, month = {2016/01/01}, pages = {1-18}, abstract = { We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model. }, url = {http://arxiv.org/abs/1503.07083v1}, author = {Andrew M. Childs and David Gosset and Zak Webb} } @conference {1712, title = {Computational Security of Quantum Encryption}, booktitle = {Computational Security of Quantum Encryption. In: Nascimento A., Barreto P. (eds) Information Theoretic Security. }, year = {2016}, month = {2016/11/10}, abstract = {

Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notions of semantic security and indistinguishability, and, in analogy with the classical work of Goldwasser and Micali, show that these notions are equivalent. Finally, we construct secure quantum encryption schemes from basic primitives. In particular, we show that quantum-secure one-way functions imply IND-CCA1-secure symmetric-key quantum encryption, and that quantum-secure trapdoor one-way permutations imply semantically-secure public-key quantum encryption.

}, url = {https://link.springer.com/chapter/10.1007\%2F978-3-319-49175-2_3}, author = {Gorjan Alagic and Anne Broadbent and Bill Fefferman and Tommaso Gagliardoni and Christian Schaffner and Michael St. Jules} } @article {1915, title = {Demonstration of a small programmable quantum computer with atomic qubits}, journal = {Nature}, volume = {536}, year = {2016}, month = {2016/08/04}, pages = {63-66}, abstract = {

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here, we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully-connected set of gate operations that are native to the hardware and have a mean fidelity of 98 \%. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ) and Bernstein-Vazirani (BV) algorithms with average success rates of 95 \% and 90 \%, respectively. We also perform a coherent quantum Fourier transform (QFT) on five trappedion qubits for phase estimation and period finding with average fidelities of 62 \% and 84 \%, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

}, doi = {10.1038/nature18648}, url = {http://www.nature.com/nature/journal/v536/n7614/full/nature18648.html}, author = {S. Debnath and N. M. Linke and C. Figgatt and K. A. Landsman and K. Wright and C. Monroe} } @article {1452, title = {Detecting Consistency of Overlapping Quantum Marginals by Separability}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/03/03}, pages = {032105}, abstract = { The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability. }, doi = {10.1103/PhysRevA.93.032105}, url = {http://arxiv.org/abs/1509.06591}, author = {Jianxin Chen and Zhengfeng Ji and Nengkun Yu and Bei Zeng} } @article {1815, title = {Double Quantum Dot Floquet Gain Medium}, journal = {Physical Review X}, volume = {6}, year = {2016}, month = {2016/11/07}, pages = {041027}, abstract = {

Strongly driving a two-level quantum system with light leads to a ladder of Floquet states separated by the photon energy. Nanoscale quantum devices allow the interplay of confined electrons, phonons, and photons to be studied under strong driving conditions. Here we show that a single electron in a periodically driven DQD functions as a \"Floquet gain medium,\" where population imbalances in the DQD Floquet quasi-energy levels lead to an intricate pattern of gain and loss features in the cavity response. We further measure a large intra-cavity photon number n_c in the absence of a cavity drive field, due to equilibration in the Floquet picture. Our device operates in the absence of a dc current -- one and the same electron is repeatedly driven to the excited state to generate population inversion. These results pave the way to future studies of non-classical light and thermalization of driven quantum systems.

}, doi = {10.1103/PhysRevX.6.041027}, url = {http://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.041027}, author = {J. Stehlik and Y.-Y. Liu and C. Eichler and T. R. Hartke and X. Mi and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1784, title = {Effective Field Theory for Rydberg Polaritons}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/09/09}, pages = {113601}, abstract = {

We study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). We develop an EFT in one dimension and show how a suitably long medium can be used to prepare shallow N-body bound states. We then derive the effective N-body interaction potential for Rydberg polaritons and the associated N-body contact force that arises in the EFT. We use the contact force to find the leading order corrections to the binding energy of the N-body bound states and determine the photon number at which the EFT description breaks down. We find good agreement throughout between the predictions of EFT and numerical simulations of the exact two and three photon wavefunction transmission.

}, doi = {http://dx.doi.org/10.1103/PhysRevLett.117.113601}, url = {http://arxiv.org/abs/1605.05651}, author = {Michael Gullans and J. D. Thompson and Y. Wang and Q. -Y. Liang and V. Vuletic and M. D. Lukin and Alexey V. Gorshkov} } @article {2004, title = {Entanglement and spin-squeezing without infinite-range interactions}, year = {2016}, month = {2016/12/22}, abstract = {

Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/r α ) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α = 0) case. This indifference to the interaction range persists up to a critical value α = 2D/3, above which squeezing degrades continuously. Boundaryinduced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.

}, url = {https://arxiv.org/abs/1612.07805}, author = {Michael Foss-Feig and Zhe-Xuan Gong and Alexey V. Gorshkov and Charles W. Clark} } @article {1735, title = {Entangling distant resonant exchange qubits via circuit quantum electrodynamics}, journal = {Physical Review B}, volume = {94}, year = {2016}, month = {2016/11/16}, pages = {205421}, abstract = {

We investigate a hybrid quantum system consisting of spatially separated resonant exchange qubits, defined in three-electron semiconductor triple quantum dots, that are coupled via a superconducting transmission line resonator. Drawing on methods from circuit quantum electrodynamics and Hartmann-Hahn double resonance techniques, we analyze three specific approaches for implementing resonator-mediated two-qubit entangling gates in both dispersive and resonant regimes of interaction. We calculate entangling gate fidelities as well as the rate of relaxation via phonons for resonant exchange qubits in silicon triple dots and show that such an implementation is particularly well-suited to achieving the strong coupling regime. Our approach combines the favorable coherence properties of encoded spin qubits in silicon with the rapid and robust long-range entanglement provided by circuit QED systems.

}, doi = {10.1103/PhysRevB.94.205421}, url = {https://doi.org/10.1103/PhysRevB.94.205421}, author = {V. Srinivasa and J. M. Taylor and C. Tahan} } @article {1910, title = {Experimental demonstration of quantum fault tolerance}, year = {2016}, month = {2016/11/21}, abstract = {

Quantum computers will eventually reach a size at which quantum error correction (QEC) becomes imperative. In order to make quantum information robust to errors introduced by qubit imperfections and flawed control operations, QEC protocols encode a logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent correction or detection of errors without destroying the logical state itself through direct measurement. While several experiments have shown a reduction of high intrinsic or artificially introduced errors in logical qubits, fault-tolerant encoding of a logical qubit has never been demonstrated. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. This advantage persists in the face of large added error rates and experimental calibration errors.

}, url = {https://arxiv.org/abs/1611.06946}, author = {N. M. Linke and M. Gutierrez and K. A. Landsman and C. Figgatt and S. Debnath and K. R. Brown and C. Monroe} } @conference {1903, title = {Exponential Separation of Quantum Communication and Classical Information}, booktitle = {20th Annual Conference on Quantum Information Processing (QIP)}, year = {2016}, month = {2016/11/28}, abstract = {
We exhibit a Boolean function for which the quantum communication complexity is exponentially larger than the classical information complexity. An exponential separation in the other direction was already known from the work of Kerenidis et. al. [SICOMP 44, pp. 1550-1572], hence our work implies that these two complexity measures are incomparable. As classical information complexity is an upper bound on quantum information complexity, which in turn is equal to amortized quantum communication complexity, our work implies that a tight direct sum result for distributional quantum communication complexity cannot hold. The function we use to present such a separation is the Symmetric k-ary Pointer Jumping function introduced by Rao and Sinha [ECCC TR15-057], whose classical communication complexity is exponentially larger than its classical information complexity. In this paper, we show that the quantum communication complexity of this function is polynomially equivalent to its classical communication complexity. The high-level idea behind our proof is arguably the simplest so far for such an exponential separation between information and communication, driven by a sequence of round-elimination arguments, allowing us to simplify further the approach of Rao and Sinha.\ 
As another application of the techniques that we develop, we give a simple proof for an optimal trade-off between Alice\&$\#$39;s and Bob\&$\#$39;s communication while computing the related Greater-Than function on n bits: say Bob communicates at most b bits, then Alice must send n/exp(O(b)) bits to Bob. This holds even when allowing pre-shared entanglement. We also present a classical protocol achieving this bound.
}, url = {https://arxiv.org/abs/1611.08946}, author = {Anurag Anshu and Dave Touchette and Penghui Yao and Nengkun Yu} } @article {1912, title = {Figures of merit for quantum transducers}, year = {2016}, month = {2016/10/04}, abstract = {

Recent technical advances have sparked renewed interest in physical systems that couple simultaneously to different parts of the electromagnetic spectrum, thus enabling transduction of signals between vastly different frequencies at the level of single photons. Such hybrid systems have demonstrated frequency conversion of classical signals and have the potential of enabling quantum state transfer, e.g., between superconducting circuits and traveling optical signals. This Letter describes a simple approach for the theoretical characterization of performance for quantum transducers. Given that, in practice, one cannot attain ideal one-to-one quantum conversion, we will explore how well the transducer performs in various scenarios ranging from classical signal detection to applications for quantum information processing. While the performance of the transducer depends on the particular application in which it enters, we show that the performance can be characterized by defining two simple parameters: the signal transfer efficiency\ η\ and the added noise\ N.

}, url = {https://arxiv.org/abs/1610.01099}, author = {Emil Zeuthen and Albert Schliesser and Anders S. S{\o}rensen and J. M. Taylor} } @article {1925, title = {A finite presentation of CNOT-dihedral operators}, year = {2016}, month = {2016/12/31}, abstract = {

We give a finite presentation by generators and relations of unitary operators expressible over the {CNOT, T, X} gate set, also known as CNOT-dihedral operators. To this end, we introduce a notion of normal form for CNOT-dihedral circuits and prove that every CNOT-dihedral operator admits a unique normal form. Moreover, we show that in the presence of certain structural rules only finitely many circuit identities are required to reduce an arbitrary CNOT-dihedral circuit to its normal form. By appropriately restricting our relations, we obtain a finite presentation of unitary operators expressible over the {CNOT, T } gate set as a corollary.

}, url = {https://arxiv.org/abs/1701.00140}, author = {Matthew Amy and Jianxin Chen and Neil J. Ross} } @article {1527, title = {Flight of a heavy particle nonlinearly coupled to a quantum bath}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/01/28}, pages = {014309}, abstract = { Fluctuation and dissipation are by-products of coupling to the {\textquoteleft}environment.{\textquoteright} The Caldeira-Leggett model, a successful paradigm of quantum Brownian motion, views the environment as a collection of harmonic oscillators linearly coupled to the system. However, symmetry considerations may forbid a linear coupling, e.g. for a neutral particle in quantum electrodynamics. We argue that nonlinear couplings can lead to a fundamentally different behavior. Specifically, we consider a heavy particle quadratically coupled to quantum fluctuations of the bath. In one dimension the particle undergoes anomalous diffusion, unfolding as a power-law distribution in space, reminiscent of L\'{e}vy flights. We suggest condensed matter analogs where similar effects may arise. }, doi = {10.1103/PhysRevB.93.014309}, url = {http://arxiv.org/abs/1508.00582}, author = {Mohammad F. Maghrebi and Matthias Kr{\"u}ger and Mehran Kardar} } @article {1597, title = {Grover search and the no-signaling principle}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/09/14}, pages = {120501}, abstract = {

From an information processing point of view, two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply superluminal signaling, and despite a form of exponential parallelism, quantum mechanics does not imply polynomial-time brute force solution of NP-complete problems. Here, we investigate the degree to which these two properties are connected. We examine four classes of deviations from quantum mechanics, for which we draw inspiration from the literature on the black hole information paradox: nonunitary dynamics, non-Born-rule measurement, cloning, and postselection. We find that each model admits superluminal signaling if and only if it admits a query complexity speedup over Grover\&$\#$39;s algorithm. Furthermore, we show that the physical resources required to send a superluminal signal scale polynomially with the resources needed to speed up Grover\&$\#$39;s algorithm. Hence, one can perform a physically reasonable experiment demonstrating superluminal signaling if and only if one can perform a reasonable experiment inducing a speedup over Grover\&$\#$39;s algorithm.

}, url = {http://arxiv.org/abs/1511.00657}, author = {Ning Bao and Adam Bouland and Stephen P. Jordan} } @article {1694, title = {High resolution adaptive imaging of a single atom}, journal = {Nature Photonics}, year = {2016}, month = {2016/07/18}, pages = {606-610}, abstract = {

We report the optical imaging of a single atom with nanometer resolution using an adaptive optical alignment technique that is applicable to general optical microscopy. By decomposing the image of a single laser-cooled atom, we identify and correct optical aberrations in the system and realize an atomic position sensitivity of \≈ 0.5 nm/Hz\−\−\−\√ with a minimum uncertainty of 1.7 nm, allowing the direct imaging of atomic motion. This is the highest position sensitivity ever measured for an isolated atom, and opens up the possibility of performing out-of-focus 3D particle tracking, imaging of atoms in 3D optical lattices or sensing forces at the yoctonewton (10\−24 N) scale.

}, doi = {10.1038/nphoton.2016.136}, url = {https://www.nature.com/nphoton/journal/v10/n9/full/nphoton.2016.136.html}, author = {J. D. Wong-Campos and K. G. Johnson and Brian Neyenhuis and J. Mizrahi and Chris Monroe} } @article {1781, title = {A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/04/19}, pages = {043616}, abstract = {

We show that for ultra-cold neutral bosonic atoms held in a three-dimensional periodic potential or optical lattice, a Hubbard model with dominant, attractive three-body interactions can be generated. In fact, we derive that the effect of pair-wise interactions can be made small or zero starting from the realization that collisions occur at the zero-point energy of an optical lattice site and the strength of the interactions is energy dependent from effective-range contributions. We determine the strength of the two- and three-body interactions for scattering from van-der-Waals potentials and near Fano-Feshbach resonances. For van-der-Waals potentials, which for example describe scattering of alkaline-earth atoms, we find that the pair-wise interaction can only be turned off for species with a small negative scattering length, leaving the 88Sr isotope a possible candidate. Interestingly, for collisional magnetic Feshbach resonances this restriction does not apply and there often exist magnetic fields where the two-body interaction is small. We illustrate this result for several known narrow resonances between alkali-metal atoms as well as chromium atoms. Finally, we compare the size of the three-body interaction with hopping rates and describe limits due to three-body recombination.

}, doi = {10.1103/PhysRevA.93.043616}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.043616}, author = {Saurabh Paul and P. R. Johnson and Eite Tiesinga} } @article {1736, title = {Interacting atomic interferometry for rotation sensing approaching the Heisenberg Limit}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/11/11}, pages = {203002}, abstract = {

Atom interferometers provide exquisite measurements of the properties of non-inertial frames. While atomic interactions are typically detrimental to good sensing, efforts to harness entanglement to improve sensitivity remain tantalizing. Here we explore the role of interactions in an analogy between atomic gyroscopes and SQUIDs, motivated by recent experiments realizing ring shaped traps for ultracold atoms. We explore the one-dimensional limit of these ring systems with a moving weak barrier, such as that provided by a blue-detuned laser beam. In this limit, we employ Luttinger liquid theory and find an analogy with the superconducting phase-slip qubit, in which the topological charge associated with persistent currents can be put into superposition. In particular, we find that strongly-interacting atoms in such a system could be used for precision rotation sensing. We compare the performance of this new sensor to an equivalent non-interacting atom interferometer, and find improvements in sensitivity and bandwidth beyond the atomic shot-noise limit.

}, doi = {10.1103/PhysRevLett.117.203002}, url = {https://doi.org/10.1103/PhysRevLett.117.203002}, author = {Stephen Ragole and J. M. Taylor} } @article {1783, title = {Joint product numerical range and geometry of reduced density matrices}, year = {2016}, month = {2016/06/23}, abstract = {The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti{\textquoteright}s theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that ruled surface emerge naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines.}, url = {http://arxiv.org/abs/1606.07422}, author = {Jianxin Chen and Cheng Guo and Zhengfeng Ji and Yiu-Tung Poon and Nengkun Yu and Bei Zeng and Jie Zhou} } @article {1695, title = {Kaleidoscope of quantum phases in a long-range interacting spin-1 chain}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/05/11}, pages = {205115}, abstract = {Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as 1/rα, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for α≲3, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a U(1) continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future. }, doi = {http://dx.doi.org/10.1103/PhysRevB.93.205115}, url = {http://arxiv.org/abs/1510.02108}, author = {Zhe-Xuan Gong and Mohammad F. Maghrebi and Anzi Hu and Michael Foss-Feig and Philip Richerme and Christopher Monroe and Alexey V. Gorshkov} } @article {1821, title = {Landauer formulation of photon transport in driven systems}, journal = {Physical Review B}, volume = {94}, year = {2016}, month = {2016/10/20}, pages = {155437}, abstract = {

Understanding the behavior of light in non-equilibrium scenarios underpins much of quantum optics and optical physics. While lasers provide a severe example of a non-equilibrium problem, recent interests in the near-equilibrium physics of photon {\textquoteleft}gases\&$\#$39;, such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one reexamine some near-equilibrium cases. Here we consider how a sinusoidal parametric coupling between two semi-infinite photonic transmission lines leads to the creation and flow of photons between the two lines. Our approach provides a photonic analogue to the Landauer transport formula, and using non-equilbrium Green\&$\#$39;s functions, we can extend it to the case of an interacting region between two photonic {\textquoteleft}leads\&$\#$39; where the sinusoid frequency plays the role of a voltage bias. Crucially, we identify both the mathematical framework and the physical regime in which photonic transport is directly analogous to electronic transport, and regimes in which other new behavior such as two-mode squeezing can emerge.

}, doi = {10.1103/PhysRevB.94.155437}, url = {https://doi.org/10.1103/PhysRevB.94.155437}, author = {Chiao-Hsuan Wang and J. M. Taylor} } @article {1789, title = {Lattice Laughlin states on the torus from conformal field theory}, journal = {Journal of Statistical Mechanics: Theory and Experiment}, volume = {2016}, year = {2016}, month = {2016/01/28}, pages = {013102}, abstract = {Conformal field theory has turned out to be a powerful tool to derive two-dimensional lattice models displaying fractional quantum Hall physics. So far most of the work has been for lattices with open boundary conditions in at least one of the two directions, but it is desirable to also be able to handle the case of periodic boundary conditions. Here, we take steps in this direction by deriving analytical expressions for a family of conformal field theory states on the torus that is closely related to the family of bosonic and fermionic Laughlin states. We compute how the states transform when a particle is moved around the torus and when the states are translated or rotated, and we provide numerical evidence in particular cases that the states become orthonormal up to a common factor for large lattices. We use these results to find the S -matrix of the states, which turns out to be the same as for the continuum Laughlin states. Finally, we show that when the states are defined on a square lattice with suitable lattice spacing they practically coincide with the Laughlin states restricted to a lattice.}, url = {http://stacks.iop.org/1742-5468/2016/i=1/a=013102}, author = {Abhinav Deshpande and Anne E B Nielsen} } @article {1834, title = {Many-body decoherence dynamics and optimised operation of a single-photon switch}, journal = {New Journal of Physics}, volume = {18}, year = {2016}, month = {2016/09/13}, pages = {092001}, abstract = {

We develop a theoretical framework to characterize the decoherence dynamics due to multi-photon scattering in an all-optical switch based on Rydberg atom induced nonlinearities. By incorporating the knowledge of this decoherence process into optimal photon storage and retrieval strategies, we establish optimised switching protocols for experimentally relevant conditions, and evaluate the corresponding limits in the achievable fidelities. Based on these results we work out a simplified description that reproduces recent experiments [arXiv:1511.09445] and provides a new interpretation in terms of many-body decoherence involving multiple incident photons and multiple gate excitations forming the switch. Aside from offering insights into the operational capacity of realistic photon switching capabilities, our work provides a complete description of spin wave decoherence in a Rydberg quantum optics setting, and has immediate relevance to a number of further applications employing photon storage in Rydberg media.\ 

}, doi = {10.1088/1367-2630/18/9/092001}, url = {http://iopscience.iop.org/article/10.1088/1367-2630/18/9/092001}, author = {Callum R. Murray and Alexey V. Gorshkov and Thomas Pohl} } @article {1271, title = {Many-body localization in a quantum simulator with programmable random disorder}, journal = {Nature Physics}, year = {2016}, month = {2016/06/06}, abstract = {

When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. Exceptions to quantum thermalization have been predicted and observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize in spite of strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. Here we experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium. We observe the essential signatures of MBL: memory retention of the initial state, a Poissonian distribution of energy level spacings, and entanglement growth in the system at long times. Our platform can be scaled to higher numbers of spins, where detailed modeling of MBL becomes impossible due to the complexity of representing such entangled quantum states. Moreover, the high degree of control in our experiment may guide the use of MBL states as potential quantum memories in naturally disordered quantum systems.

}, doi = {10.1038/nphys3783}, url = {http://arxiv.org/abs/1508.07026v1}, author = {Jacob Smith and Aaron Lee and Philip Richerme and Brian Neyenhuis and Paul W. Hess and Philipp Hauke and Markus Heyl and David A. Huse and Christopher Monroe} } @article {1774, title = {Mapping constrained optimization problems to quantum annealing with application to fault diagnosis}, year = {2016}, abstract = {Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave{\textquoteright}s QA hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D-Wave{\textquoteright}s hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.}, url = {http://arxiv.org/abs/1603.03111}, author = {Bian, Zhengbing and Chudak, Fabian and Israel, Robert and Lackey, Brad and Macready, William G and Roy, Aidan} } @article {1859, title = {Mapping contrained optimization problems to quantum annealing with application to fault diagnosis}, journal = {Frontiers in ICT}, volume = {3}, year = {2016}, month = {2016/07/28}, pages = {14}, abstract = {

Current quantum annealing (QA) hardware suffers from practical limitations such as finite\ temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for\ mapping Boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations.\ In particular, we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with\ a fixed sparse set of interactions and propose two new decomposition algorithms for solving problems too\ large to map directly into hardware. The mapping technique is locally structured, as hardware compatible\ Ising models are generated for each problem constraint, and variables appearing in different constraints are\ chained together using ferromagnetic couplings. By contrast, global embedding techniques generate a\ hardware-independent Ising model for all the constraints, and then use a minor-embedding algorithm to\ generate\ a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling\ performance\ of the D-Wave hardware using the local mapping technique is significantly better than global\ embedding. We validate\ the approach by applying D- Wave\’s QA hardware to circuit-based fault diagnosis.\ For circuits that embed directly, we\ find that the hardware is typically able to find all solutions from a\ min-fault diagnosis set of size N using 1000 N samples,\ using an annealing rate that is 25 times faster than\ a leading SAT-based sampling method. Furthermore, we apply\ decomposition algorithms to find min-cardinality\ faults for circuits that are up to 5 times larger than can be solved directly on current hardware.

}, url = {http://journal.frontiersin.org/article/10.3389/fict.2016.00014/full}, author = {Bian, Zhengbing and Chudak, Fabian and Robert Brian Israel and Brad Lackey and Macready, William G and Aiden Roy} } @article {2508, title = {Measurement Protocol for the Entanglement Spectrum of Cold Atoms}, journal = {Phys. Rev. X }, volume = {6(4)}, year = {2016}, month = {2016/11/22}, abstract = {

Entanglement, and, in particular the entanglement spectrum, plays a major role in characterizing many-body quantum systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to date because of the lack of an implementable measurement scheme. Here, we propose a measurement protocol to access the entanglement spectrum of many-body states in experiments with cold atoms in optical lattices. Our scheme effectively performs a Ramsey spectroscopy of the entanglement Hamiltonian and is based on the ability to produce several copies of the state under investigation together with the possibility to perform a global swap gate between two copies conditioned on the state of an auxiliary qubit. We show how the required conditional swap gate can be implemented with cold atoms, either by using Rydberg interactions or coupling the atoms to a cavity mode. We illustrate these ideas on a simple (extended) Bose-Hubbard model where such a measurement protocol reveals topological features of the Haldane phase.\ 

}, doi = {https://doi.org/10.1103/PhysRevX.6.041033}, url = {https://arxiv.org/abs/1605.08624}, author = {Hannes Pichler and Guanyu Zhu and Alireza Seif and Peter Zoller and Mohammad Hafezi} } @article {1914, title = {Multiple scattering dynamics of fermions at an isolated p-wave resonance}, journal = {Nature Communications}, volume = {7}, year = {2016}, month = {2016/07/11}, pages = {12069}, abstract = {

The wavefunction for indistinguishable fermions is anti-symmetric under particle exchange, which directly leads to the Pauli exclusion principle, and hence underlies the structure of atoms and the properties of almost all materials. In the dynamics of collisions between two indistinguishable fermions this requirement strictly prohibits scattering into 90 degree angles. Here we experimentally investigate the collisions of ultracold clouds fermionic\ 40K\ atoms by directly measuring scattering distributions. With increasing collision energy we identify the Wigner threshold for p-wave scattering with its tell-tale dumb-bell shape and no\ 90o\ yield. Above this threshold effects of multiple scattering become manifest as deviations from the underlying binary p-wave shape, adding particles either isotropically or axially. A shape resonance for\ 40K\ facilitates the separate observation of these two processes. The isotropically enhanced multiple scattering mode is a generic p-wave threshold phenomenon, while the axially enhanced mode should occur in any colliding particle system with an elastic scattering resonance.

}, doi = {10.1038/ncomms12069}, url = {http://www.nature.com/articles/ncomms12069}, author = {Ryan Thomas and Kris O. Roberts and Eite Tiesinga and Andrew C.J. Wade and P. Blair Blakie and Amita B. Deb and Niels Kj{\ae}rgaard} } @article {1162, title = {Nonequilibrium many-body steady states via Keldysh formalism}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/01/27}, pages = {014307}, abstract = { Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. While these states and their phase transitions have been studied extensively with mean field theory, the validity of the mean field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class. }, doi = {10.1103/PhysRevB.93.014307}, url = {http://arxiv.org/abs/1507.01939}, author = {Mohammad F. Maghrebi and Alexey V. Gorshkov} } @article {2005, title = {{O}bservation of {P}rethermalization in {L}ong-{R}ange {I}nteracting {S}pin {C}hains}, year = {2016}, month = {2016/08/02}, abstract = {

Statistical mechanics can predict thermal equilibrium states for most classical systems, but for an isolated quantum system there is no general understanding on how equilibrium states dynamically emerge from the microscopic Hamiltonian. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale and, instead, relax to quasi-stationary prethermal states that can be described by statistical mechanics when approximately conserved quantities are appropriately included in a generalized Gibbs ensemble (GGE). Here we experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse field Ising Hamiltonian following a sudden quench. For sufficiently long-ranged interactions the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. In this case, the prethermal state cannot be described by a GGE, but rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a significantly broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.

}, url = {https://arxiv.org/abs/1608.00681}, author = {B. Neyenhuis and J. Smith and A. C. Lee and J. Zhang and P. Richerme and P. W. Hess and Z. -X. Gong and Alexey V. Gorshkov and C. Monroe} } @article {1822, title = {Observation of Optomechanical Quantum Correlations at Room Temperature}, year = {2016}, month = {2016/05/18}, abstract = {

By shining laser light through a nanomechanical beam, we measure the beam\&$\#$39;s thermally driven vibrations and perturb its motion with optical forces at a level dictated by the Heisenberg measurement-disturbance uncertainty relation. Such quantum backaction is typically difficult to observe at room temperature where the motion driven by optical quantum intensity fluctuations is many orders of magnitude smaller than the thermal motion. We demonstrate a cross-correlation technique to distinguish optically driven motion from thermally driven motion, observing this quantum backaction signature up to room temperature. While it is often difficult to absolutely calibrate optical detection, we use the scale of the quantum correlations, which is determined by fundamental constants, to gauge the size of thermal motion, demonstrating a path towards absolute thermometry with quantum mechanically calibrated ticks.

}, url = {http://arxiv.org/abs/1605.05664}, author = {T. P. Purdy and K. E. Grutter and K. Srinivasan and J. M. Taylor} } @article {1533, title = {Optimal ancilla-free Clifford+T approximation of z-rotations}, journal = {Quantum Information and Computation}, volume = {16}, year = {2016}, pages = {901-953}, abstract = {

We consider the problem of decomposing arbitrary single-qubit z-rotations into ancilla-free Clifford+T circuits, up to given epsilon. We present a new efficient algorithm for solving this problem optimally, i.e., for finding the shortest possible circuit whatsoever for the given problem instance. The algorithm requires a factoring oracle (such as a quantum computer). Even in the absence of a factoring oracle, the algorithm is still near-optimal: In this case, it finds a solution of T-count m + O(log(log(1/epsilon))), where m is the T-count of the second-to-optimal solution. In the typical case, this yields circuit decompositions of T-count 3log_2(1/epsilon) + O(log(log(1/epsilon))).

}, url = {http://arxiv.org/abs/1403.2975v2}, author = {Neil J. Ross and Peter Selinger} } @article {1715, title = {Optimal and asymptotically optimal NCT reversible circuits by the gate types}, journal = {Quantum Information \& Computation}, volume = {16}, year = {2016}, month = {2016/08/23}, pages = {1096-1112}, abstract = {

We report optimal and asymptotically optimal reversible circuits composed of NOT, CNOT, and Toffoli (NCT) gates, keeping the count by the subsets of the gate types used. This study fine tunes the circuit complexity figures for the realization of reversible functions via reversible NCT circuits. An important consequence is a result on the limitation of the use of the T-count quantum circuit metric popular in applications.

}, url = {http://arxiv.org/abs/1602.02627}, author = {Dmitri Maslov} } @article {1554, title = {Optimal quantum algorithm for polynomial interpolation}, journal = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, volume = {55}, year = {2016}, month = {2016/03/01}, pages = {16:1--16:13}, abstract = {

We consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over GF(q). A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2+1/2 quantum queries are needed to solve this problem with bounded error, whereas an algorithm of Boneh and Zhandry shows that d quantum queries are sufficient. We show that the lower bound is achievable: d/2+1/2 quantum queries suffice to determine the polynomial with bounded error. Furthermore, we show that d/2+1 queries suffice to achieve probability approaching 1 for large q. These upper bounds improve results of Boneh and Zhandry on the insecurity of cryptographic protocols against quantum attacks. We also show that our algorithm\&$\#$39;s success probability as a function of the number of queries is precisely optimal. Furthermore, the algorithm can be implemented with gate complexity poly(log q) with negligible decrease in the success probability.

}, isbn = {978-3-95977-013-2}, issn = {1868-8969}, doi = {http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.16}, url = {http://arxiv.org/abs/1509.09271}, author = {Andrew M. Childs and Wim van Dam and Shih-Han Hung and Igor E. Shparlinski} } @article {1235, title = {Optimal state discrimination and unstructured search in nonlinear quantum mechanics}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/02/11}, pages = {022314}, abstract = { Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics. }, doi = {10.1103/PhysRevA.93.022314}, url = {http://arxiv.org/abs/1507.06334}, author = {Andrew M. Childs and Joshua Young} } @article {1909, title = {Optimized tomography of continuous variable systems using excitation counting}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/11/21}, pages = {052327}, abstract = {

We propose a systematic procedure to optimize quantum state tomography protocols for continuous variable systems based on excitation counting preceded by a displacement operation. Compared with conventional tomography based on Husimi or Wigner function measurement, the excitation counting approach can significantly reduce the number of measurement settings. We investigate both informational completeness and robustness, and provide a bound of reconstruction error involving the condition number of the sensing map. We also identify the measurement settings that optimize this error bound, and demonstrate that the improved reconstruction robustness can lead to an order-of-magnitude reduction of estimation error with given resources. This optimization procedure is general and can incorporate prior information of the unknown state to further simplify the protocol.

}, doi = {10.1103/PhysRevA.94.052327}, url = {http://link.aps.org/doi/10.1103/PhysRevA.94.052327}, author = {Shen, Chao and Heeres, Reinier W. and Reinhold, Philip and Jiang, Luyao and Yi-Kai Liu and Schoelkopf, Robert J. and Jiang, Liang} } @article {1705, title = {Performance of QAOA on Typical Instances of Constraint Satisfaction Problems with Bounded Degree}, year = {2016}, month = {2016/01/08}, abstract = {We consider constraint satisfaction problems of bounded degree, with a good notion of "typicality", e.g. the negation of the variables in each constraint is taken independently at random. Using the quantum approximate optimization algorithm (QAOA), we show that μ+Ω(1/D--√) fraction of the constraints can be satisfied for typical instances, with the assignment efficiently produced by QAOA. We do so by showing that the averaged fraction of constraints being satisfied is μ+Ω(1/D--√), with small variance. Here μ is the fraction that would be satisfied by a uniformly random assignment, and D is the number of constraints that each variable can appear. CSPs with typicality include Max-kXOR and Max-kSAT. We point out how it can be applied to determine the typical ground-state energy of some local Hamiltonians. We also give a similar result for instances with "no overlapping constraints", using the quantum algorithm. We sketch how the classical algorithm might achieve some partial result.}, url = {http://arxiv.org/abs/1601.01744}, author = {Cedric Yen-Yu Lin and Yechao Zhu} } @article {1697, title = {Photoassociation of spin polarized Chromium}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/02/29}, pages = {021406}, abstract = {We report the homonuclear photoassociation (PA) of ultracold 52Cr atoms in an optical dipole trap. This constitutes the first measurement of PA in an element with total electron spin S~>1. Although Cr, with its 7S3 ground and 7P4,3,2 excited states, is expected to have a complicated PA spectrum we show that a spin polarized cloud exhibits a remarkably simple PA spectrum when circularly polarized light is applied. Over a scan range of 20 GHz below the 7P3 asymptote we observe two distinct vibrational series each following a LeRoy-Bernstein law for a C3/R3 potential with excellent agreement. We determine the C3 coefficients of the Hund{\textquoteright}s case c) relativistic adiabatic potentials to be -1.83{\textpm}0.02 a.u. and -1.46{\textpm}0.01a.u.. Theoretical non-rotating Movre-Pichler calculations enable a first assignment of the series to Ω=6u and 5g potential energy curves. In a different set of experiments we disturb the selection rules by a transverse magnetic field which leads to additional PA series.}, doi = {10.1103/PhysRevA.93.021406}, url = {http://arxiv.org/abs/1512.04378}, author = {Jahn R{\"u}hrig and Tobias B{\"a}uerle and Paul S. Julienne and Eite Tiesinga and Tilman Pfau} } @article {1832, title = {Practical Approximation of Single-Qubit Unitaries by Single-Qubit Quantum Clifford and T Circuits}, journal = {IEEE Transactions on Computers}, volume = {65}, year = {2016}, month = {2016/01/01}, pages = {161 - 172}, abstract = {

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation down to size 10-15, resulting in the optimal single-qubit circuit designs required for implementation of scalable quantum algorithms. Our implementation along with the experimental results are available in the public domain.

}, issn = {0018-9340}, doi = {10.1109/TC.2015.2409842}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=7056491http://xplorestaging.ieee.org/ielx7/12/7350319/7056491.pdf?arnumber=7056491}, author = {Vadym Kliuchnikov and Dmitri Maslov and Michele Mosca} } @article {1706, title = {Pure-state tomography with the expectation value of Pauli operators}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/03/31}, pages = {032140}, abstract = {

We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary n-qubit pure state among all quantum states. We show that only 11 Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with 16 measurements, and only 31 Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with 64 measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.

}, doi = {http://dx.doi.org/10.1103/PhysRevA.93.032140}, url = {http://arxiv.org/abs/1601.05379}, author = {Xian Ma and Tyler Jackson and Hui Zhou and Jianxin Chen and Dawei Lu and Michael D. Mazurek and Kent A.G. Fisher and Xinhua Peng and David Kribs and Kevin J. Resch and Zhengfeng Ji and Bei Zeng and Raymond Laflamme} } @article {1707, title = {Quantifying the coherence of pure quantum states}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/10/07}, pages = {042313}, abstract = {

In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an explicit characterization of the closest incoherent state to a given pure state under the trace distance measure of coherence, and we affirm a recent conjecture that the l1 measure of coherence of a pure state is never smaller than its relative entropy of coherence. We then use our result to show that the states maximizing the trace distance of coherence are exactly the maximally coherent states, and we derive a new inequality relating the negativity and distillable entanglement of pure states.

}, doi = {10.1103/PhysRevA.94.042313}, url = {https://doi.org/10.1103/PhysRevA.94.042313}, author = {Jianxin Chen and Nathaniel Johnston and Chi-Kwong Li and Sarah Plosker} } @article {1704, title = {Quantum Merlin Arthur with Exponentially Small Gap}, year = {2016}, month = {2016/01/08}, abstract = {We study the complexity of QMA proof systems with inverse exponentially small promise gap. We show that this class can be exactly characterized by PSPACE, the class of problems solvable with a polynomial amount of memory. As applications we show that a "precise" version of the Local Hamiltonian problem is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states is not as powerful as the ability to prepare the ground state of general Local Hamiltonians.}, url = {http://arxiv.org/abs/1601.01975}, author = {Bill Fefferman and Cedric Yen-Yu Lin} } @article {1330, title = {A Quantum Model for an Entropic Spring}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/06/01}, pages = {214102}, abstract = {

Motivated by understanding the emergence of thermodynamic restoring forces and oscillations, we develop a quantum-mechanical model of a bath of spins coupled to the elasticity of a material. We show our model reproduces the behavior of a variety of entropic springs while enabling investigation of non-equilibrium resonator states in the quantum domain. We find our model emerges naturally in disordered elastic media such as glasses, and is an additional, expected effect in systems with anomalous specific heat and 1/f noise at low temperatures due to two-level systems that fluctuate.

}, doi = {http://dx.doi.org/10.1103/PhysRevB.93.214102}, url = {http://arxiv.org/abs/1507.08658v1}, author = {Chiao-Hsuan Wang and J. M. Taylor} } @article {1713, title = {On Quantum Obfuscation}, year = {2016}, month = {2016/02/04}, abstract = {Encryption of data is fundamental to secure communication in the modern world. Beyond encryption of data lies obfuscation, i.e., encryption of functionality. It is well-known that the most powerful means of obfuscating classical programs, so-called {\textquoteleft}{\textquoteleft}black-box obfuscation{\textquoteright},{\textquoteright} is provably impossible [Barak et al {\textquoteright}12]. However, several recent results have yielded candidate schemes that satisfy a definition weaker than black-box, and yet still have numerous applications. In this work, we initialize the rigorous study of obfuscating programs via quantum-mechanical means. We define notions of quantum obfuscation which encompass several natural variants. The input to the obfuscator can describe classical or quantum functionality, and the output can be a circuit description or a quantum state. The obfuscator can also satisfy one of a number of obfuscation conditions: black-box, information-theoretic black-box, indistinguishability, and best possible; the last two conditions come in three variants: perfect, statistical, and computational. We discuss many applications, including CPA-secure quantum encryption, quantum fully-homomorphic encryption, and public-key quantum money. We then prove several impossibility results, extending a number of foundational papers on classical obfuscation to the quantum setting. We prove that quantum black-box obfuscation is impossible in a setting where adversaries can possess more than one output of the obfuscator. In particular, generic transformation of quantum circuits into black-box-obfuscated quantum circuits is impossible. We also show that statistical indistinguishability obfuscation is impossible, up to an unlikely complexity-theoretic collapse. Our proofs involve a new tool: chosen-ciphertext-secure encryption of quantum data, which was recently shown to be possible assuming quantum-secure one-way functions exist [Alagic et al {\textquoteright}16].}, url = {http://arxiv.org/abs/1602.01771}, author = {Gorjan Alagic and Bill Fefferman} } @article {1733, title = {A Quantum Version of Sch{\"o}ning{\textquoteright}s Algorithm Applied to Quantum 2-SAT}, journal = {Quantum Information and Computation}, volume = {16}, year = {2016}, month = {2016/03/22}, abstract = {

We study a quantum algorithm that consists of a simple quantum Markov process, and we analyze its behavior on restricted versions of Quantum 2-SAT. We prove that the algorithm solves this decision problem with high probability for n qubits, L clauses, and promise gap c in time O(n^2 L^2 c^{-2}). If the Hamiltonian is additionally polynomially gapped, our algorithm efficiently produces a state that has high overlap with the satisfying subspace. The Markov process we study is a quantum analogue of Sch\"oning\&$\#$39;s probabilistic algorithm for k-SAT.

}, url = {http://arxiv.org/abs/1603.06985}, author = {Edward Farhi and Shelby Kimmel and Kristan Temme} } @article {1911, title = {Quantum-Enhanced Machine Learning}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/09/20}, pages = {130501}, abstract = {

The emerging field of quantum machine learning has the potential to substantially aid in the problems and scope of artificial intelligence. This is only enhanced by recent successes in the field of classical machine learning. In this work we propose an approach for the systematic treatment of machine learning, from the perspective of quantum information. Our approach is general and covers all three main branches of machine learning: supervised, unsupervised, and reinforcement learning. While quantum improvements in supervised and unsupervised learning have been reported, reinforcement learning has received much less attention. Within our approach, we tackle the problem of quantum enhancements in reinforcement learning as well, and propose a systematic scheme for providing improvements. As an example, we show that quadratic improvements in learning efficiency, and exponential improvements in performance over limited time periods, can be obtained for a broad class of learning problems.

}, doi = {10.1103/PhysRevLett.117.130501}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.117.130501}, author = {Dunjko, Vedran and J. M. Taylor and Briegel, Hans J.} } @article {1957, title = {A quasi-mode theory of chiral phonons}, year = {2016}, month = {2016/12/29}, abstract = {

The coherence properties of mechanical resonators are often limited by multiple unavoidable forms of loss -- including phonon-phonon and phonon-defect scattering -- which result in the scattering of sound into other resonant modes and into the phonon bath. Dynamic suppression of this scattering loss can lift constraints on device structure and can improve tolerance to defects in the material, even after fabrication. Inspired by recent experiments, here we introduce a model of phonon losses resulting from disorder in a whispering gallery mode resonator with acousto-optical coupling between optical and mechanical modes. We show that a typical elastic scattering mechanism of high quality factor (Q) mechanical modes flips the direction of phonon propagation via high-angle scattering, leading to damping into modes with the opposite parity. When the optical mode overlaps co-propagating high-Q and bulk mechanical modes, the addition of laser cooling via sideband-resolved damping of the mechanical mode of a chosen parity also damps and modifies the response of the bulk modes of the same parity. This, in turn, simultaneously improves the quality factor and reduces the thermal load of the counter-propagating high-Q modes, leading to the dynamical creation of a cold phononic shield. We compare our theoretical results to the recent experiments of Kim et al., and find quantitative agreement with our theory.

}, url = {https://arxiv.org/abs/1612.09240}, author = {Xunnong Xu and Seunghwi Kim and Gaurav Bahl and J. M. Taylor} } @article {1187, title = {Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms}, journal = {Physical Review A}, volume = {93}, year = {2016}, month = {2016/05/06}, abstract = {

We show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the Sn symmetry that permutes atoms occupying different vibrational levels of the trap and the SU(N) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU(N) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.

}, doi = {10.1103/PhysRevA.93.051601}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.051601}, author = {Michael E. Beverland and Gorjan Alagic and Michael J. Martin and Andrew P. Koller and Ana M. Rey and Alexey V. Gorshkov} } @article {1883, title = {Robust Protocols for Securely Expanding Randomness and Distributing Keys Using Untrusted Quantum Devices}, journal = {Journal of the ACM}, volume = {63}, year = {2016}, month = {2016/10/26}, pages = {33:1{\textendash}33:63}, abstract = {

Randomness is a vital resource for modern-day information processing, especially for cryptography. A wide range of applications critically rely on abundant, high-quality random numbers generated securely. Here, we show how to expand a random seed at an exponential rate without trusting the underlying quantum devices. Our approach is secure against the most general adversaries, and has the following new features: cryptographic level of security, tolerating a constant level of imprecision in devices, requiring only unit size quantum memory (for each device component) in an honest implementation, and allowing a large natural class of constructions for the protocol. In conjunction with a recent work by Chung et al. [2014], it also leads to robust unbounded expansion using just 2 multipart devices. When adapted for distributing cryptographic keys, our method achieves, for the first time, exponential expansion combined with cryptographic security and noise tolerance. The proof proceeds by showing that the R{\'e}nyi divergence of the outputs of the protocol (for a specific bounding operator) decreases linearly as the protocol iterates. At the heart of the proof are a new uncertainty principle on quantum measurements and a method for simulating trusted measurements with untrusted devices.

}, keywords = {key distribution, nonlocal games, privacy, quantum cryptography, random-number generation, untrusted device}, issn = {0004-5411}, doi = {10.1145/2885493}, url = {http://doi.acm.org/10.1145/2885493}, author = {Carl Miller and Yaoyun Shi} } @article {1772, title = {Self-organization of atoms coupled to a chiral reservoir}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/11/29}, pages = {053855}, abstract = {

Tightly confined modes of light, as in optical nanofibers or photonic crystal waveguides, can lead to large optical coupling in atomic systems, which mediates long-range interactions between atoms. These one-dimensional systems can naturally possess couplings that are asymmetric between modes propagating in different directions. Strong long-range interaction among atoms via these modes can drive them to a self-organized periodic distribution. In this paper, we examine the self-organizing behavior of atoms in one dimension coupled to a chiral reservoir. We determine the solution to the equations of motion in different parameter regimes, relative to both the detuning of the pump laser that initializes the atomic dipole-dipole interactions and the degree of reservoir chirality. In addition, we calculate possible experimental signatures such as reflectivity from self-organized atoms and motional sidebands.

}, doi = {10.1103/PhysRevA.94.053855}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.053855}, author = {Zachary Eldredge and Pablo Solano and Darrick Chang and Alexey V. Gorshkov} } @article {1603, title = {Serialized Quantum Error Correction Protocol for High-Bandwidth Quantum Repeaters}, journal = {New Journal of Physics}, volume = {18}, year = {2016}, month = {2016/09/02}, pages = {093008}, abstract = {

Advances in single photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code. Such error-corrected communication is equivalent to a novel quantum repeater scheme, but crucial questions regarding implementation and system requirements remain open. Here we show that long range entangled bit generation with rates approaching $10^8$ ebits/s may be possible using a completely serialized protocol, in which photons are generated, entangled, and error corrected via sequential, one-way interactions with a minimal number of matter qubits. Provided loss and error rates of the required elements are below the threshold for quantum error correction, this scheme demonstrates improved performance over transmission of single photons. We find improvement in ebit rates at large distances using this serial protocol and various quantum error correcting codes.

}, doi = {10.1088/1367-2630/18/9/093008}, url = {http://iopscience.iop.org/article/10.1088/1367-2630/18/9/093008/meta}, author = {Andrew N. Glaudell and Edo Waks and J. M. Taylor} } @article {1692, title = {Sisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum Dot}, journal = {Physical Review Letters}, volume = {117}, year = {2016}, month = {2016/07/25}, pages = {056801}, abstract = {

A strongly driven quantum system, coupled to a thermalizing bath, generically evolves into a highly non-thermal state as the external drive competes with the equilibrating force of the bath. We demonstrate a notable exception to this picture for a microwave resonator interacting with a periodically driven double quantum dot (DQD). In the limit of strong driving and long times, we show that the resonator field can be driven into a thermal state with a chemical potential given by a harmonic of the drive frequency. Such tunable chemical potentials are achievable with current devices and would have broad utility for quantum simulation in circuit quantum electrodynamics. As an example, we show how several DQDs embedded in an array of microwave resonators can induce a phase transition to a Bose-Einstein condensate of light.

}, doi = {http://dx.doi.org/10.1103/PhysRevLett.117.056801}, url = {http://arxiv.org/abs/1512.01248}, author = {Michael Gullans and J. Stehlik and Y. -Y. Liu and J. R. Petta and J. M. Taylor} } @article {1818, title = {Space-Efficient Error Reduction for Unitary Quantum Computations}, journal = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, volume = {55}, year = {2016}, month = {2016/04/27}, pages = {14:1--14:14}, abstract = {

This paper develops general space-efficient methods for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness\ c\ and soundnesss, either with or without a witness (corresponding to QMA and BQP, respectively). To convert this computation into a new computation with error at most\ 2\−p, the most space-efficient method known requires extra workspace of\ O(plog1c\−s)\ qubits. This space requirement is too large for scenarios like logarithmic-space quantum computations. This paper presents error-reduction methods for unitary quantum computations (i.e., computations without intermediate measurements) that require extra workspace of just\ O(logpc\−s)\ qubits. This in particular gives the first methods of strong amplification for logarithmic-space unitary quantum computations with two-sided bounded error. This also leads to a number of consequences in complexity theory, such as the uselessness of quantum witnesses in bounded-error logarithmic-space unitary quantum computations, the PSPACE upper bound for QMA with exponentially-small completeness-soundness gap, and strong amplification for matchgate computations.

}, isbn = {978-3-95977-013-2}, issn = {1868-8969}, doi = {http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.14}, url = {http://drops.dagstuhl.de/opus/volltexte/2016/6297}, author = {Bill Fefferman and Hirotada Kobayashi and Cedric Yen-Yu Lin and Tomoyuki Morimae and Harumichi Nishimura} } @article {1907, title = {Steady-state superradiance with Rydberg polaritons}, journal = {arXiv:1611.00797}, year = {2016}, month = {2016/11/02}, abstract = {

A steady-state superradiant laser can be used to generate ultranarrow-linewidth light, and thus has important applications in the fields of quantum information and precision metrology. However, the light produced by such a laser is still essentially classical. Here, we show that the introduction of a Rydberg medium into a cavity containing atoms with a narrow optical transition can lead to the steady-state superradiant emission of ultranarrow-linewidth\ nonclassical\ light. The cavity nonlinearity induced by the Rydberg medium strongly modifies the superradiance threshold, and leads to a Mollow triplet in the cavity output spectrum\−this behavior can be understood as an unusual analogue of resonance fluorescence. The cavity output spectrum has an extremely sharp central peak, with a linewidth that can be far narrower than that of a classical superradiant laser. This unprecedented spectral sharpness, together with the nonclassical nature of the light, could lead to new applications in which spectrally pure\ quantum\ light is desired.

}, url = {https://arxiv.org/abs/1611.00797}, author = {Zhe-Xuan Gong and Minghui Xu and Michael Foss-Feig and James K. Thompson and Ana Maria Rey and Murray Holland and Alexey V. Gorshkov} } @article {2006, title = {Subwavelength-width optical tunnel junctions for ultracold atoms}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/12/27}, pages = {063422}, abstract = {

We propose a method for creating far-field optical barrier potentials for ultracold atoms with widths that are narrower than the diffraction limit and can approach tens of nanometers. The reduced widths stem from the nonlinear atomic response to control fields that create spatially varying dark resonances. The subwavelength barrier is the result of the geometric scalar potential experienced by an atom prepared in such a spatially varying dark state. The performance of this technique, as well as its applications to the study of many-body physics and to the implementation of quantum-information protocols with ultracold atoms, are discussed, with a focus on the implementation of tunnel junctions.

}, doi = {10.1103/PhysRevA.94.063422}, url = {http://link.aps.org/doi/10.1103/PhysRevA.94.063422}, author = {Jendrzejewski, F. and Eckel, S. and Tiecke, T. G. and G. Juzeliunas and Campbell, G. K. and Jiang, Liang and Alexey V. Gorshkov} } @article {1782, title = {Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/08/05}, pages = {023607}, abstract = {

We determine the exact time evolution of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a hexagonal optical lattice. The dynamical evolution is triggered by ramping the lattice potential up, such that the interaction strength Uf is much larger than the hopping amplitude Jf. The quench initiates collective oscillations with frequency |Uf|/(2π) in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the order parameter Δ. The latter is not reproduced by treating the time evolution in mean-field theory. The momentum density-density or noise correlation functions oscillate at frequency |Uf|/2π as well as its second harmonic. For a very deep lattice, with negligible tunneling energy, the oscillations of momentum occupation numbers are undamped. Non-zero tunneling after the quench leads to dephasing of the different momentum modes and a subsequent damping of the oscillations. This occurs even for a finite-temperature initial BCS state, but not for a non-interacting Fermi gas. We therefore propose to use this dephasing to detect a BCS state. Finally, we predict that the noise correlation functions in a honeycomb lattice will develop strong anti-correlations near the Dirac point.

}, doi = {http://dx.doi.org/10.1103/PhysRevA.94.023607}, url = {http://arxiv.org/abs/1602.00979}, author = {Marlon Nuske and L. Mathey and Eite Tiesinga} } @article {1689, title = {Tomography is necessary for universal entanglement detection with single-copy observables}, journal = {Physical Review Letters}, volume = {116}, year = {2016}, month = {2016/06/07}, pages = {230501}, abstract = {Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.}, doi = {10.1103/PhysRevLett.116.230501}, url = {http://arxiv.org/abs/1511.00581}, author = {Dawei Lu and Tao Xin and Nengkun Yu and Zhengfeng Ji and Jianxin Chen and Guilu Long and Jonathan Baugh and Xinhua Peng and Bei Zeng and Raymond Laflamme} } @article {1191, title = {Topological phases with long-range interactions}, journal = {Physical Review B}, volume = {93}, year = {2016}, month = {2016/01/08}, pages = {041102}, abstract = { Topological phases of matter are primarily studied in quantum many-body systems with short-range interactions. Whether various topological phases can survive in the presence of long-range interactions, however, is largely unknown. Here we show that a paradigmatic example of a symmetry-protected topological phase, the Haldane phase of an antiferromagnetic spin-1 chain, surprisingly remains intact in the presence of arbitrarily slowly decaying power-law interactions. The influence of long-range interactions on the topological order is largely quantitative, and we expect similar results for more general systems. Our conclusions are based on large-scale matrix-product-state simulations and two complementary effective-field-theory calculations. The striking agreement between the numerical and analytical results rules out finite-size effects. The topological phase considered here should be experimentally observable in a recently developed trapped-ion quantum simulator. }, doi = {10.1103/PhysRevB.93.041102}, url = {http://arxiv.org/abs/1505.03146}, author = {Zhe-Xuan Gong and Mohammad F. Maghrebi and Anzi Hu and Michael L. Wall and Michael Foss-Feig and Alexey V. Gorshkov} } @article {1517, title = {Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb tester}, journal = {Theory of Computing}, volume = {12}, year = {2016}, month = {2016/11/28}, pages = {1-35}, abstract = {

Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity $Q(f)$, and show that $B(f)=\Theta(Q(f)^2)$. This result gives a new method to upper bound the quantum query complexity: we give a method of finding bomb query algorithms from classical algorithms, which then provide nonconstructive upper bounds on $Q(f)=\Theta(\sqrt{B(f)})$. We subsequently were able to give explicit quantum algorithms matching our upper bound method. We apply this method on the single-source shortest paths problem on unweighted graphs, obtaining an algorithm with $O(n^{1.5})$ quantum query complexity, improving the best known algorithm of $O(n^{1.5}\sqrt{\log n})$ [arXiv:quant-ph/0606127]. Applying this method to the maximum bipartite matching problem gives an $O(n^{1.75})$ algorithm, improving the best known trivial $O(n^2)$ upper bound.

}, doi = {10.4086/toc.2016.v012a018}, url = {http://theoryofcomputing.org/articles/v012a018/}, author = {Cedric Yen-Yu Lin and Han-Hsuan Lin} } @article {1823, title = {Wannier functions using a discrete variable representation for optical lattices}, journal = {Physical Review A}, volume = {94}, year = {2016}, month = {2016/09/07}, pages = {033606}, abstract = {

We propose a numerical method using the discrete variable representation (DVR) for constructing real-valued Wannier functions localized in a unit cell for both symmetric and asymmetric periodic potentials. We apply these results to finding Wannier functions for ultracold atoms trapped in laser-generated optical lattices. Following S. Kivelson [Phys. Rev. B26, 4269 (1982)], for a symmetric lattice with inversion symmetry, we construct Wannier functions as eigenstates of the position operators\ x,y, and\ z\ restricted to single-particle Bloch functions belonging to one or more bands. To ensure that the Wannier functions are real-valued, we numerically obtain the band structure and real-valued eigenstates using a uniform Fourier grid DVR. We then show, by a comparison of tunneling energies, that the Wannier functions are accurate for both inversion-symmetric and asymmetric potentials to better than 10 significant digits when using double-precision arithmetic. The calculations are performed for an optical lattice with double-wells per unit cell with tunable asymmetry along the\ x\ axis and a single sinusoidal potential along the perpendicular directions. Localized functions at the two potential minima within each unit cell are similarly constructed, but using a superposition of single-particle solutions from the two lowest bands. We finally use these localized basis functions to determine the two-body interaction energies in the Bose-Hubbard model and show the dependence of these energies on lattice asymmetry.

}, doi = {http://dx.doi.org/10.1103/PhysRevA.94.033606}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.033606}, author = {Saurabh Paul and Eite Tiesinga} } @article {1602, title = {Whose Information? Information About What?}, journal = {Quantum [Un]Speakables II: 50 Years of Bell{\textquoteright}s Theorem}, year = {2016}, month = {2016/01/01}, author = {Jeffrey Bub and Anton Zeilinger and Reinhold Bertlmann} } @article {1393, title = {Yang-Baxter operators need quantum entanglement to distinguish knots}, journal = {Journal of Physics A}, volume = {49}, year = {2016}, month = {2016/01/12}, pages = {075203}, abstract = { Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if this gate is non-entangling, then the resulting invariant of knots is trivial. We thus obtain a general connection between topological entanglement and quantum entanglement, as suggested by Kauffman et al. }, doi = {10.1088/1751-8113/49/7/075203}, url = {http://arxiv.org/abs/1507.05979}, author = {Gorjan Alagic and Michael Jarret and Stephen P. Jordan} } @article {1472, title = {2D Superexchange mediated magnetization dynamics in an optical lattice}, journal = {Science}, volume = {348}, year = {2015}, month = {2015/04/30}, pages = {540 - 544}, abstract = { The competition of magnetic exchange interactions and tunneling underlies many complex quantum phenomena observed in real materials. We study non-equilibrium magnetization dynamics in an extended 2D system by loading effective spin-1/2 bosons into a spin-dependent optical lattice, and we use the lattice to separately control the resonance conditions for tunneling and superexchange. After preparing a non-equilibrium anti-ferromagnetically ordered state, we observe relaxation dynamics governed by two well-separated rates, which scale with the underlying Hamiltonian parameters associated with superexchange and tunneling. Remarkably, with tunneling off-resonantly suppressed, we are able to observe superexchange dominated dynamics over two orders of magnitude in magnetic coupling strength, despite the presence of vacancies. In this regime, the measured timescales are in agreement with simple theoretical estimates, but the detailed dynamics of this 2D, strongly correlated, and far-from-equilibrium quantum system remain out of reach of current computational techniques. }, doi = {10.1126/science.aaa1385}, url = {http://arxiv.org/abs/1411.7036v1}, author = {R. C. Brown and R. Wyllie and S. B. Koller and E. A. Goldschmidt and Michael Foss-Feig and J. V. Porto} } @article {1390, title = {Adiabatic optimization without local minima}, journal = {Quantum Information and Computation}, volume = {15}, year = {2015}, month = {2015/05/01}, pages = {181-199}, abstract = { Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms. Here we investigate the even more basic question of whether adiabatic optimization algorithms always succeed in polynomial time for trivial optimization problems in which there are no local energy minima other than the global minimum. Surprisingly, we find a counterexample in which the potential is a single basin on a graph, but the eigenvalue gap is exponentially small as a function of the number of vertices. In this counterexample, the ground state wavefunction consists of two "lobes" separated by a region of exponentially small amplitude. Conversely, we prove if the ground state wavefunction is single-peaked then the eigenvalue gap scales at worst as one over the square of the number of vertices. }, url = {http://arxiv.org/abs/1405.7552}, author = {Michael Jarret and Stephen P. Jordan} } @article {1838, title = {Atom induced cavities and tunable long-range interactions between atoms trapped near photonic crystals}, journal = {Nature Photon. 9, 326 (2015)}, year = {2015}, month = {2015/03/03}, abstract = {

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, achieving tunable, coherent long-range interactions between atoms is an outstanding challenge, which currently leaves a large class of models inaccessible to quantum simulation. Here, we propose a solution exploiting the powerful new platform of cold atoms trapped near nano-photonic systems. We show that the dielectric contrast of an atom trapped near a photonic crystal can seed a localized cavity mode around the atomic position. In a dynamic form of \“all-atomic\” cavity QED, the length of these cavity modes can be tuned, and atoms separated by the order of the e\↵ective cavity length can interact coherently with each other. Considering realistic conditions such as fabrication disorder and photon losses, coherent long-range potentials or spin interactions can be dominant in the system over length scales up to hundreds of wavelengths.

}, doi = {doi:10.1038/nphoton.2015.57}, url = {http://www.nature.com/nphoton/journal/v9/n5/full/nphoton.2015.57.html}, author = {J S Douglas and H Habibian and Alexey V. Gorshkov and H J Kimble and D E Chang} } @article {1190, title = {Bilayer fractional quantum Hall states with ultracold dysprosium}, journal = {Physical Review A}, volume = {92}, year = {2015}, month = {2015/09/10}, pages = {033609}, abstract = { We show how dipolar interactions between dysprosium atoms in an optical lattice can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible tunneling. Microwave and spatially dependent optical dressing fields are used to define an effective spin-1/2 or spin-1 degree of freedom in each atom. Thinking of spin-1/2 particles as hardcore bosons, dipole-dipole interactions give rise to boson hopping, topological flat bands with Chern number 1, and the \nu = 1/2 Laughlin state. Thinking of spin-1 particles as two-component hardcore bosons, dipole-dipole interactions again give rise to boson hopping, topological flat bands with Chern number 2, and the bilayer Halperin (2,2,1) state. By adjusting the optical fields, we find a phase diagram, in which the (2,2,1) state competes with superfluidity. Generalizations to solid-state magnetic dipoles are discussed. }, doi = {10.1103/PhysRevA.92.033609}, url = {http://arxiv.org/abs/1505.03099v1}, author = {Norman Y. Yao and Steven D. Bennett and Chris R. Laumann and Benjamin L. Lev and Alexey V. Gorshkov} } @article {1334, title = {Bounds on quantum communication via Newtonian gravity}, journal = {New Journal of Physics}, volume = {17}, year = {2015}, month = {2015/01/15}, pages = {015006}, abstract = {Newtonian gravity yields specific observable consequences, the most striking of which is the emergence of a $1/r^2$ force. In so far as communication can arise via such interactions between distant particles, we can ask what would be expected for a theory of gravity that only allows classical communication. Many heuristic suggestions for gravity-induced decoherence have this restriction implicitly or explicitly in their construction. Here we show that communication via a $1/r^2$ force has a minimum noise induced in the system when the communication cannot convey quantum information, in a continuous time analogue to Bell{\textquoteright}s inequalities. Our derived noise bounds provide tight constraints from current experimental results on any theory of gravity that does not allow quantum communication. }, doi = {10.1088/1367-2630/17/1/015006}, url = {http://arxiv.org/abs/1404.3214v2}, author = {D. Kafri and G. J. Milburn and J. M. Taylor} } @article {1336, title = {Capacitively coupled singlet-triplet qubits in the double charge resonant regime}, journal = {Physical Review B}, volume = {92}, year = {2015}, month = {2015/12/01}, pages = {235301}, abstract = {We investigate a method for entangling two singlet-triplet qubits in adjacent double quantum dots via capacitive interactions. In contrast to prior work, here we focus on a regime with strong interactions between the qubits. The interplay of the interaction energy and simultaneous large detunings for both double dots gives rise to the double charge resonant regime, in which the unpolarized (1111) and fully polarized (0202) four-electron states in the absence of interqubit tunneling are near degeneracy, while being energetically well-separated from the partially polarized (0211 and 1102) states. A controlled-phase gate may be realized by combining time evolution in this regime in the presence of intraqubit tunneling and the interqubit Coulomb interaction with refocusing {\pi} pulses that swap the singly occupied singlet and triplet states of the two qubits via, e.g., magnetic gradients. We calculate the fidelity of this entangling gate, incorporating models for two types of noise - classical, Gaussian-distributed charge fluctuations in the single-qubit detunings and charge relaxation within the low-energy subspace via electron-phonon interaction - and identify parameter regimes that optimize the fidelity. The rates of phonon-induced decay for pairs of GaAs or Si double quantum dots vary with the sizes of the dipolar and quadrupolar contributions and are several orders of magnitude smaller for Si, leading to high theoretical gate fidelities for coupled singlet-triplet qubits in Si dots. We also consider the dependence of the capacitive coupling on the relative orientation of the double dots and find that a linear geometry provides the fastest potential gate. }, url = {http://arxiv.org/abs/1408.4740v2}, author = {V. Srinivasa and J. M. Taylor} } @article {1338, title = {A chemical potential for light}, journal = {Physical Review B}, volume = {92}, year = {2015}, month = {2014/05/22}, pages = {174305}, abstract = {Photons are not conserved in interactions with other matter. Consequently, when understanding the equation of state and thermodynamics of photons, while we have a concept of temperature for energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semi-conductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott Insulator-superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources and even electron-like circuits with light. }, doi = {10.1103/PhysRevB.92.174305}, url = {http://arxiv.org/abs/1405.5821v2}, author = {M. Hafezi and P. Adhikari and J. M. Taylor} } @article {1696, title = {Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems}, year = {2015}, month = {2015/10/05}, abstract = {Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)\~{}1/rα, directly relevant to ion-trap experiments. Using bosonization and renormalization group theory, we find CSB for α smaller than a critical exponent αc(<=3) depending on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal symmetry due to long-range interactions, and is described by a new universality class akin to the Berezinskii-Kosterlitz-Thouless transition. Our analytical findings are in good agreement with a numerical calculation. Signatures of the CSB phase should be accessible in existing trapped-ion experiments.}, url = {http://arxiv.org/abs/1510.01325}, author = {Mohammad F. Maghrebi and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1507, title = {Coulomb bound states of strongly interacting photons}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, month = {2015/09/16}, pages = {123601}, abstract = { We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. }, doi = {10.1103/PhysRevLett.115.123601}, url = {http://arxiv.org/abs/1505.03859v1}, author = {Mohammad F. Maghrebi and Michael Gullans and P. Bienias and S. Choi and I. Martin and O. Firstenberg and M. D. Lukin and H. P. B{\"u}chler and Alexey V. Gorshkov} } @article {1515, title = {Demonstration of Robust Quantum Gate Tomography via Randomized Benchmarking}, journal = {New Journal of Physics}, volume = {17}, year = {2015}, month = {2015/11/05}, pages = {113019}, abstract = { Typical quantum gate tomography protocols struggle with a self-consistency problem: the gate operation cannot be reconstructed without knowledge of the initial state and final measurement, but such knowledge cannot be obtained without well-characterized gates. A recently proposed technique, known as randomized benchmarking tomography (RBT), sidesteps this self-consistency problem by designing experiments to be insensitive to preparation and measurement imperfections. We implement this proposal in a superconducting qubit system, using a number of experimental improvements including implementing each of the elements of the Clifford group in single {\textquoteleft}atomic{\textquoteright} pulses and custom control hardware to enable large overhead protocols. We show a robust reconstruction of several single-qubit quantum gates, including a unitary outside the Clifford group. We demonstrate that RBT yields physical gate reconstructions that are consistent with fidelities obtained by randomized benchmarking. }, doi = {10.1088/1367-2630/17/11/113019}, url = {http://arxiv.org/abs/1505.06686}, author = {Blake R. Johnson and Marcus P. da Silva and Colm A. Ryan and Shelby Kimmel and Jerry M. Chow and Thomas A. Ohki} } @article {1462, title = {Discontinuity of Maximum Entropy Inference and Quantum Phase Transitions}, journal = {New Journal of Physics}, volume = {17}, year = {2015}, month = {2015/08/10}, pages = {083019}, abstract = { In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit. }, doi = {10.1088/1367-2630/17/8/083019}, url = {http://arxiv.org/abs/1406.5046v2}, author = {Jianxin Chen and Zhengfeng Ji and Chi-Kwong Li and Yiu-Tung Poon and Yi Shen and Nengkun Yu and Bei Zeng and Duanlu Zhou} } @article {2561, title = {Driving Rabi oscillations at the giant dipole resonance in xenon}, journal = {Phys. Rev. A }, volume = {92}, year = {2015}, month = {11/23/2015}, abstract = {

Free-electron lasers (FELs) produce short and very intense light pulses in the XUV and x-ray regimes. We investigate the possibility to drive Rabi oscillations in xenon with an intense FEL pulse by using the unusually large dipole strength of the giant-dipole resonance (GDR). The GDR decays within less than 30 as due to its position, which is above the 4d ionization threshold. We find that intensities around 1018 W/cm2 are required to induce Rabi oscillations with a period comparable to the lifetime. The pulse duration should not exceed 100 as because xenon will be fully ionized within a few lifetimes. Rabi oscillations reveal themselves also in the photoelectron spectrum in form of Autler-Townes splittings extending over several tens of electronvolt.

}, doi = {https://doi.org/10.1103/PhysRevA.92.053424}, url = {https://arxiv.org/abs/1511.00058}, author = {Stefan Pabst and Daochen Wang and Robin Santra} } @article {1526, title = {Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/04/16}, pages = {151602}, abstract = { A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown that the mutual information in D dimensions can be mapped to classical thermodynamic entropy in D+1 dimensions. As a specific example, we compute the mutual information both analytically and numerically for a range of separation distances between two bodies in D=2 dimensions and find a logarithmic correction to the area law at short separations. A key advantage of our method is that it allows the strong subadditivity property---notoriously difficult to prove for quantum systems---to be easily verified. }, doi = {10.1103/PhysRevLett.114.151602}, url = {http://arxiv.org/abs/1412.5613v2}, author = {Mohammad F. Maghrebi and Homer Reid} } @article {1473, title = {Entangling two transportable neutral atoms via local spin exchange}, journal = {Nature}, volume = {527}, year = {2015}, month = {2015/11/02}, pages = {208-211}, abstract = { To advance quantum information science a constant pursuit is the search for physical systems that meet the stringent requirements for creating and preserving quantum entanglement. In atomic physics, robust two-qubit entanglement is typically achieved by strong, long-range interactions in the form of Coulomb interactions between ions or dipolar interactions between Rydberg atoms. While these interactions allow fast gates, atoms subject to these interactions must overcome the associated coupling to the environment and cross-talk among qubits. Local interactions, such as those requiring significant wavefunction overlap, can alleviate these detrimental effects yet present a new challenge: To distribute entanglement, qubits must be transported, merged for interaction, and then isolated for storage and subsequent operations. Here we show how, via a mobile optical tweezer, it is possible to prepare and locally entangle two ultracold neutral atoms, and then separate them while preserving their entanglement. While ultracold neutral atom experiments have measured dynamics consistent with spin entanglement, we are now able to demonstrate two-particle coherence via application of a local gradient and parity measurements; this new entanglement-verification protocol could be applied to arbitrary spin-entangled states of spatially-separated atoms. The local entangling operation is achieved via ultracold spin-exchange interactions, and quantum tunneling is used to combine and separate atoms. Our toolset provides a framework for dynamically entangling remote qubits via local operations within a large-scale quantum register. }, doi = {10.1038/nature16073}, url = {http://arxiv.org/abs/1507.05586}, author = {A. M. Kaufman and B. J. Lester and Michael Foss-Feig and M. L. Wall and A. M. Rey and C. A. Regal} } @article {1188, title = {Fractional Quantum Hall States of Rydberg Polaritons}, journal = {Physical Review A}, volume = {91}, year = {2015}, month = {2015/03/31}, pages = {033838}, abstract = { We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1/2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator -- a lattice-based, fractional quantum Hall state of light. }, doi = {10.1103/PhysRevA.91.033838}, url = {http://arxiv.org/abs/1411.6624v1}, author = {Mohammad F. Maghrebi and Norman Y. Yao and Mohammad Hafezi and Thomas Pohl and Ofer Firstenberg and Alexey V. Gorshkov} } @article {1331, title = {Framework for learning agents in quantum environments}, year = {2015}, month = {2015/07/30}, abstract = {In this paper we provide a broad framework for describing learning agents in general quantum environments. We analyze the types of classically specified environments which allow for quantum enhancements in learning, by contrasting environments to quantum oracles. We show that whether or not quantum improvements are at all possible depends on the internal structure of the quantum environment. If the environments are constructed and the internal structure is appropriately chosen, or if the agent has limited capacities to influence the internal states of the environment, we show that improvements in learning times are possible in a broad range of scenarios. Such scenarios we call luck-favoring settings. The case of constructed environments is particularly relevant for the class of model-based learning agents, where our results imply a near-generic improvement. }, url = {http://arxiv.org/abs/1507.08482v1}, author = {Vedran Dunjko and J. M. Taylor and Hans J. Briegel} } @article {1337, title = {From membrane-in-the-middle to mirror-in-the-middle with a high-reflectivity sub-wavelength grating}, journal = {Annalen der Physik}, volume = {527}, year = {2015}, month = {2015/01/02}, pages = {81 - 88}, abstract = {We demonstrate a "membrane in the middle" optomechanical system using a silicon nitride membrane patterned as a subwavelength grating. The grating has a reflectivity of over 99.8\%, effectively creating two sub-cavities, with free spectral ranges of 6 GHz, optically coupled via photon tunneling. Measurements of the transmission and reflection spectra show an avoided crossing where the two sub-cavities simultaneously come into resonance, with a frequency splitting of 54 MHz. We derive expressions for the lineshapes of the symmetric and antisymmetric modes at the avoided crossing, and infer the grating reflection, transmission, absorption, and scattering through comparison with the experimental data. }, doi = {10.1002/andp.201400142}, url = {http://arxiv.org/abs/1407.1709v1}, author = {Corey Stambaugh and Haitan Xu and Utku Kemiktarak and J. M. Taylor and John Lawall} } @article {1247, title = {Hamiltonian simulation with nearly optimal dependence on all parameters}, journal = {Proceedings of the 56th IEEE Symposium on Foundations of Computer Science}, year = {2015}, month = {2015/01/08}, pages = {792-809}, abstract = { We present an algorithm for sparse Hamiltonian simulation that has optimal dependence on all parameters of interest (up to log factors). Previous algorithms had optimal or near-optimal scaling in some parameters at the cost of poor scaling in others. Hamiltonian simulation via a quantum walk has optimal dependence on the sparsity $d$ at the expense of poor scaling in the allowed error $\epsilon$. In contrast, an approach based on fractional-query simulation provides optimal scaling in $\epsilon$ at the expense of poor scaling in $d$. Here we combine the two approaches, achieving the best features of both. By implementing a linear combination of quantum walk steps with coefficients given by Bessel functions, our algorithm achieves near-linear scaling in $\tau := d \|H\|_{\max} t$ and sublogarithmic scaling in $1/\epsilon$. Our dependence on $\epsilon$ is optimal, and we prove a new lower bound showing that no algorithm can have sublinear dependence on $\tau$. }, doi = {10.1109/FOCS.2015.54}, url = {http://arxiv.org/abs/1501.01715}, author = {Dominic W. Berry and Andrew M. Childs and Robin Kothari} } @article {1500, title = {Injection Locking of a Semiconductor Double Quantum Dot Micromaser}, journal = {Physical Review A}, volume = {92}, year = {2015}, month = {2015/11/02}, pages = {053802}, abstract = { Emission linewidth is an important figure of merit for masers and lasers. We recently demonstrated a semiconductor double quantum dot (DQD) micromaser where photons are generated through single electron tunneling events. Charge noise directly couples to the DQD energy levels, resulting in a maser linewidth that is more than 100 times larger than the Schawlow-Townes prediction. Here we demonstrate a linewidth narrowing of more than a factor 10 by locking the DQD emission to a coherent tone that is injected to the input port of the cavity. We measure the injection locking range as a function of cavity input power and show that it is in agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models. }, doi = {10.1103/PhysRevA.92.053802}, url = {http://arxiv.org/abs/1508.04147}, author = {Y. -Y. Liu and J. Stehlik and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1790, title = {Laplacian matrices and Alexandrov topologies of digraphs}, journal = {Linear Algebra and its Applications}, volume = {481}, year = {2015}, month = {2015/09/15}, pages = {174 - 185}, abstract = {We explore the spectral properties of digraph Laplacians and how they relate to topological properties of digraphs (such as openness, closure, and strong connectedness) under the Alexandrov topology.}, keywords = {Laplacian matrix}, issn = {0024-3795}, doi = {http://dx.doi.org/10.1016/j.laa.2015.04.031}, url = {http://www.sciencedirect.com/science/article/pii/S0024379515002840}, author = {Aaron Ostrander} } @article {1274, title = {Large effective three-body interaction in a double-well optical lattice}, journal = {Phys. Rev. A 92, 023602}, volume = {92}, year = {2015}, month = {2015/08/03}, pages = {023602}, abstract = { We study ultracold atoms in an optical lattice with two local minima per unit cell and show that the low energy states of a multi-band Bose-Hubbard (BH) Hamiltonian with only pair-wise interactions is equivalent to an effective single-band Hamiltonian with strong three-body interactions. We focus on a double-well optical lattice with a symmetric double well along the $x$ axis and single well structure along the perpendicular directions. Tunneling and two-body interaction energies are obtained from an exact band-structure calculation and numerically-constructed Wannier functions in order to construct a BH Hamiltonian spanning the lowest two bands. Our effective Hamiltonian is constructed from the ground state of the $N$-atom Hamiltonian for each unit cell obtained within the subspace spanned by the Wannier functions of two lowest bands. The model includes hopping between ground states of neighboring unit cells. We show that such an effective Hamiltonian has strong three-body interactions that can be easily tuned by changing the lattice parameters. Finally, relying on numerical mean-field simulations, we show that the effective Hamiltonian is an excellent approximation of the two-band BH Hamiltonian over a wide range of lattice parameters, both in the superfluid and Mott insulator regions. }, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.023602}, author = {Saurabh Paul and Eite Tiesinga} } @article {1599, title = {The Measurement Problem from the Perspective of an Information Theoretic Interpretation of Quantum Mechanics}, journal = {Entropy}, volume = {17}, year = {2015}, month = {10/28/2015}, pages = {7374-7386}, abstract = {The aim of this paper is to consider the consequences of an information-theoretic interpretation of quantum mechanics for the measurement problem. The motivating idea of the interpretation is that the relation between quantum mechanics and the structure of information is analogous to the relation between special relativity and the structure of space-time. Insofar as quantum mechanics deals with a class of probabilistic correlations that includes correlations structurally different from classical correlations, the theory is about the structure of information: the possibilities for representing, manipulating, and communicating information in a genuinely indeterministic quantum world in which measurement outcomes are intrinsically random are different than we thought. Part of the measurement problem is deflated as a pseudo-problem on this view, and the theory has the resources to deal with the remaining part, given certain idealizations in the treatment of macrosystems.}, doi = {10.3390/e17117374}, url = {http://www.mdpi.com/1099-4300/17/11/7374}, author = {Jeffrey Bub} } @article {1440, title = {The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases) }, journal = {Communications in Mathematical Physics}, volume = {333}, year = {2015}, month = {2014/10/10}, pages = {351 - 365}, abstract = { A long-standing open question asks for the minimum number of vectors needed to form an unextendible product basis in a given bipartite or multipartite Hilbert space. A partial solution was found by Alon and Lovasz in 2001, but since then only a few other cases have been solved. We solve all remaining bipartite cases, as well as a large family of multipartite cases. }, doi = {10.1007/s00220-014-2186-7}, url = {http://arxiv.org/abs/1301.1406v1}, author = {Jianxin Chen and Nathaniel Johnston} } @article {1259, title = {Momentum switches}, journal = {Quantum Information and Computation}, volume = {15}, year = {2015}, month = {2015/05/01}, pages = {601-621}, abstract = { Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct momentum switches, graphs that route particles depending on their momenta. We also give an example where there is no exact momentum switch, although we construct an arbitrarily good approximation. }, url = {http://arxiv.org/abs/1406.4510v1}, author = {Andrew M. Childs and David Gosset and Daniel Nagaj and Mouktik Raha and Zak Webb} } @article {1178, title = {Nearly-linear light cones in long-range interacting quantum systems}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/04/13}, pages = {157201}, abstract = { In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems. }, doi = {10.1103/PhysRevLett.114.157201}, url = {http://arxiv.org/abs/1410.3466v1}, author = {Michael Foss-Feig and Zhe-Xuan Gong and Charles W. Clark and Alexey V. Gorshkov} } @article {1604, title = {Observation of optomechanical buckling phase transitions}, year = {2015}, month = {2015/10/16}, abstract = {

Correlated phases of matter provide long-term stability for systems as diverse as solids, magnets, and potential exotic quantum materials. Mechanical systems, such as relays and buckling transition spring switches can yield similar stability by exploiting non-equilibrium phase transitions. Curiously, in the optical domain, observations of such phase transitions remain elusive. However, efforts to integrate optical and mechanical systems -- optomechanics -- suggest that a hybrid approach combining the quantum control of optical systems with the engineerability of mechanical systems may provide a new avenue for such explorations. Here we report the first observation of the buckling of an optomechanical system, in which transitions between stable mechanical states corresponding to both first- and second-order phase transitions are driven by varying laser power and detuning. Our results enable new applications in photonics and, given rapid progress in pushing optomechanical systems into the quantum regime, the potential for explorations of quantum phase transitions.

}, url = {http://arxiv.org/abs/1510.04971v1}, author = {Haitan Xu and Utku Kemiktarak and Jingyun Fan and Stephen Ragole and John Lawall and J. M. Taylor} } @article {1329, title = {Optical Control of Donor Spin Qubits in Silicon}, journal = {Physical Review B}, volume = {92}, year = {2015}, month = {2015/11/11}, pages = {195411}, abstract = {We show how to achieve optical, spin-selective transitions from the ground state to excited orbital states of group-V donors (P, As, Sb, Bi) in silicon. We consider two approaches based on either resonant, far-infrared (IR) transitions of the neutral donor or resonant, near-IR excitonic transitions. For far-IR light, we calculate the dipole matrix elements between the valley-orbit and spin-orbit split states for all the goup-V donors using effective mass theory. We then calculate the maximum rate and amount of electron-nuclear spin-polarization achievable through optical pumping with circularly polarized light. We find this approach is most promising for Bi donors due to their large spin-orbit and valley-orbit interactions. Using near-IR light, spin-selective excitation is possible for all the donors by driving a two-photon $\Lambda$-transition from the ground state to higher orbitals with even parity. We show that externally applied electric fields or strain allow similar, spin-selective $\Lambda$-transition to odd-parity excited states. We anticipate these results will be useful for future spectroscopic investigations of donors, quantum control and state preparation of donor spin qubits, and for developing a coherent interface between donor spin qubits and single photons. }, doi = {10.1103/PhysRevB.92.195411}, url = {http://arxiv.org/abs/1507.07929}, author = {Michael Gullans and J. M. Taylor} } @article {1532, title = {Optimal ancilla-free Clifford+V approximation of z-rotations}, journal = {Quantum Information and Computation}, volume = {15}, year = {2015}, month = {2015/03/06}, pages = {932-950}, abstract = { We describe a new efficient algorithm to approximate z-rotations by ancilla-free Clifford+V circuits, up to a given precision epsilon. Our algorithm is optimal in the presence of an oracle for integer factoring: it outputs the shortest Clifford+V circuit solving the given problem instance. In the absence of such an oracle, our algorithm is still near-optimal, producing circuits of V-count m + O(log(log(1/epsilon))), where m is the V-count of the third-to-optimal solution. A restricted version of the algorithm approximates z-rotations in the Pauli+V gate set. Our method is based on previous work by the author and Selinger on the optimal ancilla-free approximation of z-rotations using Clifford+T gates and on previous work by Bocharov, Gurevich, and Svore on the asymptotically optimal ancilla-free approximation of z-rotations using Clifford+V gates. }, url = {http://arxiv.org/abs/1409.4355v2}, author = {Neil J. Ross} } @article {1282, title = {Optimization of collisional Feshbach cooling of an ultracold nondegenerate gas}, journal = {Physical Review A}, volume = {91}, year = {2015}, month = {2015/04/20}, pages = {043626}, abstract = { We optimize a collision-induced cooling process for ultracold atoms in the nondegenerate regime. It makes use of a Feshbach resonance, instead of rf radiation in evaporative cooling, to selectively expel hot atoms from a trap. Using functional minimization we analytically show that for the optimal cooling process the resonance energy must be tuned such that it linearly follows the temperature. Here, optimal cooling is defined as maximizing the phase-space density after a fixed cooling duration. The analytical results are confirmed by numerical Monte-Carlo simulations. In order to simulate more realistic experimental conditions, we show that background losses do not change our conclusions, while additional non-resonant two-body losses make a lower initial resonance energy with non-linear dependence on temperature preferable. }, doi = {10.1103/PhysRevA.91.043626}, url = {http://arxiv.org/abs/1412.8473v1}, author = {Marlon Nuske and Eite Tiesinga and L. Mathey} } @article {1333, title = {Optomechanical reference accelerometer}, journal = {Metrologia}, volume = {52}, year = {2015}, month = {2015/09/08}, pages = {654}, abstract = {

We present an optomechanical accelerometer with high dynamic range, high bandwidth and read-out noise levels below 8 ${\mu}$g/$\sqrt{\mathrm{Hz}}$. The straightforward assembly and low cost of our device make it a prime candidate for on-site reference calibrations and autonomous navigation. We present experimental data taken with a vacuum sealed, portable prototype and deduce the achieved bias stability and scale factor accuracy. Additionally, we present a comprehensive model of the device physics that we use to analyze the fundamental noise sources and accuracy limitations of such devices.

}, doi = {10.1088/0026-1394/52/5/654}, url = {http://iopscience.iop.org/article/10.1088/0026-1394/52/5/654/meta;jsessionid=C2B417A5CD50B9B57EE14C78E1783802.ip-10-40-1-105}, author = {Oliver Gerberding and Felipe Guzman Cervantes and John Melcher and Jon R. Pratt and J. M. Taylor} } @article {1512, title = {Oracles with Costs}, journal = {10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)}, volume = {44}, year = {2015}, month = {2015/02/07}, pages = {1-26}, abstract = { While powerful tools have been developed to analyze quantum query complexity, there are still many natural problems that do not fit neatly into the black box model of oracles. We create a new model that allows multiple oracles with differing costs. This model captures more of the difficulty of certain natural problems. We test this model on a simple problem, Search with Two Oracles, for which we create a quantum algorithm that we prove is asymptotically optimal. We further give some evidence, using a geometric picture of Grover{\textquoteright}s algorithm, that our algorithm is exactly optimal. }, isbn = {978-3-939897-96-5}, issn = {1868-8969}, doi = {10.4230/LIPIcs.TQC.2015.1}, url = {http://arxiv.org/abs/1502.02174}, author = {Shelby Kimmel and Cedric Yen-Yu Lin and Han-Hsuan Lin} } @article {1189, title = {Parafermionic zero modes in ultracold bosonic systems}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, month = {2015/08/06}, pages = {065301}, abstract = { Exotic topologically protected zero modes with parafermionic statistics (also called fractionalized Majorana modes) have been proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. The fractionalized statistics of these modes takes them an important step beyond the simplest non-Abelian anyons, Majorana fermions. Building on recent advances towards the realization of fractional quantum Hall states of bosonic ultracold atoms, we propose a realization of parafermions in a system consisting of Bose-Einstein-condensate trenches within a bosonic fractional quantum Hall state. We show that parafermionic zero modes emerge at the endpoints of the trenches and give rise to a topologically protected degeneracy. We also discuss methods for preparing and detecting these modes. }, doi = {10.1103/PhysRevLett.115.065301}, url = {http://arxiv.org/abs/1504.04012v2}, author = {Mohammad F. Maghrebi and Sriram Ganeshan and David J. Clarke and Alexey V. Gorshkov and Jay D. Sau} } @article {1585, title = {Phase Retrieval Without Small-Ball Probability Assumptions: Stability and Uniqueness}, journal = {SampTA}, year = {2015}, month = {2015/05/25}, pages = {411-414}, abstract = {We study stability and uniqueness for the phase retrieval problem. That is, we ask when is a signal x ∈ R n stably and uniquely determined (up to small perturbations), when one performs phaseless measurements of the form yi = |a T i x| 2 (for i = 1, . . . , N), where the vectors ai ∈ R n are chosen independently at random, with each coordinate aij ∈ R being chosen independently from a fixed sub-Gaussian distribution D. It is well known that for many common choices of D, certain ambiguities can arise that prevent x from being uniquely determined. In this note we show that for any sub-Gaussian distribution D, with no additional assumptions, most vectors x cannot lead to such ambiguities. More precisely, we show stability and uniqueness for all sets of vectors T ⊂ R n which are not too peaky, in the sense that at most a constant fraction of their mass is concentrated on any one coordinate. The number of measurements needed to recover x ∈ T depends on the complexity of T in a natural way, extending previous results of Eldar and Mendelson [12].}, url = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=\&arnumber=7148923\&tag=1}, author = {Felix Krahmer and Yi-Kai Liu} } @article {1332, title = {Phonon-Assisted Gain in a Semiconductor Double Quantum Dot Maser}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/05/13}, pages = {196802}, abstract = {We develop a microscopic model for the recently demonstrated double quantum dot (DQD) maser. In characterizing the gain of this device we find that, in addition to the direct stimulated emission of photons, there is a large contribution from the simultaneous emission of a photon and a phonon, i.e., the phonon sideband. We show that this phonon-assisted gain typically dominates the overall gain which leads to masing. Recent experimental data are well fit with our model. }, doi = {10.1103/PhysRevLett.114.196802}, url = {http://arxiv.org/abs/1501.03499v3}, author = {Michael Gullans and Y. -Y. Liu and J. Stehlik and J. R. Petta and J. M. Taylor} } @article {1464, title = {The Power of Quantum Fourier Sampling}, year = {2015}, month = {2015/07/20}, abstract = { A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer, unless the PH collapses. Aaronson and Arkhipov take this further by considering a distribution that can be sampled efficiently by linear optical quantum computation, that under two feasible conjectures, cannot even be approximately sampled classically within bounded total variation distance, unless the PH collapses. In this work we use Quantum Fourier Sampling to construct a class of distributions that can be sampled by a quantum computer. We then argue that these distributions cannot be approximately sampled classically, unless the PH collapses, under variants of the Aaronson and Arkhipov conjectures. In particular, we show a general class of quantumly sampleable distributions each of which is based on an "Efficiently Specifiable" polynomial, for which a classical approximate sampler implies an average-case approximation. This class of polynomials contains the Permanent but also includes, for example, the Hamiltonian Cycle polynomial, and many other familiar $\#$P-hard polynomials. Although our construction, unlike that proposed by Aaronson and Arkhipov, likely requires a universal quantum computer, we are able to use this additional power to weaken the conjectures needed to prove approximate sampling hardness results. }, url = {http://arxiv.org/abs/1507.05592v1}, author = {Bill Fefferman and Chris Umans} } @article {1565, title = {Programming the Quantum Future}, journal = {Communications of the ACM}, volume = {58}, year = {2015}, month = {2015/08/01}, pages = {52-61}, abstract = {The earliest computers, like the ENIAC, were rare and heroically difficult to program. That difficulty stemmed from the requirement that algorithms be expressed in a "vocabulary" suited to the particular hardware available, ranging from function tables for the ENIAC to more conventional arithmetic and movement operations on later machines. Introduction of symbolic programming languages, exemplified by FORTRAN, solved a major difficulty for the next generation of computing devices by enabling specification of an algorithm in a form more suitable for human understanding, then translating this specification to a form executable by the machine. The "programming language" used for such specification bridged a semantic gap between the human and the computing device. It provided two important features: high-level abstractions, taking care of automated bookkeeping, and modularity, making it easier to reason about sub-parts of programs.}, doi = {10.1145/2699415}, url = {http://cacm.acm.org/magazines/2015/8/189851-programming-the-quantum-future/fulltext$\#$comments}, author = {D. Scott Alexander and Neil J. Ross and Peter Selinger and Jonathan M. Smith and Beno{\^\i}t Valiron} } @article {1596, title = {Quantum Compressed Sensing Using 2-Designs}, year = {2015}, month = {2015/10/29}, abstract = {We develop a method for quantum process tomography that combines the efficiency of compressed sensing with the robustness of randomized benchmarking. Our method is robust to state preparation and measurement errors, and it achieves a quadratic speedup over conventional tomography when the unknown process is a generic unitary evolution. Our method is based on PhaseLift, a convex programming technique for phase retrieval. We show that this method achieves approximate recovery of almost all signals, using measurements sampled from spherical or unitary 2-designs. This is the first positive result on PhaseLift using 2-designs. We also show that exact recovery of all signals is possible using unitary 4-designs. Previous positive results for PhaseLift required spherical 4-designs, while PhaseLift was known to fail in certain cases when using spherical 2-designs.}, url = {http://arxiv.org/abs/1510.08887}, author = {Shelby Kimmel and Yi-Kai Liu} } @article {1601, title = {Quantum Entanglement and Information}, journal = {The Stanford Encyclopedia of Philosophy}, year = {2015}, month = {02/07/2015}, abstract = {Quantum entanglement is a physical resource, like energy, associated with the peculiar nonclassical correlations that are possible between separated quantum systems. Entanglement can be measured, transformed, and purified. A pair of quantum systems in an entangled state can be used as a quantum information channel to perform computational and cryptographic tasks that are impossible for classical systems. The general study of the information-processing capabilities of quantum systems is the subject of quantum information theory.}, url = {http://plato.stanford.edu/archives/sum2015/entries/qt-entangle/}, author = {Jeffrey Bub and Edward N. Zalta} } @article {1675, title = {Quantum many-body models with cold atoms coupled to photonic crystals}, journal = {Nature Photonics}, volume = {9}, year = {2015}, month = {2015/04/04}, pages = {326 - 331}, issn = {1749-4885}, doi = {10.1038/nphoton.2015.57}, url = {http://www.nature.com/doifinder/10.1038/nphoton.2015.57}, author = {Douglas, J. S. and Habibian, H. and Hung, C.-L. and Alexey V. Gorshkov and Kimble, H. J. and Chang, D. E.} } @article {1494, title = {Quantum Nonlinear Optics Near Optomechanical Instabilities}, journal = {Physical Review A}, volume = {91}, year = {2015}, month = {2015/01/09}, pages = {013818}, abstract = { Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation pressure interaction. Here we show that it is not necessary to reach the single-photon strong-coupling regime in order to realize significant optomechanical nonlinearities. Instead, nonlinearities at the few quanta level can be achieved, even with weak-coupling, in a two-mode optomechanical system driven near instability. In this limit, we establish a new figure of merit for realizing strong nonlinearity which scales with the single-photon optomechanical coupling and the sideband resolution of the mechanical mode with respect to the cavity linewidth. We find that current devices based on optomechanical crystals, thought to be in the weak-coupling regime, can still achieve strong quantum nonlinearity; enabling deterministic interactions between single photons. }, doi = {10.1103/PhysRevA.91.013818}, url = {http://arxiv.org/abs/1404.3726v2}, author = {Xunnong Xu and Michael Gullans and J. M. Taylor} } @article {1592, title = {Quantum vs Classical Proofs and Subset Verification}, year = {2015}, month = {2015/10/22}, abstract = {We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only classical witnesses, cannot verify certain properties of subsets given implicitly via an oracle. We use this framework to prove an oracle separation between QCMA and QMA using an {\textquoteleft}{\textquoteleft}in-place{\textquoteright}{\textquoteright} permutation oracle, making the first progress on this question since Aaronson and Kuperberg in 2007. We also use the framework to prove a particularly simple standard oracle separation between QCMA and AM.}, url = {http://arxiv.org/abs/1510.06750}, author = {Bill Fefferman and Shelby Kimmel} } @article {1513, title = {Robust Single-Qubit Process Calibration via Robust Phase Estimation}, journal = {Physical Review A}, volume = {92}, year = {2015}, month = {2015/12/08}, pages = {062315}, abstract = { An important step in building a quantum computer is calibrating experimentally implemented quantum gates to produce operations that are close to ideal unitaries. The calibration step involves estimating the error in gates and then using controls to correct the implementation. Quantum process tomography is a standard technique for estimating these errors, but is both time consuming, (when one only wants to learn a few key parameters), and requires resources, like perfect state preparation and measurement, that might not be available. With the goal of efficiently estimating specific errors using minimal resources, we develop a parameter estimation technique, which can gauge two key parameters (amplitude and off-resonance errors) in a single-qubit gate with provable robustness and efficiency. In particular, our estimates achieve the optimal efficiency, Heisenberg scaling. Our main theorem making this possible is a robust version of the phase estimation procedure of Higgins et al. [B. L. Higgins, New J. Phys. 11, 073023 (2009)]. }, doi = {10.1103/PhysRevA.92.062315}, url = {http://arxiv.org/abs/1502.02677}, author = {Shelby Kimmel and Guang Hao Low and Theodore J. Yoder} } @article {1304, title = {Self-heterodyne detection of the {\it in-situ} phase of an atomic-SQUID}, journal = {Physical Review A}, volume = {92}, year = {2015}, month = {2015/09/03}, pages = {033602}, abstract = { We present theoretical and experimental analysis of an interferometric measurement of the {\it in-situ} phase drop across and current flow through a rotating barrier in a toroidal Bose-Einstein condensate (BEC). This experiment is the atomic analog of the rf-superconducting quantum interference device (SQUID). The phase drop is extracted from a spiral-shaped density profile created by the spatial interference of the expanding toroidal BEC and a reference BEC after release from all trapping potentials. We characterize the interferometer when it contains a single particle, which is initially in a coherent superposition of a torus and reference state, as well as when it contains a many-body state in the mean-field approximation. The single-particle picture is sufficient to explain the origin of the spirals, to relate the phase-drop across the barrier to the geometry of a spiral, and to bound the expansion times for which the {\it in-situ} phase can be accurately determined. Mean-field estimates and numerical simulations show that the inter-atomic interactions shorten the expansion time scales compared to the single-particle case. Finally, we compare the mean-field simulations with our experimental data and confirm that the interferometer indeed accurately measures the {\it in-situ} phase drop. }, doi = {10.1103/PhysRevA.92.033602}, url = {http://arxiv.org/abs/1506.09149v2}, author = {Ranchu Mathew and Avinash Kumar and Stephen Eckel and Fred Jendrzejewski and Gretchen K. Campbell and Mark Edwards and Eite Tiesinga} } @article {1499, title = {Semiconductor double quantum dot micromaser}, journal = {Science}, volume = {347}, year = {2015}, month = {2015/01/15}, pages = {285 - 287}, abstract = { The coherent generation of light, from masers to lasers, relies upon the specific structure of the individual emitters that lead to gain. Devices operating as lasers in the few-emitter limit provide opportunities for understanding quantum coherent phenomena, from THz sources to quantum communication. Here we demonstrate a maser that is driven by single electron tunneling events. Semiconductor double quantum dots (DQDs) serve as a gain medium and are placed inside of a high quality factor microwave cavity. We verify maser action by comparing the statistics of the emitted microwave field above and below the maser threshold. }, doi = {10.1126/science.aaa2501}, url = {http://arxiv.org/abs/1507.06359v1}, author = {Y. -Y. Liu and J. Stehlik and C. Eichler and Michael Gullans and J. M. Taylor and J. R. Petta} } @article {1265, title = {Simulating Hamiltonian dynamics with a truncated Taylor series}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/03/03}, pages = {090502}, abstract = { We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of physical systems. As in another recent algorithm, the cost of our method depends only logarithmically on the inverse of the desired precision, which is optimal. However, we simplify the algorithm and its analysis by using a method for implementing linear combinations of unitary operations to directly apply the truncated Taylor series. }, doi = {10.1103/PhysRevLett.114.090502}, url = {http://arxiv.org/abs/1412.4687v1}, author = {Dominic W. Berry and Andrew M. Childs and Richard Cleve and Robin Kothari and Rolando D. Somma} } @article {1785, title = {Tensor network non-zero testing}, journal = {Quantum Information \& Computation}, volume = {15}, year = {2015}, month = {2015/07/01}, pages = {885-899}, abstract = {Tensor networks are a central tool in condensed matter physics. In this paper, we initiate the study of tensor network non-zero testing (TNZ): Given a tensor network T, does T represent a non-zero vector? We show that TNZ is not in the Polynomial-Time Hierarchy unless the hierarchy collapses. We next show (among other results) that the special cases of TNZ on non-negative and injective tensor networks are in NP. Using this, we make a simple observation: The commuting variant of the MA-complete stoquastic k-SAT problem on D-dimensional qudits is in NP for logarithmic k and constant D. This reveals the first class of quantum Hamiltonians whose commuting variant is known to be in NP for all (1) logarithmic k, (2) constant D, and (3) for arbitrary interaction graphs.}, url = {http://arxiv.org/abs/1406.5279}, author = {Sevag Gharibian and Zeph Landau and Seung Woo Shin and Guoming Wang} } @article {1339, title = {Tunable Spin Qubit Coupling Mediated by a Multi-Electron Quantum Dot}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/06/04}, pages = {226803}, abstract = {We present an approach for entangling electron spin qubits localized on spatially separated impurity atoms or quantum dots via a multi-electron, two-level quantum dot. The effective exchange interaction mediated by the dot can be understood as the simplest manifestation of Ruderman-Kittel-Kasuya-Yosida exchange, and can be manipulated through gate voltage control of level splittings and tunneling amplitudes within the system. This provides both a high degree of tuneability and a means for realizing high-fidelity two-qubit gates between spatially separated spins, yielding an experimentally accessible method of coupling donor electron spins in silicon via a hybrid impurity-dot system. }, doi = {10.1103/PhysRevLett.114.226803}, url = {http://arxiv.org/abs/1312.1711v3}, author = {V. Srinivasa and H. Xu and J. M. Taylor} } @article {1450, title = {Universal Subspaces for Local Unitary Groups of Fermionic Systems}, journal = {Communications in Mathematical Physics}, volume = {333}, year = {2015}, month = {2014/10/10}, pages = {541 - 563}, abstract = { Let $\mathcal{V}=\wedge^N V$ be the $N$-fermion Hilbert space with $M$-dimensional single particle space $V$ and $2N\le M$. We refer to the unitary group $G$ of $V$ as the local unitary (LU) group. We fix an orthonormal (o.n.) basis $\ket{v_1},...,\ket{v_M}$ of $V$. Then the Slater determinants $e_{i_1,...,i_N}:= \ket{v_{i_1}\we v_{i_2}\we...\we v_{i_N}}$ with $i_1<...3. If $M$ is even, the well known BCS states are not LU-equivalent to any single occupancy state. Our main result is that for N=3 and $M$ even there is a universal subspace $\cW\subseteq\cS$ spanned by $M(M-1)(M-5)/6$ states $e_{i_1,...,i_N}$. Moreover the number $M(M-1)(M-5)/6$ is minimal. }, doi = {10.1007/s00220-014-2187-6}, url = {http://arxiv.org/abs/1301.3421v2}, author = {Lin Chen and Jianxin Chen and Dragomir Z. Djokovic and Bei Zeng} } @article {1376, title = {Adaptive change of basis in entropy-based moment closures for linear kinetic equations}, journal = {Journal of Computational Physics}, volume = {258}, year = {2014}, month = {2014/02/01}, pages = {489 - 508}, abstract = { Entropy-based (M_N) moment closures for kinetic equations are defined by a constrained optimization problem that must be solved at every point in a space-time mesh, making it important to solve these optimization problems accurately and efficiently. We present a complete and practical numerical algorithm for solving the dual problem in one-dimensional, slab geometries. The closure is only well-defined on the set of moments that are realizable from a positive underlying distribution, and as the boundary of the realizable set is approached, the dual problem becomes increasingly difficult to solve due to ill-conditioning of the Hessian matrix. To improve the condition number of the Hessian, we advocate the use of a change of polynomial basis, defined using a Cholesky factorization of the Hessian, that permits solution of problems nearer to the boundary of the realizable set. We also advocate a fixed quadrature scheme, rather than adaptive quadrature, since the latter introduces unnecessary expense and changes the computationally realizable set as the quadrature changes. For very ill-conditioned problems, we use regularization to make the optimization algorithm robust. We design a manufactured solution and demonstrate that the adaptive-basis optimization algorithm reduces the need for regularization. This is important since we also show that regularization slows, and even stalls, convergence of the numerical simulation when refining the space-time mesh. We also simulate two well-known benchmark problems. There we find that our adaptive-basis, fixed-quadrature algorithm uses less regularization than alternatives, although differences in the resulting numerical simulations are more sensitive to the regularization strategy than to the choice of basis. }, doi = {10.1016/j.jcp.2013.10.049}, url = {http://arxiv.org/abs/1306.2881v1}, author = {Graham W. Alldredge and Cory D. Hauck and Dianne P. O{\textquoteright}Leary and Andr{\'e} L. Tits} } @article {1839, title = {Beyond the spin model approximation for Ramsey spectroscopy}, journal = {Phys. Rev. Lett.}, volume = {112}, year = {2014}, pages = {123001}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.123001}, author = {A P Koller and M Beverland and Alexey V. Gorshkov and A M Rey} } @article {1232, title = {The Bose-Hubbard model is QMA-complete}, journal = {Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014)}, volume = {8572}, year = {2014}, month = {2014/07/08}, pages = {308-319}, abstract = { The Bose-Hubbard model is a system of interacting bosons that live on the vertices of a graph. The particles can move between adjacent vertices and experience a repulsive on-site interaction. The Hamiltonian is determined by a choice of graph that specifies the geometry in which the particles move and interact. We prove that approximating the ground energy of the Bose-Hubbard model on a graph at fixed particle number is QMA-complete. In our QMA-hardness proof, we encode the history of an n-qubit computation in the subspace with at most one particle per site (i.e., hard-core bosons). This feature, along with the well-known mapping between hard-core bosons and spin systems, lets us prove a related result for a class of 2-local Hamiltonians defined by graphs that generalizes the XY model. By avoiding the use of perturbation theory in our analysis, we circumvent the need to multiply terms in the Hamiltonian by large coefficients. }, doi = {10.1007/978-3-662-43948-7_26}, url = {http://arxiv.org/abs/1311.3297v1}, author = {Andrew M. Childs and David Gosset and Zak Webb} } @article {1340, title = {A classical channel model for gravitational decoherence}, journal = {New Journal of Physics}, volume = {16}, year = {2014}, month = {2014/06/26}, pages = {065020}, abstract = {We show that, by treating the gravitational interaction between two mechanical resonators as a classical measurement channel, a gravitational decoherence model results that is equivalent to a model first proposed by Diosi. The resulting decoherence model implies that the classically mediated gravitational interaction between two gravitationally coupled resonators cannot create entanglement. The gravitational decoherence rate ( and the complementary heating rate) is of the order of the gravitationally induced normal mode splitting of the two resonators. }, doi = {10.1088/1367-2630/16/6/065020}, url = {http://arxiv.org/abs/1401.0946v1}, author = {D. Kafri and J. M. Taylor and G. J. Milburn} } @article {1391, title = {Classical simulation of Yang-Baxter gates}, journal = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)}, volume = {27}, year = {2014}, month = {2014/07/05}, pages = {161-175}, abstract = { A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological braiding corresponds to a quantum circuit. A basic question is when such a representation affords universal quantum computation. In this work, we show how to classically simulate these circuits when the gate in question belongs to certain families of solutions to the Yang-Baxter equation. These include all of the qubit (i.e., $d = 2$) solutions, and some simple families that include solutions for arbitrary $d \ge 2$. Our main tool is a probabilistic classical algorithm for efficient simulation of a more general class of quantum circuits. This algorithm may be of use outside the present setting. }, doi = {10.4230/LIPIcs.TQC.2014.161}, url = {http://arxiv.org/abs/1407.1361v1}, author = {Gorjan Alagic and Aniruddha Bapat and Stephen P. Jordan} } @article {1230, title = {The computational power of matchgates and the XY interaction on arbitrary graphs}, journal = {Quantum Information and Computation}, volume = {14}, year = {2014}, month = {2014/09/01}, pages = {901-916}, abstract = { Matchgates are a restricted set of two-qubit gates known to be classically simulable when acting on nearest-neighbor qubits on a path, but universal for quantum computation when the qubits are arranged on certain other graphs. Here we characterize the power of matchgates acting on arbitrary graphs. Specifically, we show that they are universal on any connected graph other than a path or a cycle, and that they are classically simulable on a cycle. We also prove the same dichotomy for the XY interaction, a proper subset of matchgates related to some implementations of quantum computing. }, url = {http://arxiv.org/abs/1308.1463v1}, author = {Daniel J. Brod and Andrew M. Childs} } @article {1518, title = {The computational power of normalizer circuits over black-box groups}, year = {2014}, month = {2014/09/16}, abstract = { This work presents a precise connection between Clifford circuits, Shor{\textquoteright}s factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems. We show that all these different forms of quantum computation belong to a common new restricted model of quantum operations that we call \emph{black-box normalizer circuits}. To define these, we extend the previous model of normalizer circuits [arXiv:1201.4867v1,arXiv:1210.3637,arXiv:1409.3208], which are built of quantum Fourier transforms, group automorphism and quadratic phase gates associated to an Abelian group $G$. In previous works, the group $G$ is always given in an explicitly decomposed form. In our model, we remove this assumption and allow $G$ to be a black-box group. While standard normalizer circuits were shown to be efficiently classically simulable [arXiv:1201.4867v1,arXiv:1210.3637,arXiv:1409.3208], we find that normalizer circuits are powerful enough to factorize and solve classically-hard problems in the black-box setting. We further set upper limits to their computational power by showing that decomposing finite Abelian groups is complete for the associated complexity class. In particular, solving this problem renders black-box normalizer circuits efficiently classically simulable by exploiting the generalized stabilizer formalism in [arXiv:1201.4867v1,arXiv:1210.3637,arXiv:1409.3208]. Lastly, we employ our connection to draw a few practical implications for quantum algorithm design: namely, we give a no-go theorem for finding new quantum algorithms with black-box normalizer circuits, a universality result for low-depth normalizer circuits, and identify two other complete problems. }, url = {http://arxiv.org/abs/1409.4800v1}, author = {Juan Bermejo-Vega and Cedric Yen-Yu Lin and Maarten Van den Nest} } @article {1226, title = {Constructing elliptic curve isogenies in quantum subexponential time}, journal = {Journal of Mathematical Cryptology}, volume = {8}, year = {2014}, month = {2014/01/01}, pages = {1 - 29}, abstract = { Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to be computationally difficult. The fastest known classical algorithm takes exponential time, and prior to our work no faster quantum algorithm was known. Recently, public-key cryptosystems based on the presumed hardness of this problem have been proposed as candidates for post-quantum cryptography. In this paper, we give a subexponential-time quantum algorithm for constructing isogenies, assuming the Generalized Riemann Hypothesis (but with no other assumptions). Our algorithm is based on a reduction to a hidden shift problem, together with a new subexponential-time algorithm for evaluating isogenies from kernel ideals (under only GRH), and represents the first nontrivial application of Kuperberg{\textquoteright}s quantum algorithm for the hidden shift problem. This result suggests that isogeny-based cryptosystems may be uncompetitive with more mainstream quantum-resistant cryptosystems such as lattice-based cryptosystems. }, doi = {10.1515/jmc-2012-0016}, url = {http://arxiv.org/abs/1012.4019v2}, author = {Andrew M. Childs and David Jao and Vladimir Soukharev} } @article {1516, title = {Different Strategies for Optimization Using the Quantum Adiabatic Algorithm }, year = {2014}, month = {2014/01/28}, abstract = { We present the results of a numerical study, with 20 qubits, of the performance of the Quantum Adiabatic Algorithm on randomly generated instances of MAX 2-SAT with a unique assignment that maximizes the number of satisfied clauses. The probability of obtaining this assignment at the end of the quantum evolution measures the success of the algorithm. Here we report three strategies which consistently increase the success probability for the hardest instances in our ensemble: decreasing the overall evolution time, initializing the system in excited states, and adding a random local Hamiltonian to the middle of the evolution. }, url = {http://arxiv.org/abs/1401.7320v1}, author = {Elizabeth Crosson and Edward Farhi and Cedric Yen-Yu Lin and Han-Hsuan Lin and Peter Shor} } @article {bian2014discrete, title = {Discrete optimization using quantum annealing on sparse Ising models}, journal = {Frontiers in Physics}, volume = {2}, year = {2014}, month = {2014/09/01}, pages = {56}, publisher = {Frontiers}, abstract = {This paper discusses techniques for solving discrete optimization problems using quantum annealing. Practical issues likely to affect the computation include precision limitations, finite temperature, bounded energy range, sparse connectivity, and small numbers of qubits. To address these concerns we propose a way of finding energy representations with large classical gaps between ground and first excited states, efficient algorithms for mapping non-compatible Ising models into the hardware, and the use of decomposition methods for problems that are too large to fit in hardware. We validate the approach by describing experiments with D-Wave quantum hardware for low density parity check decoding with up to 1000 variables.}, author = {Bian, Zhengbing and Chudak, Fabian and Israel, Robert and Brad Lackey and Macready, William G and Roy, Aidan} } @article {1600, title = {"Einstein and Bohr Meet Alice and Bob{\textquoteright}, Logic and Science Facing the New Technologies}, journal = {Proceedings of the 14th Congress for Logic (Nancy), Logic, Methodology and Philosophy of Science}, year = {2014}, month = {2014/01/01}, author = {Jeffrey Bub and Peter Schroeder-Heister and Gerhard Heinzmann and Wilfrid Hodges and Pierre Edouard Bour} } @article {1264, title = {Exponential improvement in precision for simulating sparse Hamiltonians}, journal = {Proceedings of the 46th ACM Symposium on Theory of Computing (STOC 2014)}, year = {2014}, month = {2014/05/31}, pages = {283-292}, abstract = { We provide a quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods. Specifically, we show that a $d$-sparse Hamiltonian $H$ acting on $n$ qubits can be simulated for time $t$ with precision $\epsilon$ using $O\big(\tau \frac{\log(\tau/\epsilon)}{\log\log(\tau/\epsilon)}\big)$ queries and $O\big(\tau \frac{\log^2(\tau/\epsilon)}{\log\log(\tau/\epsilon)}n\big)$ additional 2-qubit gates, where $\tau = d^2 \|{H}\|_{\max} t$. Unlike previous approaches based on product formulas, the query complexity is independent of the number of qubits acted on, and for time-varying Hamiltonians, the gate complexity is logarithmic in the norm of the derivative of the Hamiltonian. Our algorithm is based on a significantly improved simulation of the continuous- and fractional-query models using discrete quantum queries, showing that the former models are not much more powerful than the discrete model even for very small error. We also simplify the analysis of this conversion, avoiding the need for a complex fault correction procedure. Our simplification relies on a new form of "oblivious amplitude amplification" that can be applied even though the reflection about the input state is unavailable. Finally, we prove new lower bounds showing that our algorithms are optimal as a function of the error. }, isbn = {978-1-4503-2710-7}, doi = {10.1145/2591796.2591854}, url = {http://arxiv.org/abs/1312.1414v2}, author = {Dominic W. Berry and Andrew M. Childs and Richard Cleve and Robin Kothari and Rolando D. Somma} } @article {1791, title = {Extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model in an oscillating field}, journal = {Physical Review E}, volume = {89}, year = {2014}, month = {2014/02/12}, pages = {022114}, abstract = {We present numerical evidence for an extended order parameter and conjugate field for the dynamic phase transition in a Ginzburg-Landau mean-field model driven by an oscillating field. The order parameter, previously taken to be the time-averaged magnetization, comprises the deviations of the Fourier components of the magnetization from their values at the critical period. The conjugate field, previously taken to be the time-averaged magnetic field, comprises the even Fourier components of the field. The scaling exponents β and δ associated with the extended order parameter and conjugate field are shown numerically to be consistent with their values in the equilibrium mean-field model.}, doi = {10.1103/PhysRevE.89.022114}, url = {http://link.aps.org/doi/10.1103/PhysRevE.89.022114}, author = {Daniel T. Robb and Aaron Ostrander} } @article {1389, title = {The Fundamental Gap for a Class of Schr{\"o}dinger Operators on Path and Hypercube Graphs}, journal = {Journal of Mathematical Physics}, volume = {55}, year = {2014}, month = {2014/03/06}, pages = {052104}, abstract = { We consider the difference between the two lowest eigenvalues (the fundamental gap) of a Schr\"{o}dinger operator acting on a class of graphs. In particular, we derive tight bounds for the gap of Schr\"{o}dinger operators with convex potentials acting on the path graph. Additionally, for the hypercube graph, we derive a tight bound for the gap of Schr\"{o}dinger operators with convex potentials dependent only upon vertex Hamming weight. Our proof makes use of tools from the literature of the fundamental gap theorem as proved in the continuum combined with techniques unique to the discrete case. We prove the tight bound for the hypercube graph as a corollary to our path graph results. }, doi = {10.1063/1.4878120}, url = {http://arxiv.org/abs/1403.1473v1}, author = {Michael Jarret and Stephen P. Jordan} } @article {1477, title = {Hong-Ou-Mandel atom interferometry in tunnel-coupled optical tweezers}, journal = {Science}, volume = {345}, year = {2014}, month = {2014/06/26}, pages = {306 - 309}, abstract = { The quantum statistics of atoms is typically observed in the behavior of an ensemble via macroscopic observables. However, quantum statistics modifies the behavior of even two particles, inducing remarkable consequences that are at the heart of quantum science. Here we demonstrate near-complete control over all the internal and external degrees of freedom of two laser-cooled 87Rb atoms trapped in two optical tweezers. This full controllability allows us to implement a massive-particle analog of a Hong-Ou-Mandel interferometer where atom tunneling plays the role of a photon beamsplitter. We use the interferometer to probe the effect of quantum statistics on the two-atom dynamics under tunable initial conditions, chosen to adjust the degree of atomic indistinguishability. Our work thereby establishes laser-cooled atoms in optical tweezers as a new route to bottom-up engineering of scalable, low-entropy quantum systems. }, doi = {10.1126/science.1250057}, url = {http://arxiv.org/abs/1312.7182v2}, author = {A. M. Kaufman and B. J. Lester and C. M. Reynolds and M. L. Wall and Michael Foss-Feig and K. R. A. Hazzard and A. M. Rey and C. A. Regal} } @article {1177, title = {Kitaev chains with long-range pairing}, journal = {Physical Review Letters}, volume = {113}, year = {2014}, month = {2014/10/9}, abstract = { We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $\alpha$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($\alpha > 1$) or purely algebraically ($\alpha < 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $\alpha$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions. }, doi = {10.1103/PhysRevLett.113.156402}, url = {http://arxiv.org/abs/1405.5440v2}, author = {Davide Vodola and Luca Lepori and Elisa Ercolessi and Alexey V. Gorshkov and Guido Pupillo} } @article {1480, title = {Many-body dynamics of dipolar molecules in an optical lattice}, journal = {Physical Review Letters}, volume = {113}, year = {2014}, month = {2014/11/7}, abstract = { Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into the emergence of complex phenomena. Such insights enable the development of theoretical tools that broaden our understanding. Here, we theoretically model and experimentally probe with Ramsey spectroscopy the quantum dynamics of disordered, dipolar-interacting, ultracold molecules in a partially filled optical lattice. We report the capability to control the dipolar interaction strength, and we demonstrate that the many-body dynamics extends well beyond a nearest-neighbor or mean-field picture, and cannot be quantitatively described using previously available theoretical tools. We develop a novel cluster expansion technique and demonstrate that our theoretical method accurately captures the measured dependence of the spin dynamics on molecule number and on the dipolar interaction strength. In the spirit of quantum simulation, this agreement simultaneously benchmarks the new theoretical method and verifies our microscopic understanding of the experiment. Our findings pave the way for numerous applications in quantum information science, metrology, and condensed matter physics. }, doi = {10.1103/PhysRevLett.113.195302}, url = {http://arxiv.org/abs/1402.2354v1}, author = {Kaden R. A. Hazzard and Bryce Gadway and Michael Foss-Feig and Bo Yan and Steven A. Moses and Jacob P. Covey and Norman Y. Yao and Mikhail D. Lukin and Jun Ye and Deborah S. Jin and Ana Maria Rey} } @article {1530, title = {Nonequilibrium quantum fluctuations of a dispersive medium: Spontaneous emission, photon statistics, entropy generation, and stochastic motion }, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/7/16}, abstract = { We study the implications of quantum fluctuations of a dispersive medium, under steady rotation, either in or out of thermal equilibrium with its environment. A rotating object exhibits a quantum instability by dissipating its mechanical motion via spontaneous emission of photons, as well as internal heat generation. Universal relations are derived for the radiated energy and angular momentum as trace formulas involving the object{\textquoteright}s scattering matrix. We also compute the quantum noise by deriving the full statistics of the radiated photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy generation is quantified, and the total entropy is shown to be always increasing. Furthermore, we derive a Fokker-Planck equation governing the stochastic angular motion resulting from the fluctuating back-reaction frictional torque. As a result, we find a quantum limit on the uncertainty of the object{\textquoteright}s angular velocity in steady rotation. Finally, we show in some detail that a rotating object drags nearby objects, making them spin parallel to its axis of rotation. A scalar toy model is introduced in the first part to simplify the technicalities and ease the conceptual complexities; a detailed discussion of quantum electrodynamics is presented in the second part. }, doi = {10.1103/PhysRevA.90.012515}, url = {http://arxiv.org/abs/1401.0701v1}, author = {Mohammad F. Maghrebi and Robert L. Jaffe and Mehran Kardar} } @article {1202, title = {Non-local propagation of correlations in long-range interacting quantum systems }, journal = {Nature}, volume = {511}, year = {2014}, month = {2014/7/9}, pages = {198 - 201}, abstract = { The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated and how difficult the system will be to describe numerically. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective light cone. However, little is known about the propagation speed in systems with long-range interactions, since the best long-range bound is too loose to give the correct light-cone shape for any known spin model and since analytic solutions rarely exist. In this work, we experimentally determine the spatial and time-dependent correlations of a far-from-equilibrium quantum many-body system evolving under a long-range Ising- or XY-model Hamiltonian. For several different interaction ranges, we extract the shape of the light cone and measure the velocity with which correlations propagate through the system. In many cases we find increasing propagation velocities, which violate the Lieb-Robinson prediction, and in one instance cannot be explained by any existing theory. Our results demonstrate that even modestly-sized quantum simulators are well-poised for studying complicated many-body systems that are intractable to classical computation. }, doi = {10.1038/nature13450}, url = {http://arxiv.org/abs/1401.5088v1}, author = {Philip Richerme and Zhe-Xuan Gong and Aaron Lee and Crystal Senko and Jacob Smith and Michael Foss-Feig and Spyridon Michalakis and Alexey V. Gorshkov and Christopher Monroe} } @article {1519, title = {Normalizer circuits and a Gottesman-Knill theorem for infinite-dimensional systems }, year = {2014}, month = {2014/09/10}, abstract = { $\textit{Normalizer circuits}$ [1,2] are generalized Clifford circuits that act on arbitrary finite-dimensional systems $\mathcal{H}_{d_1}\otimes ... \otimes \mathcal{H}_{d_n}$ with a standard basis labeled by the elements of a finite Abelian group $G=\mathbb{Z}_{d_1}\times... \times \mathbb{Z}_{d_n}$. Normalizer gates implement operations associated with the group $G$ and can be of three types: quantum Fourier transforms, group automorphism gates and quadratic phase gates. In this work, we extend the normalizer formalism [1,2] to infinite dimensions, by allowing normalizer gates to act on systems of the form $\mathcal{H}_\mathbb{Z}^{\otimes a}$: each factor $\mathcal{H}_\mathbb{Z}$ has a standard basis labeled by $\textit{integers}$ $\mathbb{Z}$, and a Fourier basis labeled by $\textit{angles}$, elements of the circle group $\mathbb{T}$. Normalizer circuits become hybrid quantum circuits acting both on continuous- and discrete-variable systems. We show that infinite-dimensional normalizer circuits can be efficiently simulated classically with a generalized $\textit{stabilizer formalism}$ for Hilbert spaces associated with groups of the form $\mathbb{Z}^a\times \mathbb{T}^b \times \mathbb{Z}_{d_1}\times...\times \mathbb{Z}_{d_n}$. We develop new techniques to track stabilizer-groups based on normal forms for group automorphisms and quadratic functions. We use our normal forms to reduce the problem of simulating normalizer circuits to that of finding general solutions of systems of mixed real-integer linear equations [3] and exploit this fact to devise a robust simulation algorithm: the latter remains efficient even in pathological cases where stabilizer groups become infinite, uncountable and non-compact. The techniques developed in this paper might find applications in the study of fault-tolerant quantum computation with superconducting qubits [4,5]. }, url = {http://arxiv.org/abs/1409.3208v2}, author = {Juan Bermejo-Vega and Cedric Yen-Yu Lin and Maarten Van den Nest} } @article {1342, title = {Optical detection of radio waves through a nanomechanical transducer}, journal = {Nature}, volume = {507}, year = {2014}, month = {2014/3/5}, pages = {81 - 85}, abstract = {Low-loss transmission and sensitive recovery of weak radio-frequency (rf) and microwave signals is an ubiquitous technological challenge, crucial in fields as diverse as radio astronomy, medical imaging, navigation and communication, including those of quantum states. Efficient upconversion of rf-signals to an optical carrier would allow transmitting them via optical fibers dramatically reducing losses, and give access to the mature toolbox of quantum optical techniques, routinely enabling quantum-limited signal detection. Research in the field of cavity optomechanics has shown that nanomechanical oscillators can couple very strongly to either microwave or optical fields. An oscillator accommodating both functionalities would bear great promise as the intermediate platform in a radio-to-optical transduction cascade. Here, we demonstrate such an opto-electro-mechanical transducer utilizing a high-Q nanomembrane. A moderate voltage bias (<10V) is sufficient to induce strong coupling between the voltage fluctuations in a rf resonance circuit and the membrane{\textquoteright}s displacement, which is simultaneously coupled to light reflected off its metallized surface. The circuit acts as an antenna; the voltage signals it induces are detected as an optical phase shift with quantum-limited sensitivity. The half-wave voltage is in the microvolt range, orders of magnitude below that of standard optical modulators. The noise added by the membrane is suppressed by the electro-mechanical cooperativity C~6800 and has a temperature of 40mK, far below 300K where the entire device is operated. This corresponds to a sensitivity limit as low as 5 pV/Hz^1/2, or -210dBm/Hz in a narrow band around 1 MHz. Our work introduces an entirely new approach to all-optical, ultralow-noise detection of classical electronic signals, and sets the stage for coherent upconversion of low-frequency quantum signals to the optical domain. }, doi = {10.1038/nature13029}, url = {http://arxiv.org/abs/1307.3467v2}, author = {T. Bagci and A. Simonsen and S. Schmid and L. G. Villanueva and E. Zeuthen and J. Appel and J. M. Taylor and A. S{\o}rensen and K. Usami and A. Schliesser and E. S. Polzik} } @proceedings {1388, title = {Partial-indistinguishability obfuscation using braids}, year = {2014}, month = {2014/08/21}, abstract = {

An obfuscator is an algorithm that translates circuits into functionally-equivalent similarly-sized circuits that are hard to understand. Efficient obfuscators would have many applications in cryptography. Until recently, theoretical progress has mainly been limited to no-go results. Recent works have proposed the first efficient obfuscation algorithms for classical logic circuits, based on a notion of indistinguishability against polynomial-time adversaries. In this work, we propose a new notion of obfuscation, which we call partial-indistinguishability. This notion is based on computationally universal groups with efficiently computable normal forms, and appears to be incomparable with existing definitions. We describe universal gate sets for both classical and quantum computation, in which our definition of obfuscation can be met by polynomial-time algorithms. We also discuss some potential applications to testing quantum computers. We stress that the cryptographic security of these obfuscators, especially when composed with translation from other gate sets, remains an open question.

}, url = {http://arxiv.org/abs/1212.6358}, author = {Gorjan Alagic and Stacey Jeffery and Stephen P. Jordan} } @article {1176, title = {Persistence of locality in systems with power-law interactions}, journal = {Physical Review Letters}, volume = {113}, year = {2014}, month = {2014/7/16}, abstract = { Motivated by recent experiments with ultra-cold matter, we derive a new bound on the propagation of information in $D$-dimensional lattice models exhibiting $1/r^{\alpha}$ interactions with $\alpha>D$. The bound contains two terms: One accounts for the short-ranged part of the interactions, giving rise to a bounded velocity and reflecting the persistence of locality out to intermediate distances, while the other contributes a power-law decay at longer distances. We demonstrate that these two contributions not only bound but, except at long times, \emph{qualitatively reproduce} the short- and long-distance dynamical behavior following a local quench in an $XY$ chain and a transverse-field Ising chain. In addition to describing dynamics in numerous intractable long-range interacting lattice models, our results can be experimentally verified in a variety of ultracold-atomic and solid-state systems. }, doi = {10.1103/PhysRevLett.113.030602}, url = {http://arxiv.org/abs/1401.6174v2}, author = {Zhe-Xuan Gong and Michael Foss-Feig and Spyridon Michalakis and Alexey V. Gorshkov} } @article {1429, title = {Privacy Amplification in the Isolated Qubits Model}, journal = {Eurocrypt}, year = {2014}, month = {2014/10/15}, pages = {785-814}, abstract = { Isolated qubits are a special class of quantum devices, which can be used to implement tamper-resistant cryptographic hardware such as one-time memories (OTM{\textquoteright}s). Unfortunately, these OTM constructions leak some information, and standard methods for privacy amplification cannot be applied here, because the adversary has advance knowledge of the hash function that the honest parties will use. In this paper we show a stronger form of privacy amplification that solves this problem, using a fixed hash function that is secure against all possible adversaries in the isolated qubits model. This allows us to construct single-bit OTM{\textquoteright}s which only leak an exponentially small amount of information. We then study a natural generalization of the isolated qubits model, where the adversary is allowed to perform a polynomially-bounded number of entangling gates, in addition to unbounded local operations and classical communication (LOCC). We show that our technique for privacy amplification is also secure in this setting. }, doi = {10.1007/978-3-662-46803-6_26}, url = {http://arxiv.org/abs/1410.3918v2}, author = {Yi-Kai Liu} } @article {1840, title = {Probing many-body interactions in an optical lattice clock}, journal = {Ann. Phys.}, volume = {340}, year = {2014}, pages = {311}, url = {http://www.sciencedirect.com/science/article/pii/S0003491613002546}, author = {Rey, A M and Alexey V. Gorshkov and Kraus, C V and Martin, M J and Bishof, M and Swallows, M D and Zhang, X and Benko, C and Ye, J and Lemke, N D and Ludlow, A D} } @article {1786, title = {Quantum Algorithms for Curve Fitting}, year = {2014}, month = {2014/04/02}, abstract = {We present quantum algorithms for estimating the best-fit parameters and the quality of least-square curve fitting. The running times of these algorithms are polynomial in logn, d, κ, ν, χ, 1/Φ and 1/ϵ, where n is the number of data points to be fitted, d is the dimension of feature vectors, κ is the condition number of the design matrix, ν and χ are some parameters reflecting the variances of the design matrix and response vector, Φ is the fit quality, and ϵ is the tolerable error. Different from previous quantum algorithms for these tasks, our algorithms do not require the design matrix to be sparse, and they do completely determine the fitted curve. They are developed by combining phase estimation and the density matrix exponentiation technique for dense Hamiltonian simulation.}, url = {http://arxiv.org/abs/1402.0660}, author = {Guoming Wang} } @article {1403, title = {Quantum Algorithms for Fermionic Quantum Field Theories}, year = {2014}, month = {2014/04/28}, abstract = { Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by the characteristics of fermionic fields, and its run time is polynomial in the desired precision and the energy. Thus, it constitutes further progress towards an efficient quantum algorithm for simulating the Standard Model of particle physics. }, url = {http://arxiv.org/abs/1404.7115v1}, author = {Stephen P. Jordan and Keith S. M. Lee and John Preskill} } @article {1231, title = {Quantum computation of discrete logarithms in semigroups}, journal = {Journal of Mathematical Cryptology}, volume = {8}, year = {2014}, month = {2014/01/1}, abstract = { We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor{\textquoteright}s algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks. In contrast, we show that some generalizations of the discrete log problem are hard in semigroups despite being easy in groups. We relate a shifted version of the discrete log problem in semigroups to the dihedral hidden subgroup problem, and we show that the constructive membership problem with respect to $k \ge 2$ generators in a black-box abelian semigroup of order $N$ requires $\tilde \Theta(N^{\frac{1}{2}-\frac{1}{2k}})$ quantum queries. }, doi = {10.1515/jmc-2013-0038}, url = {http://arxiv.org/abs/1310.6238v2}, author = {Andrew M. Childs and G{\'a}bor Ivanyos} } @article {1395, title = {Quantum Computation of Scattering in Scalar Quantum Field Theories}, journal = {Quantum Information and Computation}, volume = {14}, year = {2014}, month = {2014/09/01}, pages = {1014-1080}, abstract = { Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling. }, url = {http://arxiv.org/abs/1112.4833v1}, author = {Stephen P. Jordan and Keith S. M. Lee and John Preskill} } @article {1478, title = {Quantum correlations and entanglement in far-from-equilibrium spin systems }, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/12/15}, abstract = { By applying complementary analytic and numerical methods, we investigate the dynamics of spin-$1/2$ XXZ models with variable-range interactions in arbitrary dimensions. The dynamics we consider is initiated from uncorrelated states that are easily prepared in experiments, and can be equivalently viewed as either Ramsey spectroscopy or a quantum quench. Our primary focus is the dynamical emergence of correlations and entanglement in these far-from-equilibrium interacting quantum systems: we characterize these correlations by the entanglement entropy, concurrence, and squeezing, which are inequivalent measures of entanglement corresponding to different quantum resources. In one spatial dimension, we show that the time evolution of correlation functions manifests a non-perturbative dynamic singularity. This singularity is characterized by a universal power-law exponent that is insensitive to small perturbations. Explicit realizations of these models in current experiments using polar molecules, trapped ions, Rydberg atoms, magnetic atoms, and alkaline-earth and alkali atoms in optical lattices, along with the relative merits and limitations of these different systems, are discussed. }, doi = {10.1103/PhysRevA.90.063622}, url = {http://arxiv.org/abs/1406.0937v1}, author = {Kaden R. A. Hazzard and Mauritz van den Worm and Michael Foss-Feig and Salvatore R. Manmana and Emanuele Dalla Torre and Tilman Pfau and Michael Kastner and Ana Maria Rey} } @article {1320, title = {Quantum Correlations and the Measurement Problem}, journal = {International Journal of Theoretical Physics}, volume = {53}, year = {2014}, month = {2013/6/30}, pages = {3346 - 3369}, abstract = { The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. Such correlations cannot be simulated with classical resources, which generate classical correlations represented by the points in a simplex, where the vertices of the simplex represent joint deterministic states that are the common causes of the correlations. The {\textquoteleft}no go{\textquoteright} hidden variable theorems tell us that we can{\textquoteright}t shoe-horn correlations outside the local polytope into a classical simplex by supposing that something has been left out of the story. The replacement of the classical simplex by the quantum convex set as the structure representing probabilistic correlations is the analogue for quantum mechanics of the replacement of Newton{\textquoteright}s Euclidean space and time by Minkowski spacetime in special relativity. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are generic features of correlations that lie outside the local correlation polytope. This paper is an elaboration of these ideas, and its consequences for the measurement problem of quantum mechanics. A large part of the difficulty is removed by seeing that the inconsistency in reconciling the entangled state at the end of a quantum measurement process with the definiteness of the macroscopic pointer reading and the definiteness of the correlated value of the measured micro-observable is only apparent and depends on a stipulation that is not required by the structure of the quantum possibility space. Replacing this stipulation by an alternative consistent stipulation resolves the problem. }, doi = {10.1007/s10773-013-1695-z}, url = {http://arxiv.org/abs/1210.6371v3}, author = {Jeffrey Bub} } @article {1326, title = {Quantum Interactions with Closed Timelike Curves and Superluminal Signaling }, journal = {Physical Review A}, volume = {89}, year = {2014}, month = {2014/2/12}, abstract = { There is now a significant body of results on quantum interactions with closed timelike curves (CTCs) in the quantum information literature, for both the Deutsch model of CTC interactions (D-CTCs) and the projective model (P-CTCs). As a consequence, there is a prima facie argument exploiting entanglement that CTC interactions would enable superluminal and, indeed, effectively instantaneous signaling. In cases of spacelike separation between the sender of a signal and the receiver, whether a receiver measures the local part of an entangled state or a disentangled state to access the signal can depend on the reference frame. We propose a consistency condition that gives priority to either an entangled perspective or a disentangled perspective in spacelike separated scenarios. For D-CTC interactions, the consistency condition gives priority to frames of reference in which the state is disentangled, while for P-CTC interactions the condition selects the entangled state. Using the consistency condition, we show that there is a procedure that allows Alice to signal to Bob in the past via relayed superluminal communications between spacelike separated Alice and Clio, and spacelike separated Clio and Bob. This opens the door to time travel paradoxes in the classical domain. Ralph (arXiv:1107.4675) first pointed this out for P-CTCs, but we show that Ralph{\textquoteright}s procedure for a {\textquoteright}radio to the past{\textquoteright} is flawed. Since both D-CTCs and P-CTCs allow classical information to be sent around a spacetime loop, it follows from a result by Aaronson and Watrous (Proc.Roy.Soc.A, 465:631-647 (2009)) for CTC-enhanced classical computation that a quantum computer with access to P-CTCs would have the power of PSPACE, equivalent to a D-CTC-enhanced quantum computer. }, doi = {10.1103/PhysRevA.89.022311}, url = {http://arxiv.org/abs/1309.4751v4}, author = {Jeffrey Bub and Allen Stairs} } @article {1495, title = {A Quantum Network of Silicon Qubits using Mid-Infrared Graphene Plasmons}, year = {2014}, month = {2014/07/25}, abstract = { We consider a quantum network of mid-infrared, graphene plasmons coupled to the hydrogen-like excited states of group-V donors in silicon. First, we show how to use plasmon-enhanced light-matter interactions to achieve single-shot spin readout of the donor qubits via optical excitation and electrical detection of the emitted plasmons. We then show how plasmons in high mobility graphene nanoribbons can be used to achieve high-fidelity, two-qubit gates and entanglement of distant Si donor qubits. The proposed device is readily compatible with existing technology and fabrication methods. }, url = {http://arxiv.org/abs/1407.7035v1}, author = {Michael Gullans and J. M. Taylor} } @article {1534, title = {Quipper: Concrete Resource Estimation in Quantum Algorithms}, year = {2014}, month = {2014/12/01}, abstract = {

Despite the rich literature on quantum algorithms, there is a surprisingly small amount of coverage of their concrete logical design and implementation. Most resource estimation is done at the level of complexity analysis, but actual concrete numbers (of quantum gates, qubits, etc.) can differ by orders of magnitude. The line of work we present here is a formal framework to write, and reason about, quantum algorithms. Specifically, we designed a language, Quipper, with scalability in mind, and we are able to report actual resource counts for seven non-trivial algorithms found in the quantum computer science literature.

}, url = {http://arxiv.org/abs/1412.0625v1}, author = {Jonathan M. Smith and Neil J. Ross and Peter Selinger and Beno{\^\i}t Valiron} } @article {1788, title = {Remote tomography and entanglement swapping via von Neumann{\textendash}Arthurs{\textendash}Kelly interaction }, journal = {Physical Review A}, volume = {89}, year = {2014}, month = {2014/05/09}, pages = {052107}, abstract = {We propose an interaction-based method for remote tomography and entanglement swapping. Alice arranges a von Neumann-Arthurs-Kelly interaction between a system particle P and two apparatus particles A1,A2, and then transports the latter to Bob. Bob can reconstruct the unknown initial state of particle P not received by him by quadrature measurements on A1,A2. Further, if another particle P' in Alice{\textquoteright}s hands is EPR entangled with P, it will be EPR entangled with the distant pair A1,A2. This method will be contrasted with the usual teleportation protocols.}, doi = {http://dx.doi.org/10.1103/PhysRevA.89.052107}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.89.052107}, author = {S. M. Roy and Abhinav Deshpande and Nitica Sakharwade} } @article {1514, title = {Robust Extraction of Tomographic Information via Randomized Benchmarking}, journal = {Physical Review X}, volume = {4}, year = {2014}, month = {2014/3/25}, abstract = { We describe how randomized benchmarking can be used to reconstruct the unital part of any trace-preserving quantum map, which in turn is sufficient for the full characterization of any unitary evolution, or more generally, any unital trace-preserving evolution. This approach inherits randomized benchmarking{\textquoteright}s robustness to preparation and measurement imperfections, therefore avoiding systematic errors caused by these imperfections. We also extend these techniques to efficiently estimate the average fidelity of a quantum map to unitary maps outside of the Clifford group. The unitaries we consider include operations commonly used to achieve universal quantum computation in a fault-tolerant setting. In addition, we rigorously bound the time and sampling complexities of randomized benchmarking procedures. }, doi = {10.1103/PhysRevX.4.011050}, url = {http://arxiv.org/abs/1306.2348v1}, author = {Shelby Kimmel and Marcus P. da Silva and Colm A. Ryan and Blake R. Johnson and Thomas Ohki} } @article {1506, title = {Scattering resonances and bound states for strongly interacting Rydberg polaritons }, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/11/3}, abstract = { We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments. }, doi = {10.1103/PhysRevA.90.053804}, url = {http://arxiv.org/abs/1402.7333v1}, author = {P. Bienias and S. Choi and O. Firstenberg and Mohammad F. Maghrebi and Michael Gullans and M. D. Lukin and Alexey V. Gorshkov and H. P. B{\"u}chler} } @article {1428, title = {Single-shot security for one-time memories in the isolated qubits model}, journal = {CRYPTO}, volume = {Part II}, year = {2014}, month = {2014/02/01}, pages = {19-36}, abstract = { One-time memories (OTM{\textquoteright}s) are simple, tamper-resistant cryptographic devices, which can be used to implement sophisticated functionalities such as one-time programs. Can one construct OTM{\textquoteright}s whose security follows from some physical principle? This is not possible in a fully-classical world, or in a fully-quantum world, but there is evidence that OTM{\textquoteright}s can be built using "isolated qubits" -- qubits that cannot be entangled, but can be accessed using adaptive sequences of single-qubit measurements. Here we present new constructions for OTM{\textquoteright}s using isolated qubits, which improve on previous work in several respects: they achieve a stronger "single-shot" security guarantee, which is stated in terms of the (smoothed) min-entropy; they are proven secure against adversaries who can perform arbitrary local operations and classical communication (LOCC); and they are efficiently implementable. These results use Wiesner{\textquoteright}s idea of conjugate coding, combined with error-correcting codes that approach the capacity of the q-ary symmetric channel, and a high-order entropic uncertainty relation, which was originally developed for cryptography in the bounded quantum storage model. }, doi = {10.1007/978-3-662-44381-1_2}, url = {http://arxiv.org/abs/1402.0049v2}, author = {Yi-Kai Liu} } @article {1233, title = {Spatial search by continuous-time quantum walks on crystal lattices}, journal = {Physical Review A}, volume = {89}, year = {2014}, month = {2014/5/30}, abstract = { We consider the problem of searching a general $d$-dimensional lattice of $N$ vertices for a single marked item using a continuous-time quantum walk. We demand locality, but allow the walk to vary periodically on a small scale. By constructing lattice Hamiltonians exhibiting Dirac points in their dispersion relations and exploiting the linear behaviour near a Dirac point, we develop algorithms that solve the problem in a time of $O(\sqrt N)$ for $d>2$ and $O(\sqrt N \log N)$ in $d=2$. In particular, we show that such algorithms exist even for hypercubic lattices in any dimension. Unlike previous continuous-time quantum walk algorithms on hypercubic lattices in low dimensions, our approach does not use external memory. }, doi = {10.1103/PhysRevA.89.052337}, url = {http://arxiv.org/abs/1403.2676v2}, author = {Andrew M. Childs and Yimin Ge} } @article {1295, title = {Spin-orbit-coupled topological Fulde-Ferrell states of fermions in a harmonic trap }, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/11/7}, abstract = { Motivated by recent experimental breakthroughs in generating spin-orbit coupling in ultracold Fermi gases using Raman laser beams, we present a systematic study of spin-orbit-coupled Fermi gases confined in a quasi-one-dimensional trap in the presence of an in-plane Zeeman field (which can be realized using a finite two-photon Raman detuning). We find that a topological Fulde-Ferrell state will emerge, featuring finite-momentum Cooper pairing and zero-energy Majorana excitations localized near the edge of the trap based on the self-consistent Bogoliubov-de Genes (BdG) equations. We find analytically the wavefunctions of the Majorana modes. Finally using the time-dependent BdG we show how the finite-momentum pairing field manifests itself in the expansion dynamics of the atomic cloud. }, doi = {10.1103/PhysRevA.90.053606}, url = {http://arxiv.org/abs/1404.6211v1}, author = {Lei Jiang and Eite Tiesinga and Xia-Ji Liu and Hui Hu and Han Pu} } @article {1871, title = {Strong Equivalence of Reversible Circuits is coNP-complete}, journal = {Quantum Information Computation}, volume = {14}, year = {2014}, month = {2014/11/01}, pages = {1302{\textendash}1307}, abstract = {

It is well-known that deciding equivalence of logic circuits is a coNP-complete problem. As a corollary, the problem of deciding weak equivalence of reversible circuits, i.e. allowing initialized ancilla bits in the input and ignoring \"garbage\" ancilla bits in the output, is also coNP-complete. The complexity of deciding strong equivalence, including the ancilla bits, is less obvious and may depend on gate set. Here we use Barrington\&$\#$39;s theorem to show that deciding strong equivalence of reversible circuits built from the Fredkin gate is coNP-complete. This implies coNP-completeness of deciding strong equivalence for other commonly used universal reversible gate sets, including any gate set that includes the Toffoli or Fredkin gate.

}, keywords = {complexity, reversible circuits}, issn = {1533-7146}, url = {http://dl.acm.org/citation.cfm?id=2685179.2685182}, author = {Stephen P. Jordan} } @article {1479, title = {Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect }, journal = {Physical Review Letters}, volume = {112}, year = {2014}, month = {2014/2/20}, abstract = { We investigate theoretically the suppression of two-body losses when the on-site loss rate is larger than all other energy scales in a lattice. This work quantitatively explains the recently observed suppression of chemical reactions between two rotational states of fermionic KRb molecules confined in one-dimensional tubes with a weak lattice along the tubes [Yan et al., Nature 501, 521-525 (2013)]. New loss rate measurements performed for different lattice parameters but under controlled initial conditions allow us to show that the loss suppression is a consequence of the combined effects of lattice confinement and the continuous quantum Zeno effect. A key finding, relevant for generic strongly reactive systems, is that while a single-band theory can qualitatively describe the data, a quantitative analysis must include multiband effects. Accounting for these effects reduces the inferred molecule filling fraction by a factor of five. A rate equation can describe much of the data, but to properly reproduce the loss dynamics with a fixed filling fraction for all lattice parameters we develop a mean-field model and benchmark it with numerically exact time-dependent density matrix renormalization group calculations. }, doi = {10.1103/PhysRevLett.112.070404}, url = {http://arxiv.org/abs/1310.2221v2}, author = {Bihui Zhu and Bryce Gadway and Michael Foss-Feig and Johannes Schachenmayer and Michael Wall and Kaden R. A. Hazzard and Bo Yan and Steven A. Moses and Jacob P. Covey and Deborah S. Jin and Jun Ye and Murray Holland and Ana Maria Rey} } @article {1451, title = {Symmetric Extension of Two-Qubit States}, journal = {Physical Review A}, volume = {90}, year = {2014}, month = {2014/9/17}, abstract = { Quantum key distribution uses public discussion protocols to establish shared secret keys. In the exploration of ultimate limits to such protocols, the property of symmetric extendibility of underlying bipartite states $\rho_{AB}$ plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible if there exits a tripartite state $\rho_{ABB{\textquoteright}}$, such that the $AB$ marginal state is identical to the $AB{\textquoteright}$ marginal state, i.e. $\rho_{AB{\textquoteright}}=\rho_{AB}$. For a symmetric extendible state $\rho_{AB}$, the first task of the public discussion protocol is to break this symmetric extendibility. Therefore to characterize all bi-partite quantum states that possess symmetric extensions is of vital importance. We prove a simple analytical formula that a two-qubit state $\rho_{AB}$ admits a symmetric extension if and only if $\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}$. Given the intimate relationship between the symmetric extension problem and the quantum marginal problem, our result also provides the first analytical necessary and sufficient condition for the quantum marginal problem with overlapping marginals. }, doi = {10.1103/PhysRevA.90.032318}, url = {http://arxiv.org/abs/1310.3530v2}, author = {Jianxin Chen and Zhengfeng Ji and David Kribs and Norbert L{\"u}tkenhaus and Bei Zeng} } @article {1445, title = {Unextendible Product Basis for Fermionic Systems}, journal = {Journal of Mathematical Physics}, volume = {55}, year = {2014}, month = {2014/01/01}, pages = {082207}, abstract = { We discuss the concept of unextendible product basis (UPB) and generalized UPB for fermionic systems, using Slater determinants as an analogue of product states, in the antisymmetric subspace $\wedge^ N \bC^M$. We construct an explicit example of generalized fermionic unextendible product basis (FUPB) of minimum cardinality $N(M-N)+1$ for any $N\ge2,M\ge4$. We also show that any bipartite antisymmetric space $\wedge^ 2 \bC^M$ of codimension two is spanned by Slater determinants, and the spaces of higher codimension may not be spanned by Slater determinants. Furthermore, we construct an example of complex FUPB of $N=2,M=4$ with minimum cardinality $5$. In contrast, we show that a real FUPB does not exist for $N=2,M=4$ . Finally we provide a systematic construction for FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions. }, doi = {10.1063/1.4893358}, url = {http://arxiv.org/abs/1312.4218v1}, author = {Jianxin Chen and Lin Chen and Bei Zeng} } @article {2630, title = {When the asymptotic limit offers no advantage in the local-operations-and-classical-communication paradigm}, journal = {Phys. Rev. A }, volume = {89}, year = {2014}, month = {5/9/2014}, abstract = {

We consider bipartite LOCC, the class of operations implementable by local quantum operations and classical communication between two parties. Surprisingly, there are operations that can be approximated to arbitrary precision but are impossible to implement exactly if only a finite number of messages are exchanged. This significantly complicates the analysis of what can or cannot be approximated with LOCC. Toward alleviating this problem, we exhibit two scenarios in which allowing vanishing error does not help. The first scenario is implementation of projective measurements with product measurement operators. The second scenario is the discrimination of unextendable product bases on two three-dimensional systems.

}, doi = {https://doi.org/10.1103/PhysRevA.89.052310}, author = {Honghao Fu and Debbie Leung and Laura Mancinska} } @article {1505, title = {All-Optical Switch and Transistor Gated by One Stored Photon}, journal = {Science}, volume = {341}, year = {2013}, month = {2013/07/04}, pages = {768 - 770}, abstract = { The realization of an all-optical transistor where one {\textquoteright}gate{\textquoteright} photon controls a {\textquoteright}source{\textquoteright} light beam, is a long-standing goal in optics. By stopping a light pulse in an atomic ensemble contained inside an optical resonator, we realize a device in which one stored gate photon controls the resonator transmission of subsequently applied source photons. A weak gate pulse induces bimodal transmission distribution, corresponding to zero and one gate photons. One stored gate photon produces fivefold source attenuation, and can be retrieved from the atomic ensemble after switching more than one source photon. Without retrieval, one stored gate photon can switch several hundred source photons. With improved storage and retrieval efficiency, our work may enable various new applications, including photonic quantum gates, and deterministic multiphoton entanglement. }, doi = {10.1126/science.1238169}, url = {http://arxiv.org/abs/1401.3194v1}, author = {Wenlan Chen and Kristin M. Beck and Robert B{\"u}cker and Michael Gullans and Mikhail D. Lukin and Haruka Tanji-Suzuki and Vladan Vuletic} } @article {1841, title = {Attractive Photons in a Quantum Nonlinear Medium}, journal = {Nature (London)}, volume = {502}, year = {2013}, pages = {71}, url = {http://dx.doi.org/10.1038/nature12512}, author = {Ofer Firstenberg and Thibault Peyronel and Qi-Yu Liang and Alexey V. Gorshkov and Mikhail D. Lukin and Vladan Vuletic} } @article {1426, title = {Building one-time memories from isolated qubits}, journal = {Innovations in Theoretical Computer Science (ITCS)}, year = {2013}, month = {2013/04/18}, pages = {269-286}, abstract = { One-time memories (OTM{\textquoteright}s) are simple tamper-resistant cryptographic devices, which can be used to implement one-time programs, a very general form of software protection and program obfuscation. Here we investigate the possibility of building OTM{\textquoteright}s using quantum mechanical devices. It is known that OTM{\textquoteright}s cannot exist in a fully-quantum world or in a fully-classical world. Instead, we propose a new model based on "isolated qubits" -- qubits that can only be accessed using local operations and classical communication (LOCC). This model combines a quantum resource (single-qubit measurements) with a classical restriction (on communication between qubits), and can be implemented using current technologies, such as nitrogen vacancy centers in diamond. In this model, we construct OTM{\textquoteright}s that are information-theoretically secure against one-pass LOCC adversaries that use 2-outcome measurements. Our construction resembles Wiesner{\textquoteright}s old idea of quantum conjugate coding, implemented using random error-correcting codes; our proof of security uses entropy chaining to bound the supremum of a suitable empirical process. In addition, we conjecture that our random codes can be replaced by some class of efficiently-decodable codes, to get computationally-efficient OTM{\textquoteright}s that are secure against computationally-bounded LOCC adversaries. In addition, we construct data-hiding states, which allow an LOCC sender to encode an (n-O(1))-bit messsage into n qubits, such that at most half of the message can be extracted by a one-pass LOCC receiver, but the whole message can be extracted by a general quantum receiver. }, doi = {10.1145/2554797.2554823}, url = {http://arxiv.org/abs/1304.5007v2}, author = {Yi-Kai Liu} } @article {1186, title = {Controllable quantum spin glasses with magnetic impurities embedded in quantum solids }, journal = {Physical Review B}, volume = {88}, year = {2013}, month = {2013/7/24}, abstract = { Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHo$_x$Y$_{1-x}$F$_4$. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases. }, doi = {10.1103/PhysRevB.88.014426}, url = {http://arxiv.org/abs/1307.1130v1}, author = {Mikhail Lemeshko and Norman Y. Yao and Alexey V. Gorshkov and Hendrik Weimer and Steven D. Bennett and Takamasa Momose and Sarang Gopalakrishnan} } @article {1272, title = {Controlling the group velocity of colliding atomic Bose-Einstein condensates with Feshbach resonances }, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/5/10}, abstract = { We report on a proposal to change the group velocity of a small Bose Einstein Condensate (BEC) upon collision with another BEC in analogy to slowing of light passing through dispersive media. We make use of ultracold collisions near a magnetic Feshbach resonance, which gives rise to a sharp variation in scattering length with collision energy and thereby changes the group velocity. A generalized Gross-Pitaveskii equation is derived for a small BEC moving through a larger stationary BEC. We denote the two condensates by laser and medium BEC, respectively, to highlight the analogy to a laser pulse travelling through a medium. We derive an expression for the group velocity in a homogeneous medium as well as for the difference in distance, $\delta$, covered by the laser BEC in the presence and absence of a finite-sized medium BEC with a Thomas-Fermi density distribution. For a medium and laser of the same isotopic species, the shift $\delta$ has an upper bound of twice the Thomas-Fermi radius of the medium. For typical narrow Feshbach resonances and a medium with number density $10^{15}$ cm$^{-3}$ up to 85\% of the upper bound can be achieved, making the effect experimentally observable. We also derive constraints on the experimental realization of our proposal. }, doi = {10.1103/PhysRevA.87.053608}, url = {http://arxiv.org/abs/1301.4234v2}, author = {Ranchu Mathew and Eite Tiesinga} } @article {1161, title = {Dissipative Many-body Quantum Optics in Rydberg Media}, journal = {Physical Review Letters}, volume = {110}, year = {2013}, month = {2013/4/9}, abstract = { We develop a theoretical framework for the dissipative propagation of quantized light in interacting optical media under conditions of electromagnetically induced transparency (EIT). The theory allows us to determine the peculiar spatiotemporal structure of the output of two complementary Rydberg-EIT-based light-processing modules: the recently demonstrated single-photon filter and the recently proposed single-photon subtractor, which, respectively, let through and absorb a single photon. In addition to being crucial for applications of these and other optical quantum devices, the theory opens the door to the study of exotic dissipative many-body dynamics of strongly interacting photons in nonlinear nonlocal media. }, doi = {10.1103/PhysRevLett.110.153601}, url = {http://arxiv.org/abs/1211.7060v1}, author = {Alexey V. Gorshkov and Rejish Nath and Thomas Pohl} } @article {1475, title = {Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence }, journal = {New Journal of Physics}, volume = {15}, year = {2013}, month = {2013/11/07}, pages = {113008}, abstract = { Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations. In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t=0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Ref. [1]. Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g. Bloch vector and spin-squeezing dynamics. In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence of both T_1 (spontaneous spin relaxation/excitation) and T_2 (dephasing) type decoherence processes. Even though the decoherence is local, our solution reveals that the competition between Ising dynamics and T_1 decoherence gives rise to an emergent non-local dephasing effect, thereby drastically amplifying the degradation of quantum correlations. In addition to identifying the mechanism of this deleterious effect, our solution points toward a scheme to eliminate it via measurement-based coherent feedback. }, doi = {10.1088/1367-2630/15/11/113008}, url = {http://arxiv.org/abs/1306.0172v1}, author = {Michael Foss-Feig and Kaden R A Hazzard and John J Bollinger and Ana Maria Rey and Charles W Clark} } @article {1245, title = {Easy and hard functions for the Boolean hidden shift problem}, journal = {Proceedings of TQC 2013}, volume = {22}, year = {2013}, month = {2013/04/16}, pages = {50-79}, abstract = { We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact one-query algorithm exists if and only if the function is bent. We partially characterize the hardest instances, which include delta functions. Moreover, we show that the problem is easy for random functions, since two queries suffice. Our algorithm for random functions is based on performing the pretty good measurement on several copies of a certain state; its analysis relies on the Fourier transform. We also use this approach to improve the quantum rejection sampling approach to the Boolean hidden shift problem. }, doi = {10.4230/LIPIcs.TQC.2013.50}, url = {http://arxiv.org/abs/1304.4642v1}, author = {Andrew M. Childs and Robin Kothari and Maris Ozols and Martin Roetteler} } @article {1343, title = {Electrically-protected resonant exchange qubits in triple quantum dots}, journal = {Physical Review Letters}, volume = {111}, year = {2013}, month = {2013/7/31}, abstract = {We present a modulated microwave approach for quantum computing with qubits comprising three spins in a triple quantum dot. This approach includes single- and two-qubit gates that are protected against low-frequency electrical noise, due to an operating point with a narrowband response to high frequency electric fields. Furthermore, existing double quantum dot advances, including robust preparation and measurement via spin-to-charge conversion, are immediately applicable to the new qubit. Finally, the electric dipole terms implicit in the high frequency coupling enable strong coupling with superconducting microwave resonators, leading to more robust two-qubit gates. }, doi = {10.1103/PhysRevLett.111.050502}, url = {http://arxiv.org/abs/1304.3407v2}, author = {J. M. Taylor and V. Srinivasa and J. Medford} } @article {1864, title = {Evasiveness of Graph Properties and Topological Fixed-Point Theorems}, journal = {Foundations and Trends in Theoretical Computer Science}, volume = {7}, year = {2013}, month = {2013/05/16}, pages = {337-415}, abstract = {

Many graph properties (e.g., connectedness, containing a complete subgraph) are known to be difficult to check. In a decision-tree model, the cost of an algorithm is measured by the number of edges in the graph that it queries. R. Karp conjectured in the early 1970s that all monotone graph properties are evasive -- that is, any algorithm which computes a monotone graph property must check all edges in the worst case. This conjecture is unproven, but a lot of progress has been made. Starting with the work of Kahn, Saks, and Sturtevant in 1984, topological methods have been applied to prove partial results on the Karp conjecture. This text is a tutorial on these topological methods. I give a fully self-contained account of the central proofs from the paper of Kahn, Saks, and Sturtevant, with no prior knowledge of topology assumed. I also briefly survey some of the more recent results on evasiveness.

}, issn = {1551-305X}, doi = {10.1561/0400000055}, url = {http://dx.doi.org/10.1561/0400000055}, author = {Carl Miller} } @article {1268, title = {Experimental Performance of a Quantum Simulator: Optimizing Adiabatic Evolution and Identifying Many-Body Ground States }, journal = {Physical Review A}, volume = {88}, year = {2013}, month = {2013/7/31}, abstract = { We use local adiabatic evolution to experimentally create and determine the ground state spin ordering of a fully-connected Ising model with up to 14 spins. Local adiabatic evolution -- in which the system evolution rate is a function of the instantaneous energy gap -- is found to maximize the ground state probability compared with other adiabatic methods while only requiring knowledge of the lowest $\sim N$ of the $2^N$ Hamiltonian eigenvalues. We also demonstrate that the ground state ordering can be experimentally identified as the most probable of all possible spin configurations, even when the evolution is highly non-adiabatic. }, doi = {10.1103/PhysRevA.88.012334}, url = {http://arxiv.org/abs/1305.2253v1}, author = {Philip Richerme and Crystal Senko and Jacob Smith and Aaron Lee and Simcha Korenblit and Christopher Monroe} } @article {1474, title = {Far from equilibrium quantum magnetism with ultracold polar molecules}, journal = {Physical Review Letters}, volume = {110}, year = {2013}, month = {2013/2/11}, abstract = { Recent theory has indicated how to emulate tunable models of quantum magnetism with ultracold polar molecules. Here we show that present molecule optical lattice experiments can accomplish three crucial goals for quantum emulation, despite currently being well below unit filling and not quantum degenerate. The first is to verify and benchmark the models proposed to describe these systems. The second is to prepare correlated and possibly useful states in well-understood regimes. The third is to explore many-body physics inaccessible to existing theoretical techniques. Our proposal relies on a non-equilibrium protocol that can be viewed either as Ramsey spectroscopy or an interaction quench. It uses only routine experimental tools available in any ultracold molecule experiment. }, doi = {10.1103/PhysRevLett.110.075301}, url = {http://arxiv.org/abs/1209.4076v1}, author = {Kaden R. A. Hazzard and Salvatore R. Manmana and Michael Foss-Feig and Ana Maria Rey} } @article {1273, title = {Formation and decay of Bose-Einstein condensates in an excited band of a double-well optical lattice }, journal = {Physical Review A}, volume = {88}, year = {2013}, month = {2013/9/12}, abstract = { We study the formation and collision-aided decay of an ultra-cold atomic Bose-Einstein condensate in the first excited band of a double-well 2D-optical lattice with weak harmonic confinement in the perpendicular $z$ direction. This lattice geometry is based on an experiment by Wirth et al. The double well is asymmetric, with the local ground state in the shallow well nearly degenerate with the first excited state of the adjacent deep well. We compare the band structure obtained from a tight-binding (TB) model with that obtained numerically using a plane wave basis. We find the TB model to be in quantitative agreement for the lowest two bands, qualitative for next two bands, and inadequate for even higher bands. The band widths of the excited bands are much larger than the harmonic oscillator energy spacing in the $z$ direction. We then study the thermodynamics of a non-interacting Bose gas in the first excited band. We estimate the condensate fraction and critical temperature, $T_c$, as functions of lattice parameters. For typical atom numbers, the critical energy $k_BT_c$, with $k_B$ the Boltzmann constant, is larger than the excited band widths and harmonic oscillator energy. Using conservation of total energy and atom number, we show that the temperature increases after the lattice transformation. Finally, we estimate the time scale for a two-body collision-aided decay of the condensate as a function of lattice parameters. The decay involves two processes, the dominant one in which both colliding atoms decay to the ground band, and the second involving excitation of one atom to a higher band. For this estimate, we have used TB wave functions for the lowest four bands, and numerical estimates for higher bands. The decay rate rapidly increases with lattice depth, but stays smaller than the tunneling rate between the $s$ and $p$ orbitals in adjacent wells. }, doi = {10.1103/PhysRevA.88.033615}, url = {http://arxiv.org/abs/1308.4449v1}, author = {Saurabh Paul and Eite Tiesinga} } @article {1244, title = {A framework for bounding nonlocality of state discrimination}, journal = {Communications in Mathematical Physics}, volume = {323}, year = {2013}, month = {2013/9/4}, pages = {1121 - 1153}, abstract = { We consider the class of protocols that can be implemented by local quantum operations and classical communication (LOCC) between two parties. In particular, we focus on the task of discriminating a known set of quantum states by LOCC. Building on the work in the paper "Quantum nonlocality without entanglement" [BDF+99], we provide a framework for bounding the amount of nonlocality in a given set of bipartite quantum states in terms of a lower bound on the probability of error in any LOCC discrimination protocol. We apply our framework to an orthonormal product basis known as the domino states and obtain an alternative and simplified proof that quantifies its nonlocality. We generalize this result for similar bases in larger dimensions, as well as the "rotated" domino states, resolving a long-standing open question [BDF+99]. }, doi = {10.1007/s00220-013-1784-0}, url = {http://arxiv.org/abs/1206.5822v1}, author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols} } @article {1486, title = {Individual Addressing in Quantum Computation through Spatial Refocusing}, journal = {Physical Review A}, volume = {88}, year = {2013}, month = {2013/11/21}, abstract = { Separate addressing of individual qubits is a challenging requirement for scalable quantum computation, and crosstalk between operations on neighboring qubits remains as a significant source of noise for current experimental implementation of multi-qubit platforms. We propose a scheme based on spatial refocusing from interference of several coherent laser beams to significantly reduce the crosstalk noise for any type of quantum gates. A general framework is developed for the spatial refocusing technique, in particular with practical Gaussian beams, and we show under typical experimental conditions, the crosstalk-induced infidelity of quantum gates can be reduced by several orders of magnitude with a moderate cost of a few correction laser beams. }, doi = {10.1103/PhysRevA.88.052325}, url = {http://arxiv.org/abs/1305.2798v3}, author = {Chao Shen and Zhe-Xuan Gong and Luming Duan} } @article {1246, title = {Interpolatability distinguishes LOCC from separable von Neumann measurements}, journal = {Journal of Mathematical Physics}, volume = {54}, year = {2013}, month = {2013/06/25}, pages = {112204}, abstract = { Local operations with classical communication (LOCC) and separable operations are two classes of quantum operations that play key roles in the study of quantum entanglement. Separable operations are strictly more powerful than LOCC, but no simple explanation of this phenomenon is known. We show that, in the case of von Neumann measurements, the ability to interpolate measurements is an operational principle that sets apart LOCC and separable operations. }, doi = {10.1063/1.4830335}, url = {http://arxiv.org/abs/1306.5992v1}, author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols} } @article {1536, title = {An Introduction to Quantum Programming in Quipper}, journal = {Lecture Notes in Computer Science}, volume = {7948}, year = {2013}, month = {2013/07/05}, pages = {110-124}, abstract = { Quipper is a recently developed programming language for expressing quantum computations. This paper gives a brief tutorial introduction to the language, through a demonstration of how to make use of some of its key features. We illustrate many of Quipper{\textquoteright}s language features by developing a few well known examples of Quantum computation, including quantum teleportation, the quantum Fourier transform, and a quantum circuit for addition. }, isbn = {978-3-642-38986-3}, doi = {10.1007/978-3-642-38986-3_10}, url = {http://arxiv.org/abs/1304.5485v1}, author = {Alexander S. Green and Peter LeFanu Lumsdaine and Neil J. Ross and Peter Selinger and Beno{\^\i}t Valiron} } @article {1175, title = {Kitaev honeycomb and other exotic spin models with polar molecules}, journal = {Molecular Physics}, volume = {111}, year = {2013}, month = {2013/01/01}, pages = {1908 - 1916}, abstract = { We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole-dipole interactions give rise to interactions between the spins. In particular, we show that, with sufficient microwave control, the interaction between two spins can be written as a sum of five independently controllable Hamiltonian terms proportional to the five rank-2 spherical harmonics Y_{2,q}(theta,phi), where (theta,phi) are the spherical coordinates of the vector connecting the two molecules. To demonstrate the potential of this approach beyond the simplest examples studied in [S. R. Manmana et al., arXiv:1210.5518v2], we focus on the realization of the Kitaev honeycomb model, which can support exotic non-Abelian anyonic excitations. We also discuss the possibility of generating spin Hamiltonians with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry. }, doi = {10.1080/00268976.2013.800604}, url = {http://arxiv.org/abs/1301.5636v1}, author = {Alexey V. Gorshkov and Kaden R. A. Hazzard and Ana Maria Rey} } @article {1587, title = {Multilingual Summarization: Dimensionality Reduction and a Step Towards Optimal Term Coverage}, journal = {MultiLing (Workshop on Multilingual Multi-document Summarization)}, year = {2013}, month = {2013/08/09}, pages = {55-63}, abstract = {In this paper we present three term weighting approaches for multi-lingual document summarization and give results on the DUC 2002 data as well as on the 2013 Multilingual Wikipedia feature articles data set. We introduce a new intervalbounded nonnegative matrix factorization. We use this new method, latent semantic analysis (LSA), and latent Dirichlet allocation (LDA) to give three term-weighting methods for multi-document multi-lingual summarization. Results on DUC and TAC data, as well as on the MultiLing 2013 data, demonstrate that these methods are very promising, since they achieve oracle coverage scores in the range of humans for 6 of the 10 test languages. Finally, we present three term weighting approaches for the MultiLing13 single document summarization task on the Wikipedia featured articles. Our submissions signifi- cantly outperformed the baseline in 19 out of 41 languages. }, url = {http://aclweb.org/anthology/W/W13/W13-3108.pdf}, author = {John M. Conroy and Sashka T. Davis and Jeff Kubina and Yi-Kai Liu and Dianne P. O{\textquoteright}Leary and Judith D. Schlesinger} } @article {1341, title = {A noise inequality for classical forces}, year = {2013}, month = {2013/11/18}, abstract = {Lorentz invariance requires local interactions, with force laws such as the Coulomb interaction arising via virtual exchange of force carriers such as photons. Many have considered the possibility that, at long distances or large mass scales, this process changes in some way to lead to classical behavior. Here we hypothesize that classical behavior could be due to an inability of some force carriers to convey entanglement, a characteristic measure of nonlocal, quantum behavior. We then prove that there exists a local test that allows one to verify entanglement generation, falsifying our hypothesis. Crucially, we show that noise measurements can directly verify entanglement generation. This provides a step forward for a wide variety of experimental systems where traditional entanglement tests are challenging, including entanglement generation by gravity alone between macroscopic torsional oscillators. }, url = {http://arxiv.org/abs/1311.4558v1}, author = {Dvir Kafri and J. M. Taylor} } @article {1471, title = {Non-equilibrium dynamics of Ising models with decoherence: an exact solution }, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/4/3}, abstract = { The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics: Decoherence can degrade correlations, but can also give rise to a variety of rich dynamical and steady-state behaviors. We obtain an exact analytic solution for the non-equilibrium dynamics of Ising models with arbitrary interactions and subject to the most general form of local Markovian decoherence. Our solution shows that decoherence affects the relaxation of observables more than predicted by single-particle considerations. It also reveals a dynamical phase transition, specifically a Hopf bifurcation, which is absent at the single-particle level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. }, doi = {10.1103/PhysRevA.87.042101}, url = {http://arxiv.org/abs/1209.5795v2}, author = {Michael Foss-Feig and Kaden R. A. Hazzard and John J. Bollinger and Ana Maria Rey} } @article {1865, title = {Optimal entanglement-assisted one-shot classical communication}, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/06/03}, pages = {062301}, abstract = {

The\ one-shot success probability\ of a noisy classical channel for transmitting one classical bit is the optimal probability with which the bit can be successfully sent via a single use of the channel. Prevedel\ et al.\ [Phys. Rev. Lett.106, 110505 (2011)] recently showed that for a specific channel, this quantity can be increased if the parties using the channel share an entangled quantum state. In this paper, we characterize the optimal entanglement-assisted protocols in terms of the radius of a set of operators associated with the channel. This characterization can be used to construct optimal entanglement-assisted protocols for a given classical channel and to prove the limits of such protocols. As an example, we show that the Prevedel\ et al.\ protocol is optimal for two-qubit entanglement. We also prove some tight upper bounds on the improvement that can be obtained from quantum and nonsignaling correlations.

}, doi = {10.1103/PhysRevA.87.062301}, url = {http://link.aps.org/doi/10.1103/PhysRevA.87.062301}, author = {Hemenway, Brett and Carl Miller and Shi, Yaoyun and Wootters, Mary} } @inbook {1863, title = {Optimal robust self-testing by binary nonlocal XOR games}, booktitle = {8th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2013}, volume = {22}, year = {2013}, pages = {254{\textendash}262}, publisher = {Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing}, organization = {Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing}, abstract = {

Self-testing a quantum apparatus means verifying the existence of a certain quantum state as well as the effect of the associated measuring devices based only on the statistics of the measurement outcomes. Robust (i.e., error-tolerant) self-testing quantum apparatuses are critical building blocks for quantum cryptographic protocols that rely on imperfect or untrusted devices. We devise a general scheme for proving optimal robust self-testing properties for tests based on nonlocal binary XOR games. We offer some simplified proofs of known results on self-testing, and also prove some new results.

}, keywords = {nonlocal games, quantum cryptography, Random number generation, Self-testing}, doi = {10.4230/LIPIcs.TQC.2013.254}, author = {Carl Miller and Yaoyun Shi} } @article {1497, title = {Preparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots }, journal = {Physical Review B}, volume = {88}, year = {2013}, month = {2013/7/15}, abstract = { We theoretically study the dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. In our prior work [Phys. Rev. Lett. 104, 226807 (2010)] we identified three regimes of long-term dynamics, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. In particular, when the dots are different sizes we found that the Overhauser field becomes larger in the smaller dot. Here we present a detailed theoretical analysis of these problems including a model of the polarization dynamics and the development of a new numerical method to efficiently simulate semiclassical central-spin problems. When nuclear spin noise is included, the results agree with our prior work indicating that large difference fields and dark states are stable configurations, while the elimination of the difference field is unstable; however, in the absence of noise we find all three steady states are achieved depending on parameters. These results are in good agreement with dynamic nuclear polarization experiments in double quantum dots. }, doi = {10.1103/PhysRevB.88.035309}, url = {http://arxiv.org/abs/1212.6953v3}, author = {Michael Gullans and J. J. Krich and J. M. Taylor and B. I. Halperin and M. D. Lukin} } @article {1485, title = {Prethermalization and dynamical transition in an isolated trapped ion spin chain }, journal = {New Journal of Physics}, volume = {15}, year = {2013}, month = {2013/11/26}, pages = {113051}, abstract = { We propose an experimental scheme to observe prethermalization and dynamical transition in one-dimensional XY spin chain with long range interaction and inhomogeneous lattice spacing, which can be readily implemented with the recently developed trapped-ion quantum simulator. Local physical observables are found to relax to prethermal values at intermediate time scale, followed by complete relaxation to thermal values at much longer time. The physical origin of prethermalization is explained by spotting a non-trivial structure in lower half of the energy spectrum. The dynamical behavior of the system is shown to cross difference phases when the interaction range is continuously tuned, indicating the existence of dynamical phase transition. }, doi = {10.1088/1367-2630/15/11/113051}, url = {http://arxiv.org/abs/1305.0985v1}, author = {Zhe-Xuan Gong and L. -M. Duan} } @article {1229, title = {Product Formulas for Exponentials of Commutators}, journal = {Journal of Mathematical Physics}, volume = {54}, year = {2013}, month = {2013/02/07}, pages = {062202}, abstract = { We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate unitary exponentials of (possibly nested) commutators using exponentials of the elementary operators, and we upper bound the number of elementary exponentials needed to implement the desired operation within a given error tolerance. By presenting an algorithm for quantum search using evolution according to a commutator, we show that the scaling of the number of exponentials in our product formulas with the evolution time is nearly optimal. Finally, we discuss applications of our product formulas to quantum control and to implementing anticommutators, providing new methods for simulating many-body interaction Hamiltonians. }, doi = {10.1063/1.4811386}, url = {http://arxiv.org/abs/1211.4945v2}, author = {Andrew M. Childs and Nathan Wiebe} } @article {1281, title = {Quadrature interferometry for nonequilibrium ultracold bosons in optical lattices }, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/1/22}, abstract = { We develop an interferometric technique for making time-resolved measurements of field-quadrature operators for nonequilibrium ultracold bosons in optical lattices. The technique exploits the internal state structure of magnetic atoms to create two subsystems of atoms in different spin states and lattice sites. A Feshbach resonance turns off atom-atom interactions in one spin subsystem, making it a well-characterized reference state, while atoms in the other subsystem undergo nonequilibrium dynamics for a variable hold time. Interfering the subsystems via a second beam-splitting operation, time-resolved quadrature measurements on the interacting atoms are obtained by detecting relative spin populations. The technique can provide quadrature measurements for a variety of Hamiltonians and lattice geometries (e.g., cubic, honeycomb, superlattices), including systems with tunneling, spin-orbit couplings using artificial gauge fields, and higher-band effects. Analyzing the special case of a deep lattice with negligible tunneling, we obtain the time evolution of both quadrature observables and their fluctuations. As a second application, we show that the interferometer can be used to measure atom-atom interaction strengths with super-Heisenberg scaling n^(-3/2) in the mean number of atoms per lattice site n, and standard quantum limit scaling M^(-1/2) in the number of lattice sites M. In our analysis, we require M >> 1 and for realistic systems n is small, and therefore the scaling in total atom number N = nM is below the Heisenberg limit; nevertheless, measurements testing the scaling behaviors for interaction-based quantum metrologies should be possible in this system. }, doi = {10.1103/PhysRevA.87.013423}, url = {http://arxiv.org/abs/1212.1193v2}, author = {Eite Tiesinga and Philip R. Johnson} } @article {1508, title = {Quantum Adversary (Upper) Bound}, journal = {Chicago Journal of Theoretical Computer Science}, volume = {19}, year = {2013}, month = {2013/04/05}, pages = {1 - 14}, abstract = { We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity without producing an algorithm. For example, we describe an oracle problem which we prove (non-constructively) can be solved in $O(1)$ queries, where the previous best quantum algorithm uses a polylogarithmic number of queries. We then give an explicit $O(1)$-query algorithm for this problem based on span programs. }, doi = {10.4086/cjtcs.2013.004}, url = {http://arxiv.org/abs/1101.0797v5}, author = {Shelby Kimmel} } @article {1270, title = {Quantum Catalysis of Magnetic Phase Transitions in a Quantum Simulator}, journal = {Physical Review Letters}, volume = {111}, year = {2013}, month = {2013/9/5}, abstract = { We control quantum fluctuations to create the ground state magnetic phases of a classical Ising model with a tunable longitudinal magnetic field using a system of 6 to 10 atomic ion spins. Due to the long-range Ising interactions, the various ground state spin configurations are separated by multiple first-order phase transitions, which in our zero temperature system cannot be driven by thermal fluctuations. We instead use a transverse magnetic field as a quantum catalyst to observe the first steps of the complete fractal devil{\textquoteright}s staircase, which emerges in the thermodynamic limit and can be mapped to a large number of many-body and energy-optimization problems. }, doi = {10.1103/PhysRevLett.111.100506}, url = {http://arxiv.org/abs/1303.6983v2}, author = {Philip Richerme and Crystal Senko and Simcha Korenblit and Jacob Smith and Aaron Lee and Rajibul Islam and Wesley C. Campbell and Christopher Monroe} } @article {1522, title = {Quantum Cherenkov Radiation and Non-contact Friction}, journal = {Physical Review A}, volume = {88}, year = {2013}, month = {2013/10/21}, abstract = { We present a number of arguments to demonstrate that a quantum analog of Cherenkov effect occurs when two dispersive objects are in relative motion. Specifically we show that two semi-infinite plates experience friction beyond a threshold velocity which, in their center-of-mass frame, is the phase speed of light within their medium. The loss in mechanical energy is radiated away through the plates before getting fully absorbed in the form of heat. By deriving various correlation functions inside and outside the two plates, we explicitly compute the radiation, and discuss its dependence on the reference frame. }, doi = {10.1103/PhysRevA.88.042509}, url = {http://arxiv.org/abs/1304.4909v2}, author = {Mohammad F. Maghrebi and Ramin Golestanian and Mehran Kardar} } @article {1199, title = {Quantum Logic between Remote Quantum Registers}, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/2/6}, abstract = { We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder. }, doi = {10.1103/PhysRevA.87.022306}, url = {http://arxiv.org/abs/1206.0014v1}, author = {Norman Y. Yao and Zhe-Xuan Gong and Chris R. Laumann and Steven D. Bennett and L. -M. Duan and Mikhail D. Lukin and Liang Jiang and Alexey V. Gorshkov} } @article {1842, title = {A quantum many-body spin system in an optical lattice clock}, journal = {Science}, volume = {341}, year = {2013}, pages = {632}, url = {http://www.sciencemag.org/content/341/6146/632.abstract}, author = {M J Martin and Bishof, M and Swallows, M D and X Zhang and C Benko and J von-Stecher and Alexey V. Gorshkov and Rey, A M and Jun Ye} } @article {1843, title = {Quantum Nonlinear Optics: Strongly Interacting Photons}, journal = {Opt. Photonics News}, volume = {24}, year = {2013}, pages = {48}, url = {http://www.osa-opn.org/abstract.cfm?URI=opn-24-12-48}, author = {Firstenberg, O and Lukin, M D and Peyronel, T and Liang, Q -Y and Vuletic, V and Alexey V. Gorshkov and Hofferberth, S and Pohl, T} } @article {1535, title = {Quipper: A Scalable Quantum Programming Language}, journal = {ACM SIGPLAN Notices}, volume = {48}, year = {2013}, month = {2013/06/23}, pages = {333-342}, abstract = {

The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higher-order quantum programming language. Quipper has been used to program a diverse set of non-trivial quantum algorithms, and can generate quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze quantum algorithms.

}, doi = {10.1145/2499370.2462177}, url = {http://arxiv.org/abs/1304.3390v1}, author = {Alexander S. Green and Peter LeFanu Lumsdaine and Neil J. Ross and Peter Selinger and Beno{\^\i}t Valiron} } @article {1185, title = {Realizing Fractional Chern Insulators with Dipolar Spins}, journal = {Physical Review Letters}, volume = {110}, year = {2013}, month = {2013/4/29}, abstract = { Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultra-cold polar molecules trapped in a deep optical lattice. While the orbital motion of the molecules is pinned, at finite densities, the rotational excitations form a fractional Chern insulator. We present a detailed experimental blueprint for KRb, and demonstrate that the energetics are consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications. }, doi = {10.1103/PhysRevLett.110.185302}, url = {http://arxiv.org/abs/1212.4839v1}, author = {Norman Y. Yao and Alexey V. Gorshkov and Chris R. Laumann and Andreas M. L{\"a}uchli and Jun Ye and Mikhail D. Lukin} } @article {1344, title = {The Resonant Exchange Qubit}, journal = {Physical Review Letters}, volume = {111}, year = {2013}, month = {2013/7/31}, abstract = {We introduce a solid-state qubit in which exchange interactions among confined electrons provide both the static longitudinal field and the oscillatory transverse field, allowing rapid and full qubit control via rf gate-voltage pulses. We demonstrate two-axis control at a detuning sweet-spot, where leakage due to hyperfine coupling is suppressed by the large exchange gap. A {\pi}/2-gate time of 2.5 ns and a coherence time of 19 {\mu}s, using multi-pulse echo, are also demonstrated. Model calculations that include effects of hyperfine noise are in excellent quantitative agreement with experiment. }, doi = {10.1103/PhysRevLett.111.050501}, url = {http://arxiv.org/abs/1304.3413v2}, author = {J. Medford and J. Beil and J. M. Taylor and E. I. Rashba and H. Lu and A. C. Gossard and C. M. Marcus} } @article {1525, title = {A Scattering Approach to the Dynamical Casimir Effect}, journal = {Physical Review D}, volume = {87}, year = {2013}, month = {2013/1/7}, abstract = { We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries, as well as dispersive objects in relative motion. A general (trace) formula is derived for the radiation from accelerating boundaries. Applications are provided for objects with different shapes in various dimensions, and undergoing rotational or linear motion. Within this framework, photon generation is discussed in the context of a modulated optical mirror. For dispersive objects, we find general results solely in terms of the scattering matrix. Specifically, we discuss the vacuum friction on a rotating object, and the friction on an atom moving parallel to a surface. }, doi = {10.1103/PhysRevD.87.025016}, url = {http://arxiv.org/abs/1210.1842v2}, author = {Mohammad F. Maghrebi and Ramin Golestanian and Mehran Kardar} } @article {1345, title = {Self-Consistent Measurement and State Tomography of an Exchange-Only Spin Qubit}, journal = {Nature Nanotechnology}, volume = {8}, year = {2013}, month = {2013/9/1}, pages = {654 - 659}, abstract = {We report initialization, complete electrical control, and single-shot readout of an exchange-only spin qubit. Full control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in under 2 ns. Measurement and state tomography are performed using a maximum-likelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements, and non-orthogonal control axes. }, doi = {10.1038/nnano.2013.168}, url = {http://arxiv.org/abs/1302.1933v1}, author = {J. Medford and J. Beil and J. M. Taylor and S. D. Bartlett and A. C. Doherty and E. I. Rashba and D. P. DiVincenzo and H. Lu and A. C. Gossard and C. M. Marcus} } @article {1504, title = {Single-photon nonlinear optics with graphene plasmons}, journal = {Physical Review Letters}, volume = {111}, year = {2013}, month = {2013/12/11}, abstract = { We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch. }, doi = {10.1103/PhysRevLett.111.247401}, url = {http://arxiv.org/abs/1309.2651v3}, author = {Michael Gullans and D. E. Chang and F. H. L. Koppens and F. J. Garc{\'\i}a de Abajo and M. D. Lukin} } @article {1287, title = {Soliton dynamics of an atomic spinor condensate on a Ring Lattice}, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/3/6}, abstract = { We study the dynamics of macroscopically-coherent matter waves of an ultra-cold atomic spin-one or spinor condensate on a ring lattice of six sites and demonstrate a novel type of spatio-temporal internal Josephson effect. Using a discrete solitary mode of uncoupled spin components as an initial condition, the time evolution of this many-body system is found to be characterized by two dominant frequencies leading to quasiperiodic dynamics at various sites. The dynamics of spatially-averaged and spin-averaged degrees of freedom, however, is periodic enabling an unique identification of the two frequencies. By increasing the spin-dependent atom-atom interaction strength we observe a resonance state, where the ratio of the two frequencies is a characteristic integer multiple and the spin-and-spatial degrees of freedom oscillate in "unison". Crucially, this resonant state is found to signal the onset to chaotic dynamics characterized by a broad band spectrum. In a ferromagnetic spinor condensate with attractive spin-dependent interactions, the resonance is accompanied by a transition from oscillatory- to rotational-type dynamics as the time evolution of the relative phase of the matter wave of the individual spin projections changes from bounded to unbounded. }, doi = {10.1103/PhysRevA.87.033608}, url = {http://arxiv.org/abs/1301.5851v1}, author = {Indubala I Satija and Carlos L. Pando and Eite Tiesinga} } @article {1306, title = {Spinor dynamics in an antiferromagnetic spin-1 thermal Bose gas}, journal = {Physical Review Letters}, volume = {111}, year = {2013}, month = {2013/7/9}, abstract = { We present experimental observations of coherent spin-population oscillations in a cold thermal, Bose gas of spin-1 sodium-23 atoms. The population oscillations in a multi-spatial-mode thermal gas have the same behavior as those observed in a single-spatial-mode antiferromagnetic spinor Bose Einstein condensate. We demonstrate this by showing that the two situations are described by the same dynamical equations, with a factor of two change in the spin-dependent interaction coefficient, which results from the change to particles with distinguishable momentum states in the thermal gas. We compare this theory to the measured spin population evolution after times up to a few hundreds of ms, finding quantitative agreement with the amplitude and period. We also measure the damping time of the oscillations as a function of magnetic field. }, doi = {10.1103/PhysRevLett.111.025301}, url = {http://arxiv.org/abs/1306.4255v1}, author = {Hyewon K. Pechkis and Jonathan P. Wrubel and Arne Schwettmann and Paul F. Griffin and Ryan Barnett and Eite Tiesinga and Paul D. Lett} } @article {1460, title = {Symmetries of Codeword Stabilized Quantum Codes}, journal = {8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)}, volume = {22}, year = {2013}, month = {2013/03/28}, pages = {192-206}, abstract = { Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be represented by a self-dual additive code S and a classical code C, i.,e., Q=(S,C), however this representation is in general not unique. We show that for any CWS code Q with certain permutation symmetry, one can always find a self-dual additive code S with the same permutation symmetry as Q such that Q=(S,C). As many good CWS codes have been found by starting from a chosen S, this ensures that when trying to find CWS codes with certain permutation symmetry, the choice of S with the same symmetry will suffice. A key step for this result is a new canonical representation for CWS codes, which is given in terms of a unique decomposition as union stabilizer codes. For CWS codes, so far mainly the standard form (G,C) has been considered, where G is a graph state. We analyze the symmetry of the corresponding graph of G, which in general cannot possess the same permutation symmetry as Q. We show that it is indeed the case for the toric code on a square lattice with translational symmetry, even if its encoding graph can be chosen to be translational invariant. }, doi = {10.4230/LIPIcs.TQC.2013.192}, url = {http://arxiv.org/abs/1303.7020v2}, author = {Salman Beigi and Jianxin Chen and Markus Grassl and Zhengfeng Ji and Qiang Wang and Bei Zeng} } @article {1402, title = {Testing quantum expanders is co-QMA-complete}, journal = {Physical Review A}, volume = {87}, year = {2013}, month = {2013/4/15}, abstract = { A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum expander. We show that this problem is co-QMA-complete. This has applications to testing randomized constructions of quantum expanders, and studying thermalization of open quantum systems. }, doi = {10.1103/PhysRevA.87.042317}, url = {http://arxiv.org/abs/1210.0787v2}, author = {Adam D. Bookatz and Stephen P. Jordan and Yi-Kai Liu and Pawel Wocjan} } @article {1258, title = {A Time-Efficient Quantum Walk for 3-Distinctness Using Nested Updates}, year = {2013}, month = {2013/02/28}, abstract = { We present an extension to the quantum walk search framework that facilitates quantum walks with nested updates. We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity ~O(n^{5/7}), matching the best known upper bound (obtained via learning graphs) up to log factors. Furthermore, our algorithm has time complexity ~O(n^{5/7}), improving the previous ~O(n^{3/4}). }, url = {http://arxiv.org/abs/1302.7316v1}, author = {Andrew M. Childs and Stacey Jeffery and Robin Kothari and Frederic Magniez} } @article {1184, title = {Topological phases in ultracold polar-molecule quantum magnets}, journal = {Physical Review B}, volume = {87}, year = {2013}, month = {2013/2/26}, abstract = { We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin S >= 1/2 and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases -- previously studied only in the nearest-neighbor case -- survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed. }, doi = {10.1103/PhysRevB.87.081106}, url = {http://arxiv.org/abs/1210.5518v2}, author = {Salvatore R. Manmana and E. M. Stoudenmire and Kaden R. A. Hazzard and Ana Maria Rey and Alexey V. Gorshkov} } @article {1197, title = {Topologically Protected Quantum State Transfer in a Chiral Spin Liquid}, journal = {Nature Communications}, volume = {4}, year = {2013}, month = {2013/3/12}, pages = {1585}, abstract = { Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed. }, doi = {10.1038/ncomms2531}, url = {http://arxiv.org/abs/1110.3788v1}, author = {Norman Y. Yao and Chris R. Laumann and Alexey V. Gorshkov and Hendrik Weimer and Liang Jiang and J. Ignacio Cirac and Peter Zoller and Mikhail D. Lukin} } @article {1459, title = {Uniqueness of Quantum States Compatible with Given Measurement Results}, journal = {Physical Review A}, volume = {88}, year = {2013}, month = {2013/7/11}, abstract = { We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it is known that for a d-dimensional Hilbert space, there exists a set of 4d-5 observables that uniquely determines any pure state. We show that for case (2), 5d-7 observables suffice to uniquely determine any pure state. Thus there is a gap between the results for (1) and (2), and we give some examples to illustrate this. The case of observables corresponding to reduced density matrices (RDMs) of a multipartite system is also discussed, where we improve known bounds on local dimensions for case (2) in which almost all pure states are uniquely determined by their RDMs. We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low rank quantum states. }, doi = {10.1103/PhysRevA.88.012109}, url = {http://arxiv.org/abs/1212.3503v2}, author = {Jianxin Chen and Hillary Dawkins and Zhengfeng Ji and Nathaniel Johnston and David Kribs and Frederic Shultz and Bei Zeng} } @article {1221, title = {Universal computation by multi-particle quantum walk}, journal = {Science}, volume = {339}, year = {2013}, month = {2013/02/14}, pages = {791 - 794}, abstract = { A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we consider a generalization of quantum walk to systems with more than one walker. A continuous-time multi-particle quantum walk is generated by a time-independent Hamiltonian with a term corresponding to a single-particle quantum walk for each particle, along with an interaction term. Multi-particle quantum walk includes a broad class of interacting many-body systems such as the Bose-Hubbard model and systems of fermions or distinguishable particles with nearest-neighbor interactions. We show that multi-particle quantum walk is capable of universal quantum computation. Since it is also possible to efficiently simulate a multi-particle quantum walk of the type we consider using a universal quantum computer, this model exactly captures the power of quantum computation. In principle our construction could be used as an architecture for building a scalable quantum computer with no need for time-dependent control. }, doi = {10.1126/science.1229957}, url = {http://arxiv.org/abs/1205.3782v2}, author = {Andrew M. Childs and David Gosset and Zak Webb} } @article {1444, title = {Universal Entanglers for Bosonic and Fermionic Systems}, year = {2013}, month = {2013/05/31}, abstract = { A universal entangler (UE) is a unitary operation which maps all pure product states to entangled states. It is known that for a bipartite system of particles $1,2$ with a Hilbert space $\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}$, a UE exists when $\min{(d_1,d_2)}\geq 3$ and $(d_1,d_2)\neq (3,3)$. It is also known that whenever a UE exists, almost all unitaries are UEs; however to verify whether a given unitary is a UE is very difficult since solving a quadratic system of equations is NP-hard in general. This work examines the existence and construction of UEs of bipartite bosonic/fermionic systems whose wave functions sit in the symmetric/antisymmetric subspace of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$. The development of a theory of UEs for these types of systems needs considerably different approaches from that used for UEs of distinguishable systems. This is because the general entanglement of identical particle systems cannot be discussed in the usual way due to the effect of (anti)-symmetrization which introduces "pseudo entanglement" that is inaccessible in practice. We show that, unlike the distinguishable particle case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are symmetric (resp. antisymmetric) subspaces of $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ if and only if $d\geq 3$ (resp. $d\geq 8$). To prove this we employ algebraic geometry to reason about the different algebraic structures of the bosonic/fermionic systems. Additionally, due to the relatively simple coherent state form of unentangled bosonic states, we are able to give the explicit constructions of two bosonic UEs. Our investigation provides insight into the entanglement properties of systems of indisitinguishable particles, and in particular underscores the difference between the entanglement structures of bosonic, fermionic and distinguishable particle systems. }, url = {http://arxiv.org/abs/1305.7489v1}, author = {Joel Klassen and Jianxin Chen and Bei Zeng} } @article {1398, title = {Achieving perfect completeness in classical-witness quantum Merlin-Arthur proof systems}, journal = {Quantum Information and Computation}, volume = {12}, year = {2012}, month = {2012/05/01}, pages = {461-471}, abstract = { This paper proves that classical-witness quantum Merlin-Arthur proof systems can achieve perfect completeness. That is, QCMA = QCMA1. This holds under any gate set with which the Hadamard and arbitrary classical reversible transformations can be exactly implemented, e.g., {Hadamard, Toffoli, NOT}. The proof is quantumly nonrelativizing, and uses a simple but novel quantum technique that additively adjusts the success probability, which may be of independent interest. }, url = {http://arxiv.org/abs/1111.5306v2}, author = {Stephen P. Jordan and Hirotada Kobayashi and Daniel Nagaj and Harumichi Nishimura} } @article {1346, title = {Algorithmic Cooling of a Quantum Simulator}, year = {2012}, month = {2012/07/30}, abstract = {Controlled quantum mechanical devices provide a means of simulating more complex quantum systems exponentially faster than classical computers. Such "quantum simulators" rely heavily upon being able to prepare the ground state of Hamiltonians, whose properties can be used to calculate correlation functions or even the solution to certain classical computations. While adiabatic preparation remains the primary means of producing such ground states, here we provide a different avenue of preparation: cooling to the ground state via simulated dissipation. This is in direct analogy to contemporary efforts to realize generalized forms of simulated annealing in quantum systems. }, url = {http://arxiv.org/abs/1207.7111v1}, author = {Dvir Kafri and J. M. Taylor} } @article {1279, title = {Anisotropy induced Feshbach resonances in a quantum dipolar gas of magnetic atoms }, journal = {Physical Review Letters}, volume = {109}, year = {2012}, month = {2012/9/7}, abstract = { We explore the anisotropic nature of Feshbach resonances in the collision between ultracold magnetic submerged-shell dysprosium atoms, which can only occur due to couplings to rotating bound states. This is in contrast to well-studied alkali-metal atom collisions, where most Feshbach resonances are hyperfine induced and due to rotation-less bound states. Our novel first-principle coupled-channel calculation of the collisions between open-4f-shell spin-polarized bosonic dysprosium reveals a striking correlation between the anisotropy due to magnetic dipole-dipole and electrostatic interactions and the Feshbach spectrum as a function of an external magnetic field. Over a 20 mT magnetic field range we predict about a dozen Feshbach resonances and show that the resonance locations are exquisitely sensitive to the dysprosium isotope. }, doi = {10.1103/PhysRevLett.109.103002}, url = {http://arxiv.org/abs/1203.4172v1}, author = {Alexander Petrov and Eite Tiesinga and Svetlana Kotochigova} } @article {1549, title = {On Beating the Hybrid Argument}, journal = {Proceedings, ITCS}, volume = {9}, year = {2012}, month = {2013/11/14}, pages = {809-843}, abstract = {The hybrid argument allows one to relate the distinguishability of a distribution (from uniform) to the predictability of individual bits given a prefix. The argument incurs a loss of a factor k equal to the bit-length of the distributions: -distinguishability implies only /k-predictability. This paper studies the consequences of avoiding this loss {\textendash} what we call {\textquotedblleft}beating the hybrid argument{\textquotedblright} {\textendash} and develops new proof techniques that circumvent the loss in certain natural settings. Specifically, we obtain the following results: 1. We give an instantiation of the Nisan-Wigderson generator (JCSS {\textquoteright}94) that can be broken by quantum computers, and that is o(1)-unpredictable against AC0 . This is not enough to imply indistinguishability via the hybrid argument because of the hybrid-argument loss; nevertheless, we conjecture that this generator indeed fools AC0 , and we prove this statement for a simplified version of the problem. Our conjecture implies the existence of an oracle relative to which BQP is not in the PH, a longstanding open problem. 2. We show that the {\textquotedblleft}INW{\textquotedblright} generator by Impagliazzo, Nisan, and Wigderson (STOC {\textquoteright}94) with seed length O(log n log log n) produces a distribution that is 1/ log n-unpredictable against poly-logarithmic width (general) read-once oblivious branching programs. Thus avoiding the hybrid-argument loss would lead to a breakthrough in generators against small space. 3. We study pseudorandom generators obtained from a hard function by repeated sampling. We identify a property of functions, {\textquotedblleft}resamplability,{\textquotedblright} that allows us to beat the hybrid argument, leading to new pseudorandom generators for AC0 [p] and similar classes. Although the generators have sub-linear stretch, they represent the best-known generators for these classes. Thus we establish that {\textquotedblleft}beating{\textquotedblright} or bypassing the hybrid argument would have two significant consequences in complexity, and we take steps toward that goal by developing techniques that indeed beat the hybrid argument in related (but simpler) settings, leading to best-known PRGs for certain complexity classes. }, url = {http://users.cms.caltech.edu/~umans/papers/FSUV10.pdf}, author = {Bill Fefferman and Ronen Shaltiel and Christopher Umans and Emanuele Viola} } @article {1844, title = {Cavity QED with atomic mirrors}, journal = {New J. Phys.}, volume = {14}, year = {2012}, pages = {063003}, url = {http://iopscience.iop.org/1367-2630/14/6/063003/}, author = {D E Chang and Jiang, L and Alexey V. Gorshkov and H J Kimble} } @article {1458, title = {Comment on some results of Erdahl and the convex structure of reduced density matrices}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/05/16}, pages = {072203}, abstract = { In J. Math. Phys. 13, 1608-1621 (1972), Erdahl considered the convex structure of the set of $N$-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the $m$-body setting and to the more general quantum marginal problem. We describe these extensions, but can not resolve a problem in the proof of Erdahl{\textquoteright}s claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when $2m \geq N$ every extreme point of the set of $N$-representable $m$-body reduced density matrices has a unique pre-image in both the symmetric and anti-symmetric setting. Moreover, this extends to the quantum marginal setting for a pair of complementary $m$-body and $(N-m)$-body reduced density matrices. }, doi = {10.1063/1.4736842}, url = {http://arxiv.org/abs/1205.3682v1}, author = {Jianxin Chen and Zhengfeng Ji and Mary Beth Ruskai and Bei Zeng and Duan-Lu Zhou} } @article {1443, title = {Correlations in excited states of local Hamiltonians}, journal = {Physical Review A}, volume = {85}, year = {2012}, month = {2012/4/9}, abstract = { Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix). }, doi = {10.1103/PhysRevA.85.040303}, url = {http://arxiv.org/abs/1106.1373v2}, author = {Jianxin Chen and Zhengfeng Ji and Zhaohui Wei and Bei Zeng} } @article {1347, title = {The equilibrium states of open quantum systems in the strong coupling regime}, journal = {Physical Review E}, volume = {86}, year = {2012}, month = {2012/12/26}, abstract = {In this work we investigate the late-time stationary states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is non-vanishing or equivalently if the relaxation timescales are finite. Using a variety of non-equilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system = system + environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late-times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multi-time correlations of the open system evolve towards those of the closed system thermal state. Multi-time correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations. }, doi = {10.1103/PhysRevE.86.061132}, url = {http://arxiv.org/abs/1206.2707v1}, author = {Y. Subasi and C. H. Fleming and J. M. Taylor and B. L. Hu} } @article {1448, title = {From Ground States to Local Hamiltonians}, journal = {Physical Review A}, volume = {86}, year = {2012}, month = {2012/8/30}, abstract = { Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space, by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles. }, doi = {10.1103/PhysRevA.86.022339}, url = {http://arxiv.org/abs/1110.6583v4}, author = {Jianxin Chen and Zhengfeng Ji and Bei Zeng and D. L. Zhou} } @article {1563, title = {Full Abstraction for Set-Based Models of the Symmetric Interaction Combinators}, journal = {Proceedings of the 15th International Conference on Foundations of Software Science and Computation Structures}, volume = {7213}, year = {2012}, month = {2012/01/01}, pages = {316-330}, abstract = {The symmetric interaction combinators are a model of distributed and deterministic computation based on Lafont{\textquoteright}s interaction nets, a special form of graph rewriting. The interest of the symmetric interaction combinators lies in their universality, that is, the fact that they may encode all other interaction net systems; for instance, several implementations of the lambda-calculus in the symmetric interaction combinators exist, related to Lamping{\textquoteright}s sharing graphs for optimal reduction. A certain number of observational equivalences were introduced for this system, by Lafont, Fernandez and Mackie, and the first author. In this paper, we study the problem of full abstraction with respect to one of these equivalences, using a class of very simple denotational models based on pointed sets.}, url = {https://lipn.univ-paris13.fr/~mazza/papers/CombSetSem-FOSSACS2012.pdf}, author = {Damiano Mazza and Neil J. Ross} } @article {grant2012galilean, title = {On Galilean connections and the first jet bundle}, journal = {Central European Journal of Mathematics}, volume = {10}, number = {5}, year = {2012}, month = {2012/10/01}, pages = {1889{\textendash}1895}, publisher = {Springer}, abstract = {We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations {\textemdash} sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces {\textquotedblleft}laboratory{\textquotedblright} coordinate systems, and the geodesic equations in this coordinates form a system of second-order ordinary differential equations. We then show the converse {\textemdash} the {\textquotedblleft}fundamental theorem{\textquotedblright} {\textemdash} that given such a coordinate system, and a system of second order ordinary differential equations, there exists regular Cartan connections yielding these, and such connections are completely determined by their torsion.}, author = {Grant, James DE and Brad Lackey} } @article {1792, title = {Gluon chain formation in presence of static charges}, journal = {Physical Review D}, volume = {86}, year = {2012}, month = {2012/12/10}, pages = {114015}, abstract = {We consider the origins of the gluon chain model. The model serves as a realization of the dynamics of the chromoelectric flux between static quark-antiquark sources. The derivation is based on the large-NC limit of the Coulomb gauge Hamiltonian in the presence of a background field introduced to model magnetic charge condensation inducing electric confinement.}, doi = {10.1103/PhysRevD.86.114015}, url = {http://link.aps.org/doi/10.1103/PhysRevD.86.114015}, author = {Aaron Ostrander and Santopinto, E. and Szczepaniak, A. P. and Vassallo, A.} } @article {1454, title = {Ground-State Spaces of Frustration-Free Hamiltonians}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/01/01}, pages = {102201}, abstract = { We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of {\textquoteleft}reduced spaces{\textquoteright} to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\Theta_k$ and discuss its relationship with ground states of $k$-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in $\Theta_2$ are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in $\Theta_k$ may not be the join of atoms, indicating a richer structure for $\Theta_k$ beyond the convex structure. Our study of $\Theta_k$ deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from a new angle of reduced spaces. }, doi = {10.1063/1.4748527}, url = {http://arxiv.org/abs/1112.0762v1}, author = {Jianxin Chen and Zhengfeng Ji and David Kribs and Zhaohui Wei and Bei Zeng} } @article {1227, title = {Hamiltonian Simulation Using Linear Combinations of Unitary Operations}, journal = {Quantum Information and Computation}, volume = {12}, year = {2012}, month = {2012/11/01}, pages = {901-924}, abstract = { We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation algorithms based on product formulas and, most notably, scales better with the simulation error than any known Hamiltonian simulation technique. Our main tool is a general method to nearly deterministically implement linear combinations of nearby unitary operations, which we show is optimal among a large class of methods. }, url = {http://arxiv.org/abs/1202.5822v1}, author = {Andrew M. Childs and Nathan Wiebe} } @article {1228, title = {Levinson{\textquoteright}s theorem for graphs II}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/11/21}, pages = {102207}, abstract = { We prove Levinson{\textquoteright}s theorem for scattering on an (m+n)-vertex graph with n semi-infinite paths each attached to a different vertex, generalizing a previous result for the case n=1. This theorem counts the number of bound states in terms of the winding of the determinant of the S-matrix. We also provide a proof that the bound states and incoming scattering states of the Hamiltonian together form a complete basis for the Hilbert space, generalizing another result for the case n=1. }, doi = {10.1063/1.4757665}, url = {http://arxiv.org/abs/1203.6557v2}, author = {Andrew M. Childs and David Gosset} } @article {1476, title = {Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice }, journal = {Physical Review Letters}, volume = {108}, year = {2012}, month = {2012/2/23}, abstract = { We have realized long-lived ground-state polar molecules in a 3D optical lattice, with a lifetime of up to 25 s, which is limited only by off-resonant scattering of the trapping light. Starting from a 2D optical lattice, we observe that the lifetime increases dramatically as a small lattice potential is added along the tube-shaped lattice traps. The 3D optical lattice also dramatically increases the lifetime for weakly bound Feshbach molecules. For a pure gas of Feshbach molecules, we observe a lifetime of >20 s in a 3D optical lattice; this represents a 100-fold improvement over previous results. This lifetime is also limited by off-resonant scattering, the rate of which is related to the size of the Feshbach molecule. Individually trapped Feshbach molecules in the 3D lattice can be converted to pairs of K and Rb atoms and back with nearly 100\% efficiency. }, doi = {10.1103/PhysRevLett.108.080405}, url = {http://arxiv.org/abs/1110.4420v1}, author = {Amodsen Chotia and Brian Neyenhuis and Steven A. Moses and Bo Yan and Jacob P. Covey and Michael Foss-Feig and Ana Maria Rey and Deborah S. Jin and Jun Ye} } @article {1449, title = {Minimum Entangling Power is Close to Its Maximum}, year = {2012}, month = {2012/10/04}, abstract = { Given a quantum gate $U$ acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measure when the inputs are restricted to be product states. In this paper, we mainly focus on the {\textquoteright}weakest{\textquoteright} one, i.e., the minimum entangling power, among all these entangling powers. We show that, by choosing von Neumann entropy of reduced density operator or Schmidt rank as entanglement measure, even the {\textquoteright}weakest{\textquoteright} entangling power is generically very close to its maximal possible entanglement generation. In other words, maximum, average and minimum entangling powers are generically close. We then study minimum entangling power with respect to other Lipschitiz-continuous entanglement measures and generalize our results to multipartite quantum systems. As a straightforward application, a random quantum gate will almost surely be an intrinsically fault-tolerant entangling device that will always transform every low-entangled state to near-maximally entangled state. }, url = {http://arxiv.org/abs/1210.1296v1}, author = {Jianxin Chen and Zhengfeng Ji and David W Kribs and Bei Zeng} } @article {1503, title = {Nanoplasmonic Lattices for Ultracold atoms}, journal = {Physical Review Letters}, volume = {109}, year = {2012}, month = {2012/12/6}, abstract = { We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed. }, doi = {10.1103/PhysRevLett.109.235309}, url = {http://arxiv.org/abs/1208.6293v3}, author = {Michael Gullans and T. Tiecke and D. E. Chang and J. Feist and J. D. Thompson and J. I. Cirac and P. Zoller and M. D. Lukin} } @article {1439, title = {Non-Additivity of the Entanglement of Purification (Beyond Reasonable Doubt) }, year = {2012}, month = {2012/06/06}, abstract = { We demonstrate the convexity of the difference between the regularized entanglement of purification and the entropy, as a function of the state. This is proved by means of a new asymptotic protocol to prepare a state from pre-shared entanglement and by local operations only. We go on to employ this convexity property in an investigation of the additivity of the (single-copy) entanglement of purification: using numerical results for two-qubit Werner states we find strong evidence that the entanglement of purification is different from its regularization, hence that entanglement of purification is not additive. }, url = {http://arxiv.org/abs/1206.1307v1}, author = {Jianxin Chen and Andreas Winter} } @article {1793, title = {Non-Recursively Constructible Recursive Families of Graphs}, journal = {The Electronic Journal of Combinatorics}, volume = {19}, year = {2012}, month = {2012/04/16}, abstract = {In a publication by Noy and Rib{\'o}, it was shown that recursively constructible families of graphs are recursive. The authors also conjecture that the converse holds; that is, recursive families are also recursively constructible. In this paper, we provide two specific counterexamples to this conjecture, which we then extend to an infinite family of counterexamples.}, url = {http://www.combinatorics.org/ojs/index.php/eljc/article/view/2211}, author = {Colleen Bouey and Christina Graves and Aaron Ostrander and Gregory Palma} } @article {1493, title = {Photonic quantum simulation of ground state configurations of Heisenberg square and checkerboard lattice spin systems }, year = {2012}, month = {2012/05/12}, abstract = { Photonic quantum simulators are promising candidates for providing insight into other small- to medium-sized quantum systems. The available photonic quantum technology is reaching the state where significant advantages arise for the quantum simulation of interesting questions in Heisenberg spin systems. Here we experimentally simulate such spin systems with single photons and linear optics. The effective Heisenberg-type interactions among individual single photons are realized by quantum interference at the tunable direction coupler followed by the measurement process. The effective interactions are characterized by comparing the entanglement dynamics using pairwise concurrence of a four-photon quantum system. We further show that photonic quantum simulations of generalized Heisenberg interactions on a four-site square lattice and a six-site checkerboard lattice are in reach of current technology. }, url = {http://arxiv.org/abs/1205.2801v1}, author = {Xiao-song Ma and Borivoje Dakic and Sebastian Kropatsche and William Naylor and Yang-hao Chan and Zhe-Xuan Gong and Lu-ming Duan and Anton Zeilinger and Philip Walther} } @article {1524, title = {Polymer-mediated entropic forces between scale-free objects}, journal = {Physical Review E}, volume = {86}, year = {2012}, month = {2012/12/3}, abstract = { The number of configurations of a polymer is reduced in the presence of a barrier or an obstacle. The resulting loss of entropy adds a repulsive component to other forces generated by interaction potentials. When the obstructions are scale invariant shapes (such as cones, wedges, lines or planes) the only relevant length scales are the polymer size R_0 and characteristic separations, severely constraining the functional form of entropic forces. Specifically, we consider a polymer (single strand or star) attached to the tip of a cone, at a separation h from a surface (or another cone). At close proximity, such that h<One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor networks. The graph underlying these networks is given by the triangulation of a manifold, and the structure of the tensors ensures that the overall tensor is independent of the choice of internal triangulation. This leads to quantum algorithms for additively approximating certain invariants of triangulated manifolds. We discuss the details of this construction in two specific cases. In the first case, we consider triangulated surfaces, where the triangle tensor is defined by the multiplication operator of a finite group; the resulting invariant has a simple closed-form expression involving the dimensions of the irreducible representations of the group and the Euler characteristic of the surface. In the second case, we consider triangulated 3-manifolds, where the tetrahedral tensor is defined by the so-called Fibonacci anyon model; the resulting invariant is the well-known Turaev-Viro invariant of 3-manifolds.

}, url = {http://dl.acm.org/citation.cfm?id=2481580.2481588}, author = {Gorjan Alagic and E. A. Bering} } @article {1397, title = {Quantum Algorithms for Quantum Field Theories}, journal = {Science}, volume = {336}, year = {2012}, month = {2012/05/31}, pages = {1130 - 1133}, abstract = { Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (phi-fourth theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. }, doi = {10.1126/science.1217069}, url = {http://arxiv.org/abs/1111.3633v2}, author = {Stephen P. Jordan and Keith S. M. Lee and John Preskill} } @article {1348, title = {Quantum interface between an electrical circuit and a single atom}, journal = {Physical Review Letters}, volume = {108}, year = {2012}, month = {2012/3/30}, abstract = {We show how to bridge the divide between atomic systems and electronic devices by engineering a coupling between the motion of a single ion and the quantized electric field of a resonant circuit. Our method can be used to couple the internal state of an ion to the quantized circuit with the same speed as the internal-state coupling between two ions. All the well-known quantum information protocols linking ion internal and motional states can be converted to protocols between circuit photons and ion internal states. Our results enable quantum interfaces between solid state qubits, atomic qubits, and light, and lay the groundwork for a direct quantum connection between electrical and atomic metrology standards. }, doi = {10.1103/PhysRevLett.108.130504}, url = {http://arxiv.org/abs/1111.5999v1}, author = {D. Kielpinski and D. Kafri and M. J. Woolley and G. J. Milburn and J. M. Taylor} } @article {1845, title = {Quantum nonlinear optics with single photons enabled by strongly interacting atoms}, journal = {Nature (London)}, volume = {488}, year = {2012}, pages = {57}, url = {http://www.nature.com/nature/journal/v488/n7409/full/nature11361.html}, author = {Peyronel, Thibault and Firstenberg, Ofer and Liang, Qi-Yu and Hofferberth, Sebastian and Alexey V. Gorshkov and Pohl, Thomas and Lukin, Mikhail D. and Vuletic, Vladan} } @article {1222, title = {The quantum query complexity of read-many formulas}, journal = {Lecture Notes in Computer Science}, volume = {7501}, year = {2012}, month = {2012/09/10}, pages = {337-348}, abstract = { The quantum query complexity of evaluating any read-once formula with n black-box input bits is Theta(sqrt(n)). However, the corresponding problem for read-many formulas (i.e., formulas in which the inputs have fanout) is not well understood. Although the optimal read-once formula evaluation algorithm can be applied to any formula, it can be suboptimal if the inputs have large fanout. We give an algorithm for evaluating any formula with n inputs, size S, and G gates using O(min{n, sqrt{S}, n^{1/2} G^{1/4}}) quantum queries. Furthermore, we show that this algorithm is optimal, since for any n,S,G there exists a formula with n inputs, size at most S, and at most G gates that requires Omega(min{n, sqrt{S}, n^{1/2} G^{1/4}}) queries. We also show that the algorithm remains nearly optimal for circuits of any particular depth k >= 3, and we give a linear-size circuit of depth 2 that requires Omega (n^{5/9}) queries. Applications of these results include a Omega (n^{19/18}) lower bound for Boolean matrix product verification, a nearly tight characterization of the quantum query complexity of evaluating constant-depth circuits with bounded fanout, new formula gate count lower bounds for several functions including PARITY, and a construction of an AC^0 circuit of linear size that can only be evaluated by a formula with Omega(n^{2-epsilon}) gates. }, doi = {10.1007/978-3-642-33090-2_30}, url = {http://arxiv.org/abs/1112.0548v1}, author = {Andrew M. Childs and Shelby Kimmel and Robin Kothari} } @article {1492, title = {Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions }, journal = {New Journal of Physics}, volume = {14}, year = {2012}, month = {2012/09/27}, pages = {095024}, abstract = { A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how appropriate design of laser fields can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and is scalable to levels where classical methods of simulation are intractable. }, doi = {10.1088/1367-2630/14/9/095024}, url = {http://arxiv.org/abs/1201.0776v1}, author = {Simcha Korenblit and Dvir Kafri and Wess C. Campbell and Rajibul Islam and Emily E. Edwards and Zhe-Xuan Gong and Guin-Dar Lin and Luming Duan and Jungsang Kim and Kihwan Kim and Christopher Monroe} } @article {1434, title = {Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators }, journal = {New Journal of Physics}, volume = {14}, year = {2012}, month = {2012/09/27}, pages = {095022}, abstract = { Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition. First, we show that a low-rank density matrix can be estimated using fewer copies of the state, i.e., the sample complexity of tomography decreases with the rank. Second, we show that unknown low-rank states can be reconstructed from an incomplete set of measurements, using techniques from compressed sensing and matrix completion. These techniques use simple Pauli measurements, and their output can be certified without making any assumptions about the unknown state. We give a new theoretical analysis of compressed tomography, based on the restricted isometry property (RIP) for low-rank matrices. Using these tools, we obtain near-optimal error bounds, for the realistic situation where the data contains noise due to finite statistics, and the density matrix is full-rank with decaying eigenvalues. We also obtain upper-bounds on the sample complexity of compressed tomography, and almost-matching lower bounds on the sample complexity of any procedure using adaptive sequences of Pauli measurements. Using numerical simulations, we compare the performance of two compressed sensing estimators with standard maximum-likelihood estimation (MLE). We find that, given comparable experimental resources, the compressed sensing estimators consistently produce higher-fidelity state reconstructions than MLE. In addition, the use of an incomplete set of measurements leads to faster classical processing with no loss of accuracy. Finally, we show how to certify the accuracy of a low rank estimate using direct fidelity estimation and we describe a method for compressed quantum process tomography that works for processes with small Kraus rank. }, doi = {10.1088/1367-2630/14/9/095022}, url = {http://arxiv.org/abs/1205.2300v2}, author = {Steven T. Flammia and David Gross and Yi-Kai Liu and Jens Eisert} } @article {1456, title = {Rank Reduction for the Local Consistency Problem}, journal = {Journal of Mathematical Physics}, volume = {53}, year = {2012}, month = {2012/02/09}, pages = {022202}, abstract = { We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be compatible. We prove that any compatible local density operators can be satisfied by a low rank global density operator. Then we study both fermionic and bosonic versions of the N-representability problem as applications. After applying the channel-state duality, we prove that any compatible local channels can be obtained through a global quantum channel with small Kraus rank. }, doi = {10.1063/1.3685644}, url = {http://arxiv.org/abs/1106.3235v2}, author = {Jianxin Chen and Zhengfeng Ji and Alexander Klyachko and David W. Kribs and Bei Zeng} } @article {1491, title = {Reply to Comment on "Space-Time Crystals of Trapped Ions}, year = {2012}, month = {2012/10/15}, abstract = { This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)). }, doi = {http://dx.doi.org/10.1103/PhysRevLett.109.163001}, url = {http://arxiv.org/abs/1212.6959v2}, author = {Tongcang Li and Zhe-Xuan Gong and Zhang-qi Yin and H. T. Quan and Xiaobo Yin and Peng Zhang and L. -M. Duan and Xiang Zhang} } @article {1294, title = {Resonant control of polar molecules in an optical lattice}, journal = {Physical Review A}, volume = {85}, year = {2012}, month = {2012/2/8}, abstract = { We study the resonant control of two nonreactive polar molecules in an optical lattice site, focussing on the example of RbCs. Collisional control can be achieved by tuning bound states of the intermolecular dipolar potential, by varying the applied electric field or trap frequency. We consider a wide range of electric fields and trapping geometries, showing that a three-dimensional optical lattice allows for significantly wider avoided crossings than free space or quasi-two dimensional geometries. Furthermore, we find that dipolar confinement induced resonances can be created with reasonable trapping frequencies and electric fields, and have widths that will enable useful control in forthcoming experiments. }, doi = {10.1103/PhysRevA.85.022703}, url = {http://arxiv.org/abs/1111.0227v1}, author = {Thomas M. Hanna and Eite Tiesinga and William F. Mitchell and Paul S. Julienne} } @article {1200, title = {Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor }, journal = {Nature Communications}, volume = {3}, year = {2012}, month = {2012/4/24}, pages = {800}, abstract = { The realization of a scalable quantum information processor has emerged over the past decade as one of the central challenges at the interface of fundamental science and engineering. Much progress has been made towards this goal. Indeed, quantum operations have been demonstrated on several trapped ion qubits, and other solid-state systems are approaching similar levels of control. Extending these techniques to achieve fault-tolerant operations in larger systems with more qubits remains an extremely challenging goal, in part, due to the substantial technical complexity of current implementations. Here, we propose and analyze an architecture for a scalable, solid-state quantum information processor capable of operating at or near room temperature. The architecture is applicable to realistic conditions, which include disorder and relevant decoherence mechanisms, and includes a hierarchy of control at successive length scales. Our approach is based upon recent experimental advances involving Nitrogen-Vacancy color centers in diamond and will provide fundamental insights into the physics of non-equilibrium many-body quantum systems. Additionally, the proposed architecture may greatly alleviate the stringent constraints, currently limiting the realization of scalable quantum processors. }, doi = {10.1038/ncomms1788}, url = {http://arxiv.org/abs/1012.2864v1}, author = {Norman Y. Yao and Liang Jiang and Alexey V. Gorshkov and Peter C. Maurer and Geza Giedke and J. Ignacio Cirac and Mikhail D. Lukin} } @article {1794, title = {Space-Time Crystals of Trapped Ions}, journal = {Physical Review Letters}, volume = {109}, year = {2012}, month = {2012/10/19}, pages = {163001}, abstract = {Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.}, doi = {10.1103/PhysRevLett.109.163001}, url = {http://link.aps.org/doi/10.1103/PhysRevLett.109.163001}, author = {Tongcang Li and Gong, Zhe-Xuan and Yin, Zhang-Qi and Quan, H. T. and Yin, Xiaobo and Zhang, Peng and Duan, L.-M. and Zhang, Xiang} } @article {1435, title = {A Spectral Algorithm for Latent Dirichlet Allocation}, journal = {Algorithmica}, year = {2012}, month = {2012/04/30}, pages = {193-214}, abstract = { The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic probability vectors (the distributions over words for each topic), when only the words are observed and the corresponding topics are hidden. We provide a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of mixture models, including the popular latent Dirichlet allocation (LDA) model. For LDA, the procedure correctly recovers both the topic probability vectors and the prior over the topics, using only trigram statistics (i.e., third order moments, which may be estimated with documents containing just three words). The method, termed Excess Correlation Analysis (ECA), is based on a spectral decomposition of low order moments (third and fourth order) via two singular value decompositions (SVDs). Moreover, the algorithm is scalable since the SVD operations are carried out on $k\times k$ matrices, where $k$ is the number of latent factors (e.g. the number of topics), rather than in the $d$-dimensional observed space (typically $d \gg k$). }, url = {http://arxiv.org/abs/1204.6703v4}, author = {Animashree Anandkumar and Dean P. Foster and Daniel Hsu and Sham M. Kakade and Yi-Kai Liu} } @article {1528, title = {Spontaneous emission by rotating objects: A scattering approach}, journal = {Physical Review Letters}, volume = {108}, year = {2012}, month = {2012/6/7}, abstract = { We study the quantum electrodynamics (QED) vacuum in the presence of a body rotating along its axis of symmetry and show that the object spontaneously emits energy if it is lossy. The radiated power is expressed as a general trace formula solely in terms of the scattering matrix, making an explicit connection to the conjecture of Zel{\textquoteright}dovich [JETP Lett. 14, 180 (1971)] on rotating objects. We further show that a rotating body drags along nearby objects while making them spin parallel to its own rotation axis. }, doi = {10.1103/PhysRevLett.108.230403}, url = {http://arxiv.org/abs/1202.1485v2}, author = {Mohammad F. Maghrebi and Robert L. Jaffe and Mehran Kardar} } @article {1470, title = {Steady-state many-body entanglement of hot reactive fermions}, journal = {Physical Review Letters}, volume = {109}, year = {2012}, month = {2012/12/4}, abstract = { Entanglement is typically created via systematic intervention in the time evolution of an initially unentangled state, which can be achieved by coherent control, carefully tailored non-demolition measurements, or dissipation in the presence of properly engineered reservoirs. In this paper we show that two-component Fermi gases at ~\mu K temperatures naturally evolve, in the presence of reactive two-body collisions, into states with highly entangled (Dicke-type) spin wavefunctions. The entanglement is a steady-state property that emerges---without any intervention---from uncorrelated initial states, and could be used to improve the accuracy of spectroscopy in experiments with fermionic alkaline earth atoms or fermionic groundstate molecules. }, doi = {10.1103/PhysRevLett.109.230501}, url = {http://arxiv.org/abs/1207.4741v1}, author = {Michael Foss-Feig and Andrew J. Daley and James K. Thompson and Ana Maria Rey} } @article {1510, title = {Super-Polynomial Quantum Speed-ups for Boolean Evaluation Trees with Hidden Structure}, journal = {ITCS {\textquoteright}12 Proceedings of the 3rd Innovations in Theoretical Computer Science Conference}, year = {2012}, month = {2012/01/08}, pages = {249-265}, abstract = { We give a quantum algorithm for evaluating a class of boolean formulas (such as NAND trees and 3-majority trees) on a restricted set of inputs. Due to the structure of the allowed inputs, our algorithm can evaluate a depth $n$ tree using $O(n^{2+\log\omega})$ queries, where $\omega$ is independent of $n$ and depends only on the type of subformulas within the tree. We also prove a classical lower bound of $n^{\Omega(\log\log n)}$ queries, thus showing a (small) super-polynomial speed-up. }, isbn = {978-1-4503-1115-1}, doi = {10.1145/2090236.2090258}, url = {http://arxiv.org/abs/1101.0796v3}, author = {Bohua Zhan and Shelby Kimmel and Avinatan Hassidim} } @article {1201, title = {Topological Flat Bands from Dipolar Spin Systems}, journal = {Physical Review Letters}, volume = {109}, year = {2012}, month = {2012/12/26}, abstract = { We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hardcore bosons, namely, the dressed spin-flips. These gauge fields result in topological band structures, whose bandgap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultra-cold polar molecules or spins in the solid state is considered. }, doi = {10.1103/PhysRevLett.109.266804}, url = {http://arxiv.org/abs/1207.4479v3}, author = {Norman Y. Yao and Chris R. Laumann and Alexey V. Gorshkov and Steven D. Bennett and Eugene Demler and Peter Zoller and Mikhail D. Lukin} } @article {1319, title = {Why the Tsirelson bound?}, journal = {The Probable and the Improbable: The Meaning and Role of Probability in Physics}, year = {2012}, month = {2012/08/18}, pages = {167-185}, abstract = { Wheeler{\textquoteright}s question {\textquoteright}why the quantum{\textquoteright} has two aspects: why is the world quantum and not classical, and why is it quantum rather than superquantum, i.e., why the Tsirelson bound for quantum correlations? I discuss a remarkable answer to this question proposed by Pawlowski et al (2009), who provide an information-theoretic derivation of the Tsirelson bound from a principle they call {\textquoteright}information causality.{\textquoteright} }, doi = {10.1007/978-3-642-21329-8_11}, url = {http://arxiv.org/abs/1208.3744v1}, author = {Jeffrey Bub} } @proceedings {1387, title = {Approximating the Turaev-Viro Invariant of Mapping Tori is Complete for One Clean Qubit}, year = {2011}, month = {2011/05/31}, abstract = {

The Turaev-Viro invariants are scalar topological invariants of three-dimensional manifolds. Here we show that the problem of estimating the Fibonacci version of the Turaev-Viro invariant of a mapping torus is a complete problem for the one clean qubit complexity class (DQC1). This complements a previous result showing that estimating the Turaev-Viro invariant for arbitrary manifolds presented as Heegaard splittings is a complete problem for the standard quantum computation model (BQP). We also discuss a beautiful analogy between these results and previously known results on the computational complexity of approximating the Jones polynomial.

}, url = {http://arxiv.org/abs/1105.5100}, author = {Stephen P. Jordan and Gorjan Alagic} } @article {1531, title = {Casimir force between sharp-shaped conductors}, journal = {Proceedings of the National Academy of Sciences}, volume = {108}, year = {2011}, month = {2011/04/11}, pages = {6867 - 6871}, abstract = { Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest. }, doi = {10.1073/pnas.1018079108}, url = {http://arxiv.org/abs/1010.3223v1}, author = {Mohammad F. Maghrebi and Sahand Jamal Rahi and Thorsten Emig and Noah Graham and Robert L. Jaffe and Mehran Kardar} } @article {1412, title = {Chern numbers hiding in time-of-flight images}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/12/21}, abstract = { We present a technique for detecting topological invariants -- Chern numbers -- from time-of-flight images of ultra-cold atoms. We show that the Chern numbers of integer quantum Hall states of lattice fermions leave their fingerprints in the atoms{\textquoteright} momentum distribution. We analytically demonstrate that the number of local maxima in the momentum distribution is equal to the Chern number in two limiting cases, for large hopping anisotropy and in the continuum limit. In addition, our numerical simulations beyond these two limits show that these local maxima persist for a range of parameters. Thus, an everyday observable in cold atom experiments can serve as a useful tool to characterize and visualize quantum states with non-trivial topology. }, doi = {10.1103/PhysRevA.84.063629}, url = {http://arxiv.org/abs/1105.3100v3}, author = {Erhai Zhao and Noah Bray-Ali and Carl J. Williams and I. B. Spielman and Indubala I. Satija} } @article {1484, title = {Comment on "Foundation of Statistical Mechanics under Experimentally Realistic Conditions" }, year = {2011}, month = {2011/09/22}, abstract = { Reimann [Phys. Rev. Lett. 101, 190403 (2008)] claimed that generic isolated macroscopic quantum system will equilibrate under experimentally realistic conditions by proving a theorem. We here show that the proof is invalid for most many-body systems and is unable to demonstrate equilibration in realistic experiment. }, url = {http://arxiv.org/abs/1109.4696v1}, author = {Zhe-Xuan Gong and L. -M. Duan} } @article {1433, title = {Continuous-variable quantum compressed sensing}, year = {2011}, month = {2011/11/03}, abstract = { We significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) --- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise. }, url = {http://arxiv.org/abs/1111.0853v3}, author = {Matthias Ohliger and Vincent Nesme and David Gross and Yi-Kai Liu and Jens Eisert} } @article {1866, title = {Deciding Unitary Equivalence Between Matrix Polynomials and Sets of Bipartite Quantum States}, journal = {Quantum Information and Computation}, volume = {11}, year = {2011}, month = {2001/09/01}, pages = {813{\textendash}819}, abstract = {

In this brief report, we consider the equivalence between two sets of\ m\ + 1 bipartite quantum states under local unitary transformations. For pure states, this problem corresponds to the matrix algebra question of whether two degree m matrix polynomials are unitarily equivalent; i.e.\ UAiV\† =\ Bi\ for 0 \≤\ i\ \≤\ m\ where\ U\ and\ V\ are unitary and (Ai, Bi) are arbitrary pairs of rectangular matrices. We present a randomized polynomial-time algorithm that solves this problem with an arbitrarily high success probability and outputs transforming matrices\ U\ and\ V.

}, keywords = {matrix polynomials, Schwartz-Zippel lemma, unitary transformations}, issn = {1533-7146}, url = {http://dl.acm.org/citation.cfm?id=2230936.2230942}, author = {Chitambar, Eric and Carl Miller and Shi, Yaoyun} } @article {1303, title = {Detecting paired and counterflow superfluidity via dipole oscillations}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/10/27}, abstract = { We suggest an experimentally feasible procedure to observe paired and counterflow superfluidity in ultra-cold atom systems. We study the time evolution of one-dimensional mixtures of bosonic atoms in an optical lattice following an abrupt displacement of an additional weak confining potential. We find that the dynamic responses of the paired superfluid phase for attractive inter-species interactions and the counterflow superfluid phase for repulsive interactions are qualitatively distinct and reflect the quasi long-range order that characterizes these states. These findings suggest a clear experimental procedure to detect these phases, and give an intuitive insight into their dynamics. }, doi = {10.1103/PhysRevA.84.041609}, url = {http://arxiv.org/abs/1103.3513v3}, author = {Anzi Hu and L. Mathey and Eite Tiesinga and Ippei Danshita and Carl J. Williams and Charles W. Clark} } @article {1520, title = {A diagrammatic expansion of the Casimir energy in multiple reflections: theory and applications }, journal = {Physical Review D}, volume = {83}, year = {2011}, month = {2011/2/2}, abstract = { We develop a diagrammatic representation of the Casimir energy of a multibody configuration. The diagrams represent multiple reflections between the objects and can be organized by a few simple rules. The lowest-order diagrams (or reflections) give the main contribution to the Casimir interaction which proves the usefulness of this expansion. Among some applications of this, we find analytical formulae describing the interaction between "edges", i.e. semi-infinite plates, where we also give a first example of blocking in the context of the Casimir energy. We also find the interaction of edges with a needle and describe analytically a recent model of the repulsion due to the Casimir interaction. }, doi = {10.1103/PhysRevD.83.045004}, url = {http://arxiv.org/abs/1012.1060v1}, author = {Mohammad F. Maghrebi} } @article {1430, title = {Direct Fidelity Estimation from Few Pauli Measurements}, journal = {Physical Review Letters}, volume = {106}, year = {2011}, month = {2011/6/8}, abstract = { We describe a simple method for certifying that an experimental device prepares a desired quantum state rho. Our method is applicable to any pure state rho, and it provides an estimate of the fidelity between rho and the actual (arbitrary) state in the lab, up to a constant additive error. The method requires measuring only a constant number of Pauli expectation values, selected at random according to an importance-weighting rule. Our method is faster than full tomography by a factor of d, the dimension of the state space, and extends easily and naturally to quantum channels. }, doi = {10.1103/PhysRevLett.106.230501}, url = {http://arxiv.org/abs/1104.4695v3}, author = {Steven T. Flammia and Yi-Kai Liu} } @article {1171, title = {d-Wave Superfluidity in Optical Lattices of Ultracold Polar Molecules}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/12/29}, abstract = { Recent work on ultracold polar molecules, governed by a generalization of the t-J Hamiltonian, suggests that molecules may be better suited than atoms for studying d-wave superfluidity due to stronger interactions and larger tunability of the system. We compute the phase diagram for polar molecules in a checkerboard lattice consisting of weakly coupled square plaquettes. In the simplest experimentally realizable case where there is only tunneling and an XX-type spin-spin interaction, we identify the parameter regime where d-wave superfluidity occurs. We also find that the inclusion of a density-density interaction destroys the superfluid phase and that the inclusion of a spin-density or an Ising-type spin-spin interaction can enhance the superfluid phase. We also propose schemes for experimentally realizing the perturbative calculations exhibiting enhanced d-wave superfluidity. }, doi = {10.1103/PhysRevA.84.063639}, url = {http://arxiv.org/abs/1110.5330v2}, author = {Kevin A. Kuns and Ana Maria Rey and Alexey V. Gorshkov} } @article {1488, title = {Dynamics of Overhauser Field under nuclear spin diffusion in a quantum dot }, journal = {New Journal of Physics}, volume = {13}, year = {2011}, month = {2011/03/25}, pages = {033036}, abstract = { The coherence of electron spin can be significantly enhanced by locking the Overhauser field from nuclear spins using the nuclear spin preparation. We propose a theoretical model to calculate the long time dynamics of the Overhauser field under intrinsic nuclear spin diffusion in a quantum dot. We obtain a simplified diffusion equation that can be numerically solved and show quantitatively how the Knight shift and the electron-mediated nuclear spin flip-flop affect the nuclear spin diffusion. The results explain several recent experimental observations, where the decay time of Overhauser field is measured under different configurations, including variation of the external magnetic field, the electron spin configuration in a double dot, and the initial nuclear spin polarization rate. }, doi = {10.1088/1367-2630/13/3/033036}, url = {http://arxiv.org/abs/0912.4322v1}, author = {Zhe-Xuan Gong and Zhang-qi Yin and L. -M. Duan} } @article {1523, title = {Electromagnetic Casimir Energies of Semi-Infinite Planes}, journal = {EPL (Europhysics Letters)}, volume = {95}, year = {2011}, month = {2011/07/01}, pages = {14001}, abstract = { Using recently developed techniques based on scattering theory, we find the electromagnetic Casimir energy for geometries involving semi-infinite planes, a case that is of particular interest in the design of microelectromechanical devices. We obtain both approximate analytic formulae and exact results requiring only modest numerical computation. Using these results, we analyze the effects of edges and orientation on the Casimir energy. We also demonstrate the accuracy, simplicity, and utility of our approximation scheme, which is based on a multiple reflection expansion. }, doi = {10.1209/0295-5075/95/14001}, url = {http://arxiv.org/abs/1102.1486v1}, author = {Mohammad F. Maghrebi and Noah Graham} } @article {1457, title = {Entanglement can completely defeat quantum noise}, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/12/15}, abstract = { We describe two quantum channels that individually cannot send any information, even classical, without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero capacity channels. But our result is stronger still, as it even allows zero-error quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver. }, doi = {10.1103/PhysRevLett.107.250504}, url = {http://arxiv.org/abs/1109.0540v1}, author = {Jianxin Chen and Toby S. Cubitt and Aram W. Harrow and Graeme Smith} } @article {1521, title = {Entropic force of polymers on a cone tip}, journal = {EPL (Europhysics Letters)}, volume = {96}, year = {2011}, month = {2011/12/01}, pages = {66002}, abstract = { We consider polymers attached to the tip of a cone, and the resulting force due to entropy loss on approaching a plate (or another cone). At separations shorter than the polymer radius of gyration R_g, the only relevant length scale is the tip-plate (or tip-tip) separation h, and the entropic force is given by F=A kT/h. The universal amplitude A can be related to (geometry dependent) correlation exponents of long polymers. We compute A for phantom polymers, and for self-avoiding (including star) polymers by epsilon-expansion, as well as by numerical simulations in 3 dimensions. }, doi = {10.1209/0295-5075/96/66002}, url = {http://arxiv.org/abs/1109.5658v2}, author = {Mohammad F. Maghrebi and Yacov Kantor and Mehran Kardar} } @article {1351, title = {Fast and robust quantum computation with ionic Wigner crystals}, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/4/15}, abstract = {We present a detailed analysis of the modulated-carrier quantum phase gate implemented with Wigner crystals of ions confined in Penning traps. We elaborate on a recent scheme, proposed by two of the authors, to engineer two-body interactions between ions in such crystals. We analyze for the first time the situation in which the cyclotron (w_c) and the crystal rotation (w_r) frequencies do not fulfill the condition w_c=2w_r. It is shown that even in the presence of the magnetic field in the rotating frame the many-body (classical) Hamiltonian describing small oscillations from the ion equilibrium positions can be recast in canonical form. As a consequence, we are able to demonstrate that fast and robust two-qubit gates are achievable within the current experimental limitations. Moreover, we describe a realization of the state-dependent sign-changing dipole forces needed to realize the investigated quantum computing scheme. }, doi = {10.1103/PhysRevA.83.042319}, url = {http://arxiv.org/abs/1011.5616v2}, author = {J. D. Baltrusch and A. Negretti and J. M. Taylor and T. Calarco} } @article {1529, title = {Implications of the Babinet Principle for Casimir Interactions}, journal = {Physical Review D}, volume = {84}, year = {2011}, month = {2011/9/1}, abstract = { We formulate the Babinet Principle (BP) as a relation between the scattering amplitudes for electromagnetic waves, and combine it with multiple scattering techniques to derive new properties of Casimir forces. We show that the Casimir force exerted by a planar conductor or dielectric on a self- complementary perforated planar mirror is approximately half that on a uniform mirror independent of the distance between them. The BP suggests that Casimir edge effects are anomalously small, supporting results obtained earlier in special cases. Finally, we illustrate how the BP can be used to estimate Casimir forces between perforated planar mirrors. }, doi = {10.1103/PhysRevD.84.061701}, url = {http://arxiv.org/abs/1103.5395v1}, author = {Mohammad F. Maghrebi and Ronen Abravanel and Robert L. Jaffe} } @article {1352, title = {Interferometry with Synthetic Gauge Fields}, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/3/3}, abstract = {We propose a compact atom interferometry scheme for measuring weak, time-dependent accelerations. Our proposal uses an ensemble of dilute trapped bosons with two internal states that couple to a synthetic gauge field with opposite charges. The trapped gauge field couples spin to momentum to allow time dependent accelerations to be continuously imparted on the internal states. We generalize this system to reduce noise and estimate the sensitivity of such a system to be S~10^-7 m / s^2 / Hz^1/2. }, doi = {10.1103/PhysRevA.83.031602}, url = {http://arxiv.org/abs/1008.3910v2}, author = {Brandon M. Anderson and J. M. Taylor and Victor M. Galitski} } @article {1349, title = {Laser cooling and optical detection of excitations in a LC electrical circuit}, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/12/27}, abstract = {We explore a method for laser cooling and optical detection of excitations in a LC electrical circuit. Our approach uses a nanomechanical oscillator as a transducer between optical and electronic excitations. An experimentally feasible system with the oscillator capacitively coupled to the LC and at the same time interacting with light via an optomechanical force is shown to provide strong electro-mechanical coupling. Conditions for improved sensitivity and quantum limited readout of electrical signals with such an "optical loud speaker" are outlined. }, doi = {10.1103/PhysRevLett.107.273601}, url = {http://arxiv.org/abs/1108.2035v1}, author = {J. M. Taylor and A. S. S{\o}rensen and C. M. Marcus and E. S. Polzik} } @article {1225, title = {Levinson{\textquoteright}s theorem for graphs}, journal = {Journal of Mathematical Physics}, volume = {52}, year = {2011}, month = {2011/06/30}, pages = {082102}, abstract = { We prove an analog of Levinson{\textquoteright}s theorem for scattering on a weighted (m+1)-vertex graph with a semi-infinite path attached to one of its vertices. In particular, we show that the number of bound states in such a scattering problem is equal to m minus half the winding number of the phase of the reflection coefficient (where each so-called half-bound state is counted as half a bound state). }, doi = {10.1063/1.3622608}, url = {http://arxiv.org/abs/1103.5077v2}, author = {Andrew M. Childs and DJ Strouse} } @article {1165, title = {Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing }, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/6/20}, abstract = { We study the modification of a traditional electromagnetically induced transparency (EIT) stored light technique that includes both EIT and four-wave mixing (FWM) in an ensemble of hot Rb atoms. The standard treatment of light storage involves the coherent and reversible mapping of one photonic mode onto a collective spin coherence. It has been shown that unwanted, competing processes such as four-wave mixing are enhanced by EIT and can significantly modify the signal optical pulse propagation. We present theoretical and experimental evidence to indicate that while a Stokes field is indeed detected upon retrieval of the signal field, any information originally encoded in a seeded Stokes field is not independently preserved during the storage process. We present a simple model that describes the propagation dynamics of the fields and the impact of FWM on the spin wave. }, doi = {10.1103/PhysRevA.83.063823}, url = {http://arxiv.org/abs/1103.2131v1}, author = {Nathaniel B. Phillips and Alexey V. Gorshkov and Irina Novikova} } @article {1447, title = {No-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems }, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/5/9}, abstract = { One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to implement, the preparation of the resource state becomes a crucial task. An appealing approach is simply to cool a strongly correlated quantum many-body system to its ground state. In addition to requiring the ground state of the system to be universal for one-way quantum computing, we also want the Hamiltonian to have non-degenerate ground state protected by a fixed energy gap, to involve only two-body interactions, and to be frustration-free so that measurements in the course of the computation leave the remaining particles in the ground space. Recently, significant efforts have been made to the search of resource states that appear naturally as ground states in spin lattice systems. The approach is proved to be successful in spin-5/2 and spin-3/2 systems. Yet, it remains an open question whether there could be such a natural resource state in a spin-1/2, i.e., qubit system. Here, we give a negative answer to this question by proving that it is impossible for a genuinely entangled qubit states to be a non-degenerate ground state of any two-body frustration-free Hamiltonian. What is more, we prove that every spin-1/2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states, a stronger result that is interesting independent of the context of one-way quantum computing. }, doi = {10.1103/PhysRevA.83.050301}, url = {http://arxiv.org/abs/1004.3787v1}, author = {Jianxin Chen and Xie Chen and Runyao Duan and Zhengfeng Ji and Bei Zeng} } @article {1467, title = {Phase diagram of the Bose Kondo-Hubbard model}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/11/16}, abstract = { We study a bosonic version of the Kondo lattice model with an on-site repulsion in the conduction band, implemented with alkali atoms in two bands of an optical lattice. Using both weak and strong-coupling perturbation theory, we find that at unit filling of the conduction bosons the superfluid to Mott insulator transition should be accompanied by a magnetic transition from a ferromagnet (in the superfluid) to a paramagnet (in the Mott insulator). Furthermore, an analytic treatment of Gutzwiller mean-field theory reveals that quantum spin fluctuations induced by the Kondo exchange cause the otherwise continuous superfluid to Mott-insulator phase transition to be first order. We show that lattice separability imposes a serious constraint on proposals to exploit excited bands for quantum simulations, and discuss a way to overcome this constraint in the context of our model by using an experimentally realized non-separable lattice. A method to probe the first-order nature of the transition based on collapses and revivals of the matter-wave field is also discussed. }, doi = {10.1103/PhysRevA.84.053619}, url = {http://arxiv.org/abs/1103.0245v2}, author = {Michael Foss-Feig and Ana Maria Rey} } @article {1174, title = {Photon-Photon Interactions via Rydberg Blockade}, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/9/22}, abstract = { We develop the theory of light propagation under the conditions of electromagnetically induced transparency (EIT) in systems involving strongly interacting Rydberg states. Taking into account the quantum nature and the spatial propagation of light, we analyze interactions involving few-photon pulses. We demonstrate that this system can be used for the generation of nonclassical states of light including trains of single photons with an avoided volume between them, for implementing photon-photon quantum gates, as well as for studying many-body phenomena with strongly correlated photons. }, doi = {10.1103/PhysRevLett.107.133602}, url = {http://arxiv.org/abs/1103.3700v1}, author = {Alexey V. Gorshkov and Johannes Otterbach and Michael Fleischhauer and Thomas Pohl and Mikhail D. Lukin} } @article {1181, title = {Quantum Magnetism with Polar Alkali Dimers}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/9/15}, abstract = { We show that dipolar interactions between ultracold polar alkali dimers in optical lattices can be used to realize a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. The model features long-range spin-spin interactions J_z and J_perp of XXZ type, long-range density-density interaction V, and long-range density-spin interaction W, all of which can be controlled in both magnitude and sign independently of each other and of the tunneling t. The "spin" is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional (orbital) degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. The presented system is expected to exhibit exotic physics and to provide insights into strongly correlated phenomena in condensed matter systems. Realistic experimental imperfections are discussed. }, doi = {10.1103/PhysRevA.84.033619}, url = {http://arxiv.org/abs/1106.1655v1}, author = {Alexey V. Gorshkov and Salvatore R. Manmana and Gang Chen and Eugene Demler and Mikhail D. Lukin and Ana Maria Rey} } @article {1846, title = {Quantum magnetism with polar alkali-metal dimers}, journal = {Phys. Rev. A}, volume = {84}, year = {2011}, pages = {033619}, url = {http://link.aps.org/abstract/PRA/v84/e033619/}, author = {Alexey V. Gorshkov and Manmana, S R and Chen, G and Demler, E and Lukin, M D and Rey, A M} } @article {1224, title = {Quantum query complexity of minor-closed graph properties}, journal = {Proc. 28th Symposium on Theoretical Aspects of Computer Science (STACS 2011), Leibniz International Proceedings in Informatics}, volume = {9}, year = {2011}, month = {2011/01/01}, pages = {661-672}, abstract = { We study the quantum query complexity of minor-closed graph properties, which include such problems as determining whether an $n$-vertex graph is planar, is a forest, or does not contain a path of a given length. We show that most minor-closed properties---those that cannot be characterized by a finite set of forbidden subgraphs---have quantum query complexity \Theta(n^{3/2}). To establish this, we prove an adversary lower bound using a detailed analysis of the structure of minor-closed properties with respect to forbidden topological minors and forbidden subgraphs. On the other hand, we show that minor-closed properties (and more generally, sparse graph properties) that can be characterized by finitely many forbidden subgraphs can be solved strictly faster, in o(n^{3/2}) queries. Our algorithms are a novel application of the quantum walk search framework and give improved upper bounds for several subgraph-finding problems. }, doi = {10.4230/LIPIcs.STACS.2011.661}, url = {http://arxiv.org/abs/1011.1443v2}, author = {Andrew M. Childs and Robin Kothari} } @article {1183, title = {Resolved atomic interaction sidebands in an optical clock transition}, journal = {Physical Review Letters}, volume = {106}, year = {2011}, month = {2011/6/22}, abstract = { We report the observation of resolved atomic interaction sidebands (ISB) in the ${}^{87}$Sr optical clock transition when atoms at microkelvin temperatures are confined in a two-dimensional (2D) optical lattice. The ISB are a manifestation of the strong interactions that occur between atoms confined in a quasi-one-dimensional geometry and disappear when the confinement is relaxed along one dimension. The emergence of ISB is linked to the recently observed suppression of collisional frequency shifts in [1]. At the current temperatures, the ISB can be resolved but are broad. At lower temperatures, ISB are predicted to be substantially narrower and usable as powerful spectroscopic tools in strongly interacting alkaline-earth gases. }, doi = {10.1103/PhysRevLett.106.250801}, url = {http://arxiv.org/abs/1102.1016v2}, author = {Michael Bishof and Yige Lin and Matthew D. Swallows and Alexey V. Gorshkov and Jun Ye and Ana Maria Rey} } @article {1196, title = {Robust Quantum State Transfer in Random Unpolarized Spin Chains}, journal = {Physical Review Letters}, volume = {106}, year = {2011}, month = {2011/1/27}, abstract = { We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed. }, doi = {10.1103/PhysRevLett.106.040505}, url = {http://arxiv.org/abs/1011.2762v2}, author = {Norman Y. Yao and Liang Jiang and Alexey V. Gorshkov and Zhe-Xuan Gong and Alex Zhai and L. -M. Duan and Mikhail D. Lukin} } @article {1301, title = {Spatial separation in a thermal mixture of ultracold $^{174}$Yb and $^{87}$Rb atoms }, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/4/21}, abstract = { We report on the observation of unusually strong interactions in a thermal mixture of ultracold atoms which cause a significant modification of the spatial distribution. A mixture of $^{87}$Rb and $^{174}$Yb with a temperature of a few $\mu$K is prepared in a hybrid trap consisting of a bichromatic optical potential superimposed on a magnetic trap. For suitable trap parameters and temperatures, a spatial separation of the two species is observed. We infer that the separation is driven by a large interaction strength between $^{174}$Yb and $^{87}$Rb accompanied by a large three-body recombination rate. Based on this assumption we have developed a diffusion model which reproduces our observations. }, doi = {10.1103/PhysRevA.83.040702}, url = {http://arxiv.org/abs/1104.1722v1}, author = {Florian Baumer and Frank M{\"u}nchow and Axel G{\"o}rlitz and Stephen E. Maxwell and Paul S. Julienne and Eite Tiesinga} } @article {2617, title = {Spectral Concentration of Positive Functions on Compact Groups}, journal = {Journal of Fourier Analysis and Applications }, volume = {17}, year = {2011}, pages = {355-373}, abstract = {

The problem of understanding the Fourier-analytic structure of the cone of
positive functions on a group has a long history. In this article, we develop the first
quantitative spectral concentration results for such functions over arbitrary compact
groups. Specifically, we describe a family of finite, positive quadrature rules for the
Fourier coefficients of band-limited functions on compact groups. We apply these
quadrature rules to establish a spectral concentration result for positive functions:
given appropriately nested band limits A \⊂ B \⊂ G, we prove a lower bound on the
fraction of L2-mass that any B-band-limited positive function has in A. Our bounds
are explicit and depend only on elementary properties of A and B; they are the first
such bounds that apply to arbitrary compact groups. They apply to finite groups as
a special case, where the quadrature rule is given by the Fourier transform on the
smallest quotient whose dual contains the Fourier support of the function.

}, doi = {https://doi.org/10.1007/s00041-011-9174-5}, author = {Gorjan Alagic and Alexander Russell} } @article {1172, title = {Spectroscopy of dipolar fermions in 2D pancakes and 3D lattices}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/9/6}, abstract = { Motivated by ongoing measurements at JILA, we calculate the recoil-free spectra of dipolar interacting fermions, for example ultracold heteronuclear molecules, in a one-dimensional lattice of two-dimensional pancakes, spectroscopically probing transitions between different internal (e.g., rotational) states. We additionally incorporate p-wave interactions and losses, which are important for reactive molecules such as KRb. Moreover, we consider other sources of spectral broadening: interaction-induced quasiparticle lifetimes and the different polarizabilities of the different rotational states used for the spectroscopy. Although our main focus is molecules, some of the calculations are also useful for optical lattice atomic clocks. For example, understanding the p-wave shifts between identical fermions and small dipolar interactions coming from the excited clock state are necessary to reach future precision goals. Finally, we consider the spectra in a deep 3D lattice and show how they give a great deal of information about static correlation functions, including \textit{all} the moments of the density correlations between nearby sites. The range of correlations measurable depends on spectroscopic resolution and the dipole moment. }, doi = {10.1103/PhysRevA.84.033608}, url = {http://arxiv.org/abs/1106.1718v1}, author = {Kaden R. A. Hazzard and Alexey V. Gorshkov and Ana Maria Rey} } @article {1847, title = {Spectroscopy of dipolar fermions in layered two-dimensional and three-dimensional lattices}, journal = {Phys. Rev. A}, volume = {84}, year = {2011}, pages = {033608}, url = {http://link.aps.org/abstract/PRA/v84/e033608/}, author = {Hazzard, K R A and Alexey V. Gorshkov and Rey, A M} } @article {1446, title = {Superactivation of the Asymptotic Zero-Error Classical Capacity of a Quantum Channel}, journal = {IEEE Transactions on Information Theory}, volume = {57}, year = {2011}, month = {2011/12/01}, pages = {8114 - 8126}, abstract = { The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly, so that they can be decoded with zero probability of error. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel. }, doi = {10.1109/TIT.2011.2169109}, url = {http://arxiv.org/abs/0906.2547v3}, author = {Toby S. Cubitt and Jianxin Chen and Aram W. Harrow} } @article {1278, title = {Superradiance of cold atoms coupled to a superconducting circuit}, journal = {Physical Review A}, volume = {83}, year = {2011}, month = {2011/6/6}, abstract = { We investigate superradiance of an ensemble of atoms coupled to an integrated superconducting LC-circuit. Particular attention is paid to the effect of inhomogeneous coupling constants. Combining perturbation theory in the inhomogeneity and numerical simulations we show that inhomogeneous coupling constants can significantly affect the superradiant relaxation process. Incomplete relaxation terminating in "dark states" can occur, from which the only escape is through individual spontaneous emission on a much longer time scale. The relaxation dynamics can be significantly accelerated or retarded, depending on the distribution of the coupling constants. On the technical side, we also generalize the previously known propagator of superradiance for identical couplings in the completely symmetric sector to the full exponentially large Hilbert space. }, doi = {10.1103/PhysRevA.83.062305}, url = {http://arxiv.org/abs/1101.5300v1}, author = {Daniel Braun and Jonathan Hoffman and Eite Tiesinga} } @article {1198, title = {Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules }, journal = {Physical Review Letters}, volume = {107}, year = {2011}, month = {2011/9/8}, abstract = { By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. In addition to XXZ spin exchange, the model features density-density interactions and novel density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method (DMRG) to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the t-J-V-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally. }, doi = {10.1103/PhysRevLett.107.115301}, url = {http://arxiv.org/abs/1106.1644v1}, author = {Alexey V. Gorshkov and Salvatore R. Manmana and Gang Chen and Jun Ye and Eugene Demler and Mikhail D. Lukin and Ana Maria Rey} } @article {1350, title = {Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate}, journal = {Physical Review A}, volume = {84}, year = {2011}, month = {2011/7/26}, abstract = {Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and sparse representations of quantum information (qubits) and a simple construction of multi-qubit gates, for all anyon models from Chern-Simons-Witten SU(2)$_k$ theory that support universal quantum computation by braiding ($k\geq 3,\ k \neq 4$). In the process, we show how the constructions of topological quantum memory and gates for $k=2,4$ connect naturally to those for $k\geq 3,\ k \neq 4$, unifying these concepts in a simple framework. Furthermore, we illustrate potential extensions of these ideas to other anyon models outside of Chern-Simons-Witten field theory. }, doi = {10.1103/PhysRevA.84.012332}, url = {http://arxiv.org/abs/1001.4085v2}, author = {Haitan Xu and J. M. Taylor} } @article {1427, title = {Universal low-rank matrix recovery from Pauli measurements}, journal = {Advances in Neural Information Processing Systems (NIPS)}, year = {2011}, month = {2011/03/14}, pages = {1638-1646}, abstract = { We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rd poly log d) Pauli measurements. This has applications in quantum state tomography, and is a non-commutative analogue of a well-known problem in compressed sensing: recovering a sparse vector from a few of its Fourier coefficients. We show that almost all sets of O(rd log^6 d) Pauli measurements satisfy the rank-r restricted isometry property (RIP). This implies that M can be recovered from a fixed ("universal") set of Pauli measurements, using nuclear-norm minimization (e.g., the matrix Lasso), with nearly-optimal bounds on the error. A similar result holds for any class of measurements that use an orthonormal operator basis whose elements have small operator norm. Our proof uses Dudley{\textquoteright}s inequality for Gaussian processes, together with bounds on covering numbers obtained via entropy duality. }, url = {http://arxiv.org/abs/1103.2816v2}, author = {Yi-Kai Liu} } @article {1501, title = {Adiabatic preparation of many-body states in optical lattices}, journal = {Physical Review A}, volume = {81}, year = {2010}, month = {2010/6/22}, abstract = { We analyze a technique for the preparation of low entropy many body states of atoms in optical lattices based on adiabatic passage. In particular, we show that this method allows preparation of strongly correlated states as stable highest energy states of Hamiltonians that have trivial ground states. As an example, we analyze the generation of antiferromagnetically ordered states by adiabatic change of a staggered field acting on the spins of bosonic atoms with ferromagnetic interactions. }, doi = {10.1103/PhysRevA.81.061603}, url = {http://arxiv.org/abs/0906.2567v3}, author = {Anders S. Sorensen and Ehud Altman and Michael Gullans and J. V. Porto and Mikhail D. Lukin and Eugene Demler} } @article {1401, title = {Approximating Turaev-Viro 3-manifold invariants is universal for quantum computation }, journal = {Physical Review A}, volume = {82}, year = {2010}, month = {2010/10/8}, abstract = { The Turaev-Viro invariants are scalar topological invariants of compact, orientable 3-manifolds. We give a quantum algorithm for additively approximating Turaev-Viro invariants of a manifold presented by a Heegaard splitting. The algorithm is motivated by the relationship between topological quantum computers and (2+1)-D topological quantum field theories. Its accuracy is shown to be nontrivial, as the same algorithm, after efficient classical preprocessing, can solve any problem efficiently decidable by a quantum computer. Thus approximating certain Turaev-Viro invariants of manifolds presented by Heegaard splittings is a universal problem for quantum computation. This establishes a novel relation between the task of distinguishing non-homeomorphic 3-manifolds and the power of a general quantum computer. }, doi = {10.1103/PhysRevA.82.040302}, url = {http://arxiv.org/abs/1003.0923v1}, author = {Gorjan Alagic and Stephen P. Jordan and Robert Koenig and Ben W. Reichardt} } @article {1242, title = {Characterization of universal two-qubit Hamiltonians}, year = {2010}, month = {2010/04/09}, abstract = { Suppose we can apply a given 2-qubit Hamiltonian H to any (ordered) pair of qubits. We say H is n-universal if it can be used to approximate any unitary operation on n qubits. While it is well known that almost any 2-qubit Hamiltonian is 2-universal (Deutsch, Barenco, Ekert 1995; Lloyd 1995), an explicit characterization of the set of non-universal 2-qubit Hamiltonians has been elusive. Our main result is a complete characterization of 2-non-universal 2-qubit Hamiltonians. In particular, there are three ways that a 2-qubit Hamiltonian H can fail to be universal: (1) H shares an eigenvector with the gate that swaps two qubits, (2) H acts on the two qubits independently (in any of a certain family of bases), or (3) H has zero trace. A 2-non-universal 2-qubit Hamiltonian can still be n-universal for some n >= 3. We give some partial results on 3-universality. Finally, we also show how our characterization of 2-universal Hamiltonians implies the well-known result that almost any 2-qubit unitary is universal. }, url = {http://arxiv.org/abs/1004.1645v2}, author = {Andrew M. Childs and Debbie Leung and Laura Mancinska and Maris Ozols} } @article {1325, title = {Contextuality in Quantum Mechanics: Testing the Klyachko Inequality}, year = {2010}, month = {2010/06/02}, abstract = { The Klyachko inequality is an inequality for the probabiities of the values of five observables of a spin-1 particle, which is satisfied by any noncontextual assignment of values to this set of observables, but is violated by the probabilities defined by a certain quantum state. We describe an experiment between two entangled spin-1 particles to test contextuality via a related inequality. We point out that a test of contextuality by measurements on a single particle to confirm the Klyachko inequality requires an assumption of non-disturbance by the measuring instrument, which is avoided in the two-particle experiment. }, url = {http://arxiv.org/abs/1006.0500v2}, author = {Jeffrey Bub and Allen Stairs} } @article {1286, title = {Creation and manipulation of Feshbach resonances with radio-frequency radiation }, journal = {New Journal of Physics}, volume = {12}, year = {2010}, month = {2010/08/12}, pages = {083031}, abstract = { We present a simple technique for studying collisions of ultracold atoms in the presence of a magnetic field and radio-frequency radiation (rf). Resonant control of scattering properties can be achieved by using rf to couple a colliding pair of atoms to a bound state. We show, using the example of 6Li, that in some ranges of rf frequency and magnetic field this can be done without giving rise to losses. We also show that halo molecules of large spatial extent require much less rf power than deeply bound states. Another way to exert resonant control is with a set of rf-coupled bound states, linked to the colliding pair through the molecular interactions that give rise to magnetically tunable Feshbach resonances. This was recently demonstrated for 87Rb [Kaufman et al., Phys. Rev. A 80:050701(R), 2009]. We examine the underlying atomic and molecular physics which made this possible. Lastly, we consider the control that may be exerted over atomic collisions by placing atoms in superpositions of Zeeman states, and suggest that it could be useful where small changes in scattering length are required. We suggest other species for which rf and magnetic field control could together provide a useful tuning mechanism. }, doi = {10.1088/1367-2630/12/8/083031}, url = {http://arxiv.org/abs/1004.0636v1}, author = {Thomas M. Hanna and Eite Tiesinga and Paul S. Julienne} } @article {1385, title = {On the degeneracy of SU(3)k topological phases}, year = {2010}, month = {2010/09/01}, abstract = {

The ground state degeneracy of an $SU(N)_k$ topological phase with $n$ quasiparticle excitations is relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for this degeneracy for any $N \> 2$. Here we present the problem in an explicit combinatorial way and analyze the case N=3. While not finding a complete closed-form solution, we obtain generating functions and solve some special cases.

}, url = {http://arxiv.org/abs/1009.0114v1}, author = {Stephen P. Jordan and Toufik Mansour and Simone Severini} } @article {1353, title = {Dynamic Nuclear Polarization in Double Quantum Dots}, journal = {Physical Review Letters}, volume = {104}, year = {2010}, month = {2010/6/4}, abstract = {We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identified, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. We show that in the case of unequal dots, build up of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, build up of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process. }, doi = {10.1103/PhysRevLett.104.226807}, url = {http://arxiv.org/abs/1003.4508v2}, author = {Michael Gullans and J. J. Krich and J. M. Taylor and H. Bluhm and B. I. Halperin and C. M. Marcus and M. Stopa and A. Yacoby and M. D. Lukin} } @article {1431, title = {Efficient Direct Tomography for Matrix Product States}, year = {2010}, month = {2010/02/24}, abstract = { In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements. Our method is exponentially faster than standard tomography, and it can also be used to certify that the unknown state is an MPS. The basic idea is to use local unitary operations to measure in the Schmidt basis, giving direct access to the MPS representation. This compares favorably with recently and independently proposed methods that recover the MPS tensors by performing a variational minimization, which is computationally intractable in certain cases. Our method also has the advantage of recovering any MPS, while other approaches were limited to special classes of states that exclude important examples such as GHZ and W states. }, url = {http://arxiv.org/abs/1002.4632v1}, author = {Olivier Landon-Cardinal and Yi-Kai Liu and David Poulin} } @article {1436, title = {Efficient quantum state tomography}, journal = {Nature Communications}, volume = {1}, year = {2010}, month = {2010/12/21}, pages = {149}, abstract = { Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions. }, doi = {10.1038/ncomms1147}, url = {http://arxiv.org/abs/1101.4366v1}, author = {Marcus Cramer and Martin B. Plenio and Steven T. Flammia and David Gross and Stephen D. Bartlett and Rolando Somma and Olivier Landon-Cardinal and Yi-Kai Liu and David Poulin} } @article {1867, title = {An Euler{\textendash}Poincar{\'e} bound for equicharacteristic {\'e}tale sheaves}, journal = {Algebra \& Number Theory}, volume = {4}, year = {2010}, month = {2010/01/14}, pages = {21 - 45}, abstract = {

The Grothendieck\–Ogg\–Shafarevich formula expresses the Euler characteristic of an {\'e}tale sheaf on a characteristic-p\ curve in terms of local data. The purpose of this paper is to prove an equicharacteristic version of this formula (a bound, rather than an equality). This follows work of R.\ Pink.

The basis for the proof of this result is the characteristic-p\ Riemann\–Hilbert correspondence, which is a functorial relationship between two different types of sheaves on a characteristic-p\ scheme. In the paper we prove a one-dimensional version of this correspondence, considering both local and global settings.

}, issn = {1937-0652}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.648.3584}, author = {Carl Miller} } @article {1848, title = {Far-field optical imaging and manipulation of individual spins with nanoscale resolution}, journal = {Nature Phys.}, volume = {6}, year = {2010}, pages = {912}, url = {http://www.nature.com/nphys/journal/v6/n11/abs/nphys1774.html}, author = {Maurer, P C and Maze, J R and Stanwix, P L and Jiang, L and Alexey V. Gorshkov and Zibrov, A A and Harke, B and Hodges, J S and Zibrov, A S and Yacoby, A and Twitchen, D and Hell, S W and Walsworth, R L and Lukin, M D} } @article {1182, title = {Fast Entanglement Distribution with Atomic Ensembles and Fluorescent Detection }, journal = {Physical Review A}, volume = {81}, year = {2010}, month = {2010/2/12}, abstract = { Quantum repeaters based on atomic ensemble quantum memories are promising candidates for achieving scalable distribution of entanglement over long distances. Recently, important experimental progress has been made towards their implementation. However, the entanglement rates and scalability of current approaches are limited by relatively low retrieval and single-photon detector efficiencies. We propose a scheme, which makes use of fluorescent detection of stored excitations to significantly increase the efficiency of connection and hence the rate. Practical performance and possible experimental realizations of the new protocol are discussed. }, doi = {10.1103/PhysRevA.81.020303}, url = {http://arxiv.org/abs/0907.3839v2}, author = {Jonatan B. Brask and Liang Jiang and Alexey V. Gorshkov and Vladan Vuletic and Anders S. Sorensen and Mikhail D. Lukin} } @article {1284, title = {Feshbach Resonances in Ultracold Gases}, journal = {Reviews of Modern Physics}, volume = {82}, year = {2010}, month = {2010/4/29}, pages = {1225 - 1286}, abstract = { Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules. }, doi = {10.1103/RevModPhys.82.1225}, url = {http://arxiv.org/abs/0812.1496v2}, author = {Cheng Chin and Rudolf Grimm and Paul Julienne and Eite Tiesinga} } @article {1469, title = {Heavy fermions in an optical lattice}, journal = {Physical Review A}, volume = {82}, year = {2010}, month = {2010/11/22}, abstract = { We employ a mean-field theory to study ground-state properties and transport of a two-dimensional gas of ultracold alklaline-earth metal atoms governed by the Kondo Lattice Hamiltonian plus a parabolic confining potential. In a homogenous system this mean-field theory is believed to give a qualitatively correct description of heavy fermion metals and Kondo insulators: it reproduces the Kondo-like scaling of the quasiparticle mass in the former, and the same scaling of the excitation gap in the latter. In order to understand ground-state properties in a trap we extend this mean-field theory via local-density approximation. We find that the Kondo insulator gap manifests as a shell structure in the trapped density profile. In addition, a strong signature of the large Fermi surface expected for heavy fermion systems survives the confinement, and could be probed in time-of-flight experiments. From a full self-consistent diagonalization of the mean-field theory we are able to study dynamics in the trap. We find that the mass enhancement of quasiparticle excitations in the heavy Fermi liquid phase manifests as slowing of the dipole oscillations that result from a sudden displacement of the trap center. }, doi = {10.1103/PhysRevA.82.053624}, url = {http://arxiv.org/abs/1007.5083v1}, author = {Michael Foss-Feig and Michael Hermele and Victor Gurarie and Ana Maria Rey} } @article {1868, title = {Matrix pencils and entanglement classification}, journal = {Journal of Mathematical Physics}, volume = {51}, year = {2010}, month = {2010/01/01}, pages = {072205}, abstract = {

Quantum entanglement plays a central role in quantum information processing. A main objective of the theory is to classify different types of entanglement according to their interconvertibility through manipulations that do not require additional entanglement to perform. While bipartite entanglement is well understood in this framework, the classification of entanglements among three or more subsystems is inherently much more difficult. In this paper, we study pure state entanglement in systems of dimension\ 2\⊗m\⊗n. Two states are considered equivalent if they can be reversibly converted from one to the other with a nonzero probability using only local quantum resources and classical communication (SLOCC). We introduce a connection between entanglement manipulations in these systems and the well-studied theory of matrix pencils. All previous attempts to study general SLOCC equivalence in such systems have relied on somewhat contrived techniques which fail to reveal the elegant structure of the problem that can be seen from the matrix pencil approach. Based on this method, we report the first polynomial-time algorithm for deciding when two2\⊗m\⊗n\ states are SLOCC equivalent. We then proceed to present a canonical form for all\ 2\⊗m\⊗n\ states based on the matrix pencil construction such that two states are equivalent if and only if they have the same canonical form. Besides recovering the previously known 26 distinct SLOCC equivalence classes in\ 2\⊗3\⊗n\ systems, we also determine the hierarchy between these classes.

}, issn = {00222488}, doi = {10.1063/1.3459069}, url = {http://scitation.aip.org/content/aip/journal/jmp/51/7/10.1063/1.3459069}, author = {Chitambar, Eric and Carl Miller and Shi, Yaoyun} } @article {1413, title = {Noise correlations of one-dimensional Bose mixtures in optical lattices}, journal = {Physical Review A}, volume = {81}, year = {2010}, month = {2010/6/2}, abstract = { We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work, we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity. Here we investigate the signature of these phases in the noise correlations of the atomic cloud after time-of-flight expansion, using both Luttinger liquid theory and the time-evolving block decimation (TEBD) method. We find that paired and counterflow superfluidity exhibit distinctive features in the noise spectra. We treat both extended and inhomogeneous systems, and our numerical work shows that the essential physics of the extended systems is present in the trapped-atom systems of current experimental interest. For paired and counterflow superfluid phases, we suggest methods for extracting Luttinger parameters from noise correlation spectroscopy. }, doi = {10.1103/PhysRevA.81.063602}, url = {http://arxiv.org/abs/1002.4918v2}, author = {Anzi Hu and L. Mathey and Carl J. Williams and Charles W. Clark} } @article {1442, title = {Optimal Perfect Distinguishability between Unitaries and Quantum Operations }, year = {2010}, month = {2010/10/12}, abstract = { We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula of optimal query time. We extend the sequential condition to general d-dimensional case. Meanwhile, we provide an upper bound and a lower bound for optimal sequential query time. In the process a new iterative method is given, the most notable innovation of which is its independence to auxiliary systems or entanglement. Following the idea, we further obtain an upper bound and a lower bound of (entanglement-assisted) q-maximal fidelities between a unitary and a quantum operation. Thus by the recursion in [1] an upper bound and a lower bound for optimal general perfect discrimination are achieved. Finally our lower bound result can be extended to the case of arbitrary two quantum operations. }, url = {http://arxiv.org/abs/1010.2298v1}, author = {Cheng Lu and Jianxin Chen and Runyao Duan} } @article {1380, title = {Permutational Quantum Computing}, journal = {Quantum Information \& Computation}, volume = {10}, year = {2010}, month = {2010/05/01}, pages = {470-497}, abstract = {

In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle trajectory, and computes by permuting particles. Whereas topological quantum computation requires anyons, permutational quantum computation can be performed with ordinary spin-1/2 particles, using a variant of the spin-network scheme of Marzuoli and Rasetti. We do not know whether permutational computation is universal. It may represent a new complexity class within BQP. Nevertheless, permutational quantum computers can in polynomial time approximate matrix elements of certain irreducible representations of the symmetric group and simulate certain processes in the Ponzano-Regge spin foam model of quantum gravity. No polynomial time classical algorithms for these problems are known.

}, url = {http://dl.acm.org/citation.cfm?id=2011369}, author = {Stephen P. Jordan} } @article {1170, title = {Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain }, journal = {Physical Review Letters}, volume = {105}, year = {2010}, month = {2010/8/5}, abstract = { We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the pi phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed. }, doi = {10.1103/PhysRevLett.105.060502}, url = {http://arxiv.org/abs/1001.0968v3}, author = {Alexey V. Gorshkov and Johannes Otterbach and Eugene Demler and Michael Fleischhauer and Mikhail D. Lukin} } @article {1455, title = {Principle of Maximum Entropy and Ground Spaces of Local Hamiltonians}, year = {2010}, month = {2010/10/13}, abstract = { The structure of the ground spaces of quantum systems consisting of local interactions is of fundamental importance to different areas of physics. In this Letter, we present a necessary and sufficient condition for a subspace to be the ground space of a k-local Hamiltonian. Our analysis are motivated by the concept of irreducible correlations studied by [Linden et al., PRL 89, 277906] and [Zhou, PRL 101, 180505], which is in turn based on the principle of maximum entropy. It establishes a better understanding of the ground spaces of local Hamiltonians and builds an intimate link of ground spaces to the correlations of quantum states. }, url = {http://arxiv.org/abs/1010.2739v4}, author = {Jianxin Chen and Zhengfeng Ji and Mary Beth Ruskai and Bei Zeng and Duanlu Zhou} } @article {1468, title = {Probing the Kondo Lattice Model with Alkaline Earth Atoms}, journal = {Physical Review A}, volume = {81}, year = {2010}, month = {2010/5/7}, abstract = { We study transport properties of alkaline-earth atoms governed by the Kondo Lattice Hamiltonian plus a harmonic confining potential, and suggest simple dynamical probes of several different regimes of the phase diagram that can be implemented with current experimental techniques. In particular, we show how Kondo physics at strong coupling, low density, and in the heavy fermion phase is manifest in the dipole oscillations of the conduction band upon displacement of the trap center. }, doi = {10.1103/PhysRevA.81.051603}, url = {http://arxiv.org/abs/0912.4762v1}, author = {Michael Foss-Feig and Michael Hermele and Ana Maria Rey} } @article {1463, title = {Pseudorandom generators and the BQP vs. PH problem}, year = {2010}, month = {2010/07/02}, abstract = { It is a longstanding open problem to devise an oracle relative to which BQP does not lie in the Polynomial-Time Hierarchy (PH). We advance a natural conjecture about the capacity of the Nisan-Wigderson pseudorandom generator [NW94] to fool AC_0, with MAJORITY as its hard function. Our conjecture is essentially that the loss due to the hybrid argument (which is a component of the standard proof from [NW94]) can be avoided in this setting. This is a question that has been asked previously in the pseudorandomness literature [BSW03]. We then make three main contributions: (1) We show that our conjecture implies the existence of an oracle relative to which BQP is not in the PH. This entails giving an explicit construction of unitary matrices, realizable by small quantum circuits, whose row-supports are "nearly-disjoint." (2) We give a simple framework (generalizing the setting of Aaronson [A10]) in which any efficiently quantumly computable unitary gives rise to a distribution that can be distinguished from the uniform distribution by an efficient quantum algorithm. When applied to the unitaries we construct, this framework yields a problem that can be solved quantumly, and which forms the basis for the desired oracle. (3) We prove that Aaronson{\textquoteright}s "GLN conjecture" [A10] implies our conjecture; our conjecture is thus formally easier to prove. The GLN conjecture was recently proved false for depth greater than 2 [A10a], but it remains open for depth 2. If true, the depth-2 version of either conjecture would imply an oracle relative to which BQP is not in AM, which is itself an outstanding open problem. Taken together, our results have the following interesting interpretation: they give an instantiation of the Nisan-Wigderson generator that can be broken by quantum computers, but not by the relevant modes of classical computation, if our conjecture is true. }, url = {http://arxiv.org/abs/1007.0305v3}, author = {Bill Fefferman and Christopher Umans} } @article {1396, title = {QMA-complete problems for stoquastic Hamiltonians and Markov matrices}, journal = {Physical Review A}, volume = {81}, year = {2010}, month = {2010/3/29}, abstract = { We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is QMA-complete. We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using certain excited states of a stoquastic Hamiltonian is universal. We also show that adiabatic evolution in the ground state of a stochastic frustration free Hamiltonian is universal. Our results give a new QMA-complete problem arising in the classical setting of Markov chains, and new adiabatically universal Hamiltonians that arise in many physical systems. }, doi = {10.1103/PhysRevA.81.032331}, url = {http://arxiv.org/abs/0905.4755v2}, author = {Stephen P. Jordan and David Gosset and Peter J. Love} } @article {1218, title = {Quantum algorithms for algebraic problems}, journal = {Reviews of Modern Physics}, volume = {82}, year = {2010}, month = {2010/1/15}, pages = {1 - 52}, abstract = { Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation, and in particular, on problems with an algebraic flavor. }, doi = {10.1103/RevModPhys.82.1}, url = {http://arxiv.org/abs/0812.0380v1}, author = {Andrew M. Childs and Wim van Dam} } @article {2616, title = {Quantum Algorithms for Simon{\textquoteright}s Problem over Nonabelian Groups}, journal = {ACM Trans. Algorithms}, volume = {6}, year = {2010}, abstract = {

Daniel Simon\&$\#$39;s 1994 discovery of an efficient quantum algorithm for finding \“hidden shifts\” of Z2n provided the first algebraic problem for which quantum computers are exponentially faster than their classical counterparts. In this article, we study the generalization of Simon\&$\#$39;s problem to arbitrary groups. Fixing a finite group G, this is the problem of recovering an involution m = (m1,\…,mn) \∈ Gn from an oracle f with the property that f(x \⋅ y) = f(x) \⇔ y \∈ {1, m}. In the current parlance, this is the hidden subgroup problem (HSP) over groups of the form Gn, where G is a nonabelian group of constant size, and where the hidden subgroup is either trivial or has order two.

Although groups of the form Gn have a simple product structure, they share important representation--theoretic properties with the symmetric groups Sn, where a solution to the HSP would yield a quantum algorithm for Graph Isomorphism. In particular, solving their HSP with the so-called \“standard method\” requires highly entangled measurements on the tensor product of many coset states.

In this article, we provide quantum algorithms with time complexity 2O(\√n) that recover hidden involutions m = (m1,\…mn) \∈ Gn where, as in Simon\&$\#$39;s problem, each mi is either the identity or the conjugate of a known element m which satisfies κ(m) = \−κ(1) for some κ \∈ Gh. Our approach combines the general idea behind Kuperberg\&$\#$39;s sieve for dihedral groups with the \“missing harmonic\” approach of Moore and Russell. These are the first nontrivial HSP algorithms for group families that require highly entangled multiregister Fourier sampling.

}, doi = {https://doi.org/10.1145/1644015.1644034}, author = {Gorjan Alagic and Cristopher Moore and Alexander Russell} } @article {1316, title = {Quantum computation and pseudo-telepathic games}, journal = {Philosophy of Science}, volume = {75}, year = {2010}, month = {2010/05/14}, pages = {458-472}, abstract = { A quantum algorithm succeeds not because the superposition principle allows {\textquoteright}the computation of all values of a function at once{\textquoteright} via {\textquoteright}quantum parallelism,{\textquoteright} but rather because the structure of a quantum state space allows new sorts of correlations associated with entanglement, with new possibilities for information-processing transformations between correlations, that are not possible in a classical state space. I illustrate this with an elementary example of a problem for which a quantum algorithm is more efficient than any classical algorithm. I also introduce the notion of {\textquoteright}pseudo-telepathic{\textquoteright} games and show how the difference between classical and quantum correlations plays a similar role here for games that can be won by quantum players exploiting entanglement, but not by classical players whose only allowed common resource consists of shared strings of random numbers (common causes of the players{\textquoteright} correlated responses in a game). }, url = {http://arxiv.org/abs/1005.2449v1}, author = {Jeffrey Bub} } @article {1269, title = {Quantum Computing}, journal = {Nature}, volume = {464}, year = {2010}, month = {2010/3/4}, pages = {45 - 53}, abstract = { Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory{\textquoteright}s inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future. }, doi = {10.1038/nature08812}, url = {http://arxiv.org/abs/1009.2267v1}, author = {Thaddeus D. Ladd and Fedor Jelezko and Raymond Laflamme and Yasunobu Nakamura and Christopher Monroe and Jeremy L. O{\textquoteright}Brien} } @article {1315, title = {Quantum probabilities: an information-theoretic interpretation}, year = {2010}, month = {2010/05/14}, abstract = { This Chapter develops a realist information-theoretic interpretation of the nonclassical features of quantum probabilities. On this view, what is fundamental in the transition from classical to quantum physics is the recognition that \emph{information in the physical sense has new structural features}, just as the transition from classical to relativistic physics rests on the recognition that space-time is structurally different than we thought. Hilbert space, the event space of quantum systems, is interpreted as a kinematic (i.e., pre-dynamic) framework for an indeterministic physics, in the sense that the geometric structure of Hilbert space imposes objective probabilistic or information-theoretic constraints on correlations between events, just as the geometric structure of Minkowski space in special relativity imposes spatio-temporal kinematic constraints on events. The interpretation of quantum probabilities is more subjectivist in spirit than other discussions in this book (e.g., the chapter by Timpson), insofar as the quantum state is interpreted as a credence function---a bookkeeping device for keeping track of probabilities---but it is also objective (or intersubjective), insofar as the credences specified by the quantum state are understood as uniquely determined, via Gleason{\textquoteright}s theorem, by objective correlational constraints on events in the nonclassical quantum event space defined by the subspace structure of Hilbert space. }, url = {http://arxiv.org/abs/1005.2448v1}, author = {Jeffrey Bub} } @article {1243, title = {Quantum property testing for bounded-degree graphs}, journal = {Proc. RANDOM}, year = {2010}, month = {2010/12/14}, pages = {365-376}, abstract = { We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion, we also prove an Omega(N^(1/4)) quantum query lower bound, thus ruling out the possibility of an exponential quantum speedup. Our quantum algorithms follow from a combination of classical property testing techniques due to Goldreich and Ron, derandomization, and the quantum algorithm for element distinctness. The quantum lower bound is obtained by the polynomial method, using novel algebraic techniques and combinatorial analysis to accommodate the graph structure. }, doi = {10.1007/978-3-642-22935-0_31}, url = {http://arxiv.org/abs/1012.3174v3}, author = {Andris Ambainis and Andrew M. Childs and Yi-Kai Liu} } @article {1432, title = {Quantum state tomography via compressed sensing}, journal = {Physical Review Letters}, volume = {105}, year = {2010}, month = {2010/10/4}, abstract = { We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rd log^2 d) measurement settings, compared to standard methods that require d^2 settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low-rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed. We present both theoretical bounds and numerical simulations. }, doi = {10.1103/PhysRevLett.105.150401}, url = {http://arxiv.org/abs/0909.3304v4}, author = {David Gross and Yi-Kai Liu and Steven T. Flammia and Stephen Becker and Jens Eisert} } @article {1206, title = {On the relationship between continuous- and discrete-time quantum walk}, journal = {Communications in Mathematical Physics}, volume = {294}, year = {2010}, month = {2009/10/10}, pages = {581 - 603}, abstract = { Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or discrete time. But whereas a continuous-time random walk can be obtained as the limit of a sequence of discrete-time random walks, the two types of quantum walk appear fundamentally different, owing to the need for extra degrees of freedom in the discrete-time case. In this article, I describe a precise correspondence between continuous- and discrete-time quantum walks on arbitrary graphs. Using this correspondence, I show that continuous-time quantum walk can be obtained as an appropriate limit of discrete-time quantum walks. The correspondence also leads to a new technique for simulating Hamiltonian dynamics, giving efficient simulations even in cases where the Hamiltonian is not sparse. The complexity of the simulation is linear in the total evolution time, an improvement over simulations based on high-order approximations of the Lie product formula. As applications, I describe a continuous-time quantum walk algorithm for element distinctness and show how to optimally simulate continuous-time query algorithms of a certain form in the conventional quantum query model. Finally, I discuss limitations of the method for simulating Hamiltonians with negative matrix elements, and present two problems that motivate attempting to circumvent these limitations. }, doi = {10.1007/s00220-009-0930-1}, url = {http://arxiv.org/abs/0810.0312v3}, author = {Andrew M. Childs} } @article {1223, title = {Simulating sparse Hamiltonians with star decompositions}, year = {2010}, month = {2010/03/18}, abstract = { We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts for time t, this algorithm uses (d^2(d+log* N)||Ht||)^{1+o(1)} queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d^4(log* N)||Ht||)^{1+o(1)}. To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces. }, doi = {10.1007/978-3-642-18073-6_8}, url = {http://arxiv.org/abs/1003.3683v2}, author = {Andrew M. Childs and Robin Kothari} } @article {1489, title = {Temperature driven structural phase transition for trapped ions and its experimental detection }, journal = {Physical Review Letters}, volume = {105}, year = {2010}, month = {2010/12/29}, abstract = { A Wigner crystal formed with trapped ion can undergo structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be solely driven by change of the system{\textquoteright}s temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology. }, doi = {10.1103/PhysRevLett.105.265703}, url = {http://arxiv.org/abs/1009.0089v1}, author = {Zhe-Xuan Gong and G. -D. Lin and L. -M. Duan} } @article {1849, title = {Thesis: Novel Systems and Methods for Quantum Communication, Quantum Computation, and Quantum Simulation}, journal = {Harvard University Physics Department}, volume = {Ph.D. Thesis}, year = {2010}, author = {Alexey V. Gorshkov} } @article {1850, title = {Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms}, journal = {Nature Phys.}, volume = {6}, year = {2010}, pages = {289}, url = {http://www.nature.com/nphys/journal/v6/n4/abs/nphys1535.html}, author = {Alexey V. Gorshkov and Hermele, M and Gurarie, V and Xu, C and Julienne, P S and Ye, J and Zoller, P and Demler, E and Lukin, M D and Rey, A M} } @article {1317, title = {Von Neumann{\textquoteright}s {\textquoteright}No Hidden Variables{\textquoteright} Proof: A Re-Appraisal}, journal = {Foundations of Physics}, volume = {40}, year = {2010}, month = {2010/6/11}, pages = {1333 - 1340}, abstract = { Since the analysis by John Bell in 1965, the consensus in the literature is that von Neumann{\textquoteright}s {\textquoteright}no hidden variables{\textquoteright} proof fails to exclude any significant class of hidden variables. Bell raised the question whether it could be shown that any hidden variable theory would have to be nonlocal, and in this sense {\textquoteright}like Bohm{\textquoteright}s theory.{\textquoteright} His seminal result provides a positive answer to the question. I argue that Bell{\textquoteright}s analysis misconstrues von Neumann{\textquoteright}s argument. What von Neumann proved was the impossibility of recovering the quantum probabilities from a hidden variable theory of dispersion free (deterministic) states in which the quantum observables are represented as the {\textquoteright}beables{\textquoteright} of the theory, to use Bell{\textquoteright}s term. That is, the quantum probabilities could not reflect the distribution of pre-measurement values of beables, but would have to be derived in some other way, e.g., as in Bohm{\textquoteright}s theory, where the probabilities are an artefact of a dynamical process that is not in fact a measurement of any beable of the system. }, doi = {10.1007/s10701-010-9480-9}, url = {http://arxiv.org/abs/1006.0499v1}, author = {Jeffrey Bub} } @article {1193, title = {Alkaline-Earth-Metal Atoms as Few-Qubit Quantum Registers}, journal = {Physical Review Letters}, volume = {102}, year = {2009}, month = {2009/3/18}, abstract = { We propose and analyze a novel approach to quantum information processing, in which multiple qubits can be encoded and manipulated using electronic and nuclear degrees of freedom associated with individual alkaline-earth atoms trapped in an optical lattice. Specifically, we describe how the qubits within each register can be individually manipulated and measured with sub-wavelength optical resolution. We also show how such few-qubit registers can be coupled to each other in optical superlattices via conditional tunneling to form a scalable quantum network. Finally, potential applications to quantum computation and precision measurements are discussed. }, doi = {10.1103/PhysRevLett.102.110503}, url = {http://arxiv.org/abs/0812.3660v2}, author = {Alexey V. Gorshkov and Ana Maria Rey and Andrew J. Daley and Martin M. Boyd and Jun Ye and Peter Zoller and Mikhail D. Lukin} } @article {1220, title = {Black-box Hamiltonian simulation and unitary implementation}, year = {2009}, month = {2009/10/22}, abstract = { We present general methods for simulating black-box Hamiltonians using quantum walks. These techniques have two main applications: simulating sparse Hamiltonians and implementing black-box unitary operations. In particular, we give the best known simulation of sparse Hamiltonians with constant precision. Our method has complexity linear in both the sparseness D (the maximum number of nonzero elements in a column) and the evolution time t, whereas previous methods had complexity scaling as D^4 and were superlinear in t. We also consider the task of implementing an arbitrary unitary operation given a black-box description of its matrix elements. Whereas standard methods for performing an explicitly specified N x N unitary operation use O(N^2) elementary gates, we show that a black-box unitary can be performed with bounded error using O(N^{2/3} (log log N)^{4/3}) queries to its matrix elements. In fact, except for pathological cases, it appears that most unitaries can be performed with only O(sqrt{N}) queries, which is optimal. }, url = {http://arxiv.org/abs/0910.4157v4}, author = {Dominic W. Berry and Andrew M. Childs} } @article {1293, title = {Collisional cooling of ultra-cold atom ensembles using Feshbach resonances }, journal = {Physical Review A}, volume = {80}, year = {2009}, month = {2009/9/8}, abstract = { We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon temperatures reached with current technologies. }, doi = {10.1103/PhysRevA.80.030702}, url = {http://arxiv.org/abs/0903.2568v1}, author = {L. Mathey and Eite Tiesinga and Paul S. Julienne and Charles W. Clark} } @article {1324, title = {Contextuality and nonlocality in {\textquoteright}no signaling{\textquoteright} theories}, journal = {Foundations of Physics}, volume = {39}, year = {2009}, month = {2009/4/21}, pages = {690 - 711}, abstract = { We define a family of {\textquoteright}no signaling{\textquoteright} bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the {\textquoteleft}no signaling{\textquoteright} polytope). We show that for certain marginal probabilities a KS-box is classical with respect to nonlocality as measured by the Clauser-Horne-Shimony-Holt correlation, i.e., no better than shared randomness as a resource in simulating a PR-box, even though such KS-boxes cannot be perfectly simulated by classical or quantum resources for all inputs. We comment on the significance of these results for contextuality and nonlocality in {\textquoteright}no signaling{\textquoteright} theories. }, doi = {10.1007/s10701-009-9307-8}, url = {http://arxiv.org/abs/0903.1462v2}, author = {Jeffrey Bub and Allen Stairs} } @article {1299, title = {Counterflow and paired superfluidity in one-dimensional Bose mixtures in optical lattices }, journal = {Physical Review A}, volume = {80}, year = {2009}, month = {2009/8/24}, abstract = { We study the quantum phases of mixtures of ultra-cold bosonic atoms held in an optical lattice that confines motion or hopping to one spatial dimension. The phases are found by using Tomonaga-Luttinger liquid theory as well as the numerical method of time evolving block decimation (TEBD). We consider a binary mixture with repulsive intra-species interactions, and either repulsive or attractive inter-species interaction. For a homogeneous system, we find paired- and counterflow-superfluid phases at different filling and hopping energies. We also predict parameter regions in which these types of superfluid order coexist with charge density wave order. We show that the Tomonaga-Luttinger liquid theory and TEBD qualitatively agree on the location of the phase boundary to superfluidity. We then describe how these phases are modified and can be detected when an additional harmonic trap is present. In particular, we show how experimentally measurable quantities, such as time-of-flight images and the structure factor, can be used to distinguish the quantum phases. Finally, we suggest applying a Feshbach ramp to detect the paired superfluid state, and a $\pi/2$ pulse followed by Bragg spectroscopy to detect the counterflow superfluid phase. }, doi = {10.1103/PhysRevA.80.023619}, url = {http://arxiv.org/abs/0906.2150v1}, author = {Anzi Hu and L. Mathey and Ippei Danshita and Eite Tiesinga and Carl J. Williams and Charles W. Clark} } @article {1254, title = {Discrete-query quantum algorithm for NAND trees}, journal = {Theory of Computing}, volume = {5}, year = {2009}, month = {2009/07/01}, pages = {119 - 123}, abstract = { Recently, Farhi, Goldstone, and Gutmann gave a quantum algorithm for evaluating NAND trees that runs in time O(sqrt(N log N)) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using O(N^{1/2 + epsilon}) queries in the conventional quantum query model, for any fixed epsilon > 0. }, doi = {10.4086/toc.2009.v005a005}, url = {http://arxiv.org/abs/quant-ph/0702160v1}, author = {Andrew M. Childs and Richard Cleve and Stephen P. Jordan and David Yeung} } @article {1386, title = {Efficient quantum circuits for arbitrary sparse unitaries}, journal = {Physical Review A}, volume = {80}, year = {2009}, month = {2009/12/1}, abstract = { Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row or column, and these entries are efficiently computable. One can formulate a model of computation based on the composition of sparse unitaries which includes the quantum Turing machine model, the quantum circuit model, anyonic models, permutational quantum computation, and discrete time quantum walks as special cases. Thus we obtain a simple unified proof that these models are all contained in BQP. Furthermore our general method for implementing sparse unitaries simplifies several existing quantum algorithms. }, doi = {10.1103/PhysRevA.80.062301}, url = {http://arxiv.org/abs/0904.2211v2}, author = {Stephen P. Jordan and Pawel Wocjan} } @article {1400, title = {Efficient quantum processing of ideals in finite rings}, year = {2009}, month = {2009/07/31}, abstract = { Suppose we are given black-box access to a finite ring R, and a list of generators for an ideal I in R. We show how to find an additive basis representation for I in poly(log |R|) time. This generalizes a recent quantum algorithm of Arvind et al. which finds a basis representation for R itself. We then show that our algorithm is a useful primitive allowing quantum computers to rapidly solve a wide variety of problems regarding finite rings. In particular we show how to test whether two ideals are identical, find their intersection, find their quotient, prove whether a given ring element belongs to a given ideal, prove whether a given element is a unit, and if so find its inverse, find the additive and multiplicative identities, compute the order of an ideal, solve linear equations over rings, decide whether an ideal is maximal, find annihilators, and test the injectivity and surjectivity of ring homomorphisms. These problems appear to be hard classically. }, url = {http://arxiv.org/abs/0908.0022v1}, author = {Pawel M. Wocjan and Stephen P. Jordan and Hamed Ahmadi and Joseph P. Brennan} } @article {1511, title = {Entanglement Cost of Nonlocal Measurements}, journal = {Physical Review A}, volume = {80}, year = {2009}, month = {2009/7/15}, abstract = { For certain joint measurements on a pair of spatially separated particles, we ask how much entanglement is needed to carry out the measurement exactly. For a class of orthogonal measurements on two qubits with partially entangled eigenstates, we present upper and lower bounds on the entanglement cost. The upper bound is based on a recent result by D. Berry [Phys. Rev. A 75, 032349 (2007)]. The lower bound, based on the entanglement production capacity of the measurement, implies that for almost all measurements in the class we consider, the entanglement required to perform the measurement is strictly greater than the average entanglement of its eigenstates. On the other hand, we show that for any complete measurement in d x d dimensions that is invariant under all local Pauli operations, the cost of the measurement is exactly equal to the average entanglement of the states associated with the outcomes. }, doi = {10.1103/PhysRevA.80.012313}, url = {http://arxiv.org/abs/0809.2264v4}, author = {Somshubhro Bandyopadhyay and Gilles Brassard and Shelby Kimmel and William K. Wootters} } @article {1384, title = {Estimating Jones and HOMFLY polynomials with One Clean Qubit}, journal = {Quantum Information and Computation}, volume = {9}, year = {2009}, month = {2009/03/01}, pages = {264-289}, abstract = {

The Jones and HOMFLY polynomials are link invariants with close connections to quantum computing. It was recently shown that finding a certain approximation to the Jones polynomial of the trace closure of a braid at the fifth root of unity is a complete problem for the one clean qubit complexity class. This is the class of problems solvable in polynomial time on a quantum computer acting on an initial state in which one qubit is pure and the rest are maximally mixed. Here we generalize this result by showing that one clean qubit computers can efficiently approximate the Jones and single-variable HOMFLY polynomials of the trace closure of a braid at any root of unity.

}, url = {http://dl.acm.org/citation.cfm?id=2011787}, author = {Stephen P. Jordan and Pawel Wocjan} } @article {1466, title = {Geometric-Phase-Effect Tunnel-Splitting Oscillations in Single-Molecule Magnets with Fourth-Order Anisotropy Induced by Orthorhombic Distortion }, journal = {EPL (Europhysics Letters)}, volume = {86}, year = {2009}, month = {2009/04/30}, pages = {27002}, abstract = { We analyze the interference between tunneling paths that occurs for a spin system with both fourth-order and second-order transverse anisotropy. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting is modulated, with zeros occurring periodically. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field. }, doi = {10.1209/0295-5075/86/27002}, url = {http://arxiv.org/abs/0809.2289v2}, author = {Michael Foss-Feig and Jonathan R. Friedman} } @article {1219, title = {Limitations on the simulation of non-sparse Hamiltonians}, year = {2009}, month = {2009/08/31}, abstract = { The problem of simulating sparse Hamiltonians on quantum computers is well studied. The evolution of a sparse N x N Hamiltonian H for time t can be simulated using O(||Ht||poly(log N)) operations, which is essentially optimal due to a no--fast-forwarding theorem. Here, we consider non-sparse Hamiltonians and show significant limitations on their simulation. We generalize the no--fast-forwarding theorem to dense Hamiltonians, ruling out generic simulations taking time o(||Ht||), even though ||H|| is not a unique measure of the size of a dense Hamiltonian $H$. We also present a stronger limitation ruling out the possibility of generic simulations taking time poly(||Ht||,log N), showing that known simulations based on discrete-time quantum walk cannot be dramatically improved in general. On the positive side, we show that some non-sparse Hamiltonians can be simulated efficiently, such as those with graphs of small arboricity. }, url = {http://arxiv.org/abs/0908.4398v2}, author = {Andrew M. Childs and Robin Kothari} } @article {1568, title = {Locality Bounds on Hamiltonians for Stabilizer Codes}, journal = {Quantum Information and Computation}, volume = {9}, year = {2009}, month = {2009/09/22}, abstract = {In this paper, we study the complexity of Hamiltonians whose groundstate is a stabilizer code. We introduce various notions of k-locality of a stabilizer code, inherited from the associated stabilizer group. A choice of generators leads to a Hamiltonian with the code in its groundspace. We establish bounds on the locality of any other Hamiltonian whose groundspace contains such a code, whether or not its Pauli tensor summands commute. Our results provide insight into the cost of creating an energy gap for passive error correction and for adiabatic quantum computing. The results simplify in the cases of XZ-split codes such as Calderbank-Shor-Steane stabilizer codes and topologically-ordered stabilizer codes arising from surface cellulations. }, url = {http://www.cs.umd.edu/~oleary/reprints/j91.pdf}, author = {Stephen S. Bullock and Dianne P. O{\textquoteright}Leary} } @article {1851, title = {Many-Body Treatment of the Collisional Frequency Shift in Fermionic Atoms}, journal = {Phys. Rev. Lett.}, volume = {103}, year = {2009}, pages = {260402}, url = {http://link.aps.org/abstract/PRL/v103/e260402/}, author = {Rey, A M and Alexey V. Gorshkov and Rubbo, C} } @article {1280, title = {Multi-channel modelling of the formation of vibrationally cold polar KRb molecules }, journal = {New Journal of Physics}, volume = {11}, year = {2009}, month = {2009/05/14}, pages = {055043}, abstract = { We describe the theoretical advances that influenced the experimental creation of vibrationally and translationally cold polar $^{40}$K$^{87}$Rb molecules \cite{nphys08,science08}. Cold molecules were created from very-weakly bound molecules formed by magnetic field sweeps near a Feshbach resonance in collisions of ultra-cold $^{40}$K and $^{87}$Rb atoms. Our analysis include the multi-channel bound-state calculations of the hyperfine and Zeeman mixed X$^1\Sigma^+$ and a$^3\Sigma^+$ vibrational levels. We find excellent agreement with the hyperfine structure observed in experimental data. In addition, we studied the spin-orbit mixing in the intermediate state of the Raman transition. This allowed us to investigate its effect on the vibrationally-averaged transition dipole moment to the lowest ro-vibrational level of the X$^1\Sigma^+$ state. Finally, we obtained an estimate of the polarizability of the initial and final ro-vibrational states of the Raman transition near frequencies relevant for optical trapping of the molecules. }, doi = {10.1088/1367-2630/11/5/055043}, url = {http://arxiv.org/abs/0901.1486v1}, author = {Svetlana Kotochigova and Eite Tiesinga and Paul S. Julienne} } @article {1298, title = {Number Fluctuations and Energy Dissipation in Sodium Spinor Condensates}, journal = {Physical Review Letters}, volume = {102}, year = {2009}, month = {2009/6/5}, abstract = { We characterize fluctuations in atom number and spin populations in F=1 sodium spinor condensates. We find that the fluctuations enable a quantitative measure of energy dissipation in the condensate. The time evolution of the population fluctuations shows a maximum. We interpret this as evidence of a dissipation-driven separatrix crossing in phase space. For a given initial state, the critical time to the separatrix crossing is found to depend exponentially on the magnetic field and linearly on condensate density. This crossing is confirmed by tracking the energy of the spinor condensate as well as by Faraday rotation spectroscopy. We also introduce a phenomenological model that describes the observed dissipation with a single coefficient. }, doi = {10.1103/PhysRevLett.102.225301}, url = {http://arxiv.org/abs/0906.2110v1}, author = {Yingmei Liu and Eduardo Gomez and Stephen E. Maxwell and Lincoln D. Turner and Eite Tiesinga and Paul D. Lett} } @article {1285, title = {Prediction of Feshbach resonances from three input parameters}, journal = {Physical Review A}, volume = {79}, year = {2009}, month = {2009/4/30}, abstract = { We have developed a model of Feshbach resonances in gases of ultracold alkali metal atoms using the ideas of multichannel quantum defect theory. Our model requires just three parameters describing the interactions - the singlet and triplet scattering lengths, and the long range van der Waals coefficient - in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to $^{6}$Li--$^{40}$K and $^{40}$K--$^{87}$Rb scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique. }, doi = {10.1103/PhysRevA.79.040701}, url = {http://arxiv.org/abs/0903.0884v2}, author = {Thomas M. Hanna and Eite Tiesinga and Paul S. Julienne} } @article {1267, title = {Protocol for Hybrid Entanglement Between a Trapped Atom and a Semiconductor Quantum Dot }, journal = {Physical Review A}, volume = {80}, year = {2009}, month = {2009/12/30}, abstract = { We propose a quantum optical interface between an atomic and solid state system. We show that quantum states in a single trapped atom can be entangled with the states of a semiconductor quantum dot through their common interaction with a classical laser field. The interference and detection of the resulting scattered photons can then herald the entanglement of the disparate atomic and solid-state quantum bits. We develop a protocol that can succeed despite a significant mismatch in the radiative characteristics of the two matter-based qubits. We study in detail a particular case of this interface applied to a single trapped \Yb ion and a cavity-coupled InGaAs semiconductor quantum dot. Entanglement fidelity and success rates are found to be robust to a broad range of experimental nonideal effects such as dispersion mismatch, atom recoil, and multi-photon scattering. We conclude that it should be possible to produce highly entangled states of these complementary qubit systems under realistic experimental conditions. }, doi = {10.1103/PhysRevA.80.062330}, url = {http://arxiv.org/abs/0907.0444v1}, author = {Edo Waks and Christopher Monroe} } @article {1370, title = {Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing }, journal = {Physical Review A}, volume = {79}, year = {2009}, month = {2009/3/24}, abstract = { Polynomially-large ground-state energy gaps are rare in many-body quantum systems, but useful for adiabatic quantum computing. We show analytically that the gap is generically polynomially-large for quadratic fermionic Hamiltonians. We then prove that adiabatic quantum computing can realize the ground states of Hamiltonians with certain random interactions, as well as the ground states of one, two, and three-dimensional fermionic interaction lattices, in polynomial time. Finally, we use the Jordan-Wigner transformation and a related transformation for spin-3/2 particles to show that our results can be restated using spin operators in a surprisingly simple manner. A direct consequence is that the one-dimensional cluster state can be found in polynomial time using adiabatic quantum computing. }, doi = {10.1103/PhysRevA.79.032331}, url = {http://arxiv.org/abs/0808.1768v1}, author = {Michael J. O{\textquoteright}Hara and Dianne P. O{\textquoteright}Leary} } @article {1425, title = {Quantum Algorithms Using the Curvelet Transform}, journal = {Proc. ACM Symposium on Theory of Computing (STOC)}, year = {2009}, month = {2009/10/28}, pages = {391-400}, abstract = { The curvelet transform is a directional wavelet transform over R^n, which is used to analyze functions that have singularities along smooth surfaces (Candes and Donoho, 2002). I demonstrate how this can lead to new quantum algorithms. I give an efficient implementation of a quantum curvelet transform, together with two applications: a single-shot measurement procedure for approximately finding the center of a ball in R^n, given a quantum-sample over the ball; and, a quantum algorithm for finding the center of a radial function over R^n, given oracle access to the function. I conjecture that these algorithms succeed with constant probability, using one quantum-sample and O(1) oracle queries, respectively, independent of the dimension n -- this can be interpreted as a quantum speed-up. To support this conjecture, I prove rigorous bounds on the distribution of probability mass for the continuous curvelet transform. This shows that the above algorithms work in an idealized "continuous" model. }, url = {http://arxiv.org/abs/0810.4968v2}, author = {Yi-Kai Liu} } @article {1302, title = {Quantum Phase Transitions and Continuous Observation of Spinor Dynamics in an Antiferromagnetic Condensate }, journal = {Physical Review Letters}, volume = {102}, year = {2009}, month = {2009/3/23}, abstract = { Condensates of spin-1 sodium display rich spin dynamics due to the antiferromagnetic nature of the interactions in this system. We use Faraday rotation spectroscopy to make a continuous and minimally destructive measurement of the dynamics over multiple spin oscillations on a single evolving condensate. This method provides a sharp signature to locate a magnetically tuned separatrix in phase space which depends on the net magnetization. We also observe a phase transition from a two- to a three-component condensate at a low but finite temperature using a Stern-Gerlach imaging technique. This transition should be preserved as a zero-temperature quantum phase transition. }, doi = {10.1103/PhysRevLett.102.125301}, url = {http://arxiv.org/abs/0902.3189v1}, author = {Yingmei Liu and Sebastian Jung and Stephen E. Maxwell and Lincoln D. Turner and Eite Tiesinga and Paul. D. Lett} } @article {1256, title = {The quantum query complexity of certification}, year = {2009}, month = {2009/03/06}, abstract = { We study the quantum query complexity of finding a certificate for a d-regular, k-level balanced NAND formula. Up to logarithmic factors, we show that the query complexity is Theta(d^{(k+1)/2}) for 0-certificates, and Theta(d^{k/2}) for 1-certificates. In particular, this shows that the zero-error quantum query complexity of evaluating such formulas is O(d^{(k+1)/2}) (again neglecting a logarithmic factor). Our lower bound relies on the fact that the quantum adversary method obeys a direct sum theorem. }, url = {http://arxiv.org/abs/0903.1291v2}, author = {Andris Ambainis and Andrew M. Childs and Fran{\c c}ois Le Gall and Seiichiro Tani} } @article {1195, title = {Realization of Coherent Optically Dense Media via Buffer-Gas Cooling}, journal = {Physical Review A}, volume = {79}, year = {2009}, month = {2009/1/6}, abstract = { We demonstrate that buffer-gas cooling combined with laser ablation can be used to create coherent optical media with high optical depth and low Doppler broadening that offers metastable states with low collisional and motional decoherence. Demonstration of this generic technique opens pathways to coherent optics with a large variety of atoms and molecules. We use helium buffer gas to cool 87Rb atoms to below 7 K and slow atom diffusion to the walls. Electromagnetically induced transparency (EIT) in this medium allows for 50\% transmission in a medium with initial OD >70 and for slow pulse propagation with large delay-bandwidth products. In the high-OD regime, we observe high-contrast spectrum oscillations due to efficient four-wave mixing. }, doi = {10.1103/PhysRevA.79.013806}, url = {http://arxiv.org/abs/0805.1416v2}, author = {Tao Hong and Alexey V. Gorshkov and David Patterson and Alexander S. Zibrov and John M. Doyle and Mikhail D. Lukin and Mara G. Prentiss} } @article {1852, title = {Slow light propagation and amplification via electromagnetically induced transparency and four-wave mixing in an optically dense atomic vapor}, journal = {J. Mod. Opt.}, volume = {56}, year = {2009}, pages = {1916}, url = {http://www.informaworld.com/smpp/content~db=all~content=a913545405}, author = {Phillips, N B and Alexey V. Gorshkov and Novikova, I} } @article {1205, title = {Universal computation by quantum walk}, journal = {Physical Review Letters}, volume = {102}, year = {2009}, month = {2009/5/4}, abstract = { In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is restricted to be a sparse matrix with all entries equal to 0 or 1, i.e., the adjacency matrix of a low-degree graph. Thus quantum walk can be regarded as a universal computational primitive, with any desired quantum computation encoded entirely in some underlying graph. The main idea of the construction is to implement quantum gates by scattering processes. }, doi = {10.1103/PhysRevLett.102.180501}, url = {http://arxiv.org/abs/0806.1972v1}, author = {Andrew M. Childs} } @article {1368, title = {The adiabatic theorem in the presence of noise}, journal = {Physical Review A}, volume = {77}, year = {2008}, month = {2008/4/22}, abstract = { We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian, coupling to low-energy quantum systems, and decoherent time-dependent perturbations in the Hamiltonian. For decoherent perturbations, we find both upper and lower bounds on the evolution time to guarantee the adiabatic approximation performs within a prescribed tolerance. Our new results include explicit definitions of constants, and we apply them to the spin-1/2 particle in a rotating magnetic field, and to the superconducting flux qubit. We compare the theoretical bounds on the superconducting flux qubit to simulation results. }, doi = {10.1103/PhysRevA.77.042319}, url = {http://arxiv.org/abs/0801.3872v1}, author = {Michael J. O{\textquoteright}Hara and Dianne P. O{\textquoteright}Leary} } @article {1438, title = {Ancilla-Assisted Discrimination of Quantum Gates}, year = {2008}, month = {2008/09/02}, abstract = { The intrinsic idea of superdense coding is to find as many gates as possible such that they can be perfectly discriminated. In this paper, we consider a new scheme of discrimination of quantum gates, called ancilla-assisted discrimination, in which a set of quantum gates on a $d-$dimensional system are perfectly discriminated with assistance from an $r-$dimensional ancilla system. The main contribution of the present paper is two-fold: (1) The number of quantum gates that can be discriminated in this scheme is evaluated. We prove that any $rd+1$ quantum gates cannot be perfectly discriminated with assistance from the ancilla, and there exist $rd$ quantum gates which can be perfectly discriminated with assistance from the ancilla. (2) The dimensionality of the minimal ancilla system is estimated. We prove that there exists a constant positive number $c$ such that for any $k\leq cr$ quantum gates, if they are $d$-assisted discriminable, then they are also $r$-assisted discriminable, and there are $c^{\prime}r\textrm{}(c^{\prime}>c)$ different quantum gates which can be discriminated with a $d-$dimensional ancilla, but they cannot be discriminated if the ancilla is reduced to an $r-$dimensional system. Thus, the order $O(r)$ of the number of quantum gates that can be discriminated with assistance from an $r-$dimensional ancilla is optimal. The results reported in this paper represent a preliminary step toward understanding the role ancilla system plays in discrimination of quantum gates as well as the power and limit of superdense coding. }, url = {http://arxiv.org/abs/0809.0336v1}, author = {Jianxin Chen and Mingsheng Ying} } @article {1192, title = {Anyonic interferometry and protected memories in atomic spin lattices}, journal = {Nature Physics}, volume = {4}, year = {2008}, month = {2008/4/20}, pages = {482 - 488}, abstract = { Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations. }, doi = {10.1038/nphys943}, url = {http://arxiv.org/abs/0711.1365v1}, author = {Liang Jiang and Gavin K. Brennen and Alexey V. Gorshkov and Klemens Hammerer and Mohammad Hafezi and Eugene Demler and Mikhail D. Lukin and Peter Zoller} } @article {1283, title = {Avoided crossings between bound states of ultracold Cesium dimers}, journal = {Physical Review A}, volume = {78}, year = {2008}, month = {2008/11/5}, abstract = { We present an efficient new computational method for calculating the binding energies of the bound states of ultracold alkali-metal dimers in the presence of magnetic fields. The method is based on propagation of coupled differential equations and does not use a basis set for the interatomic distance coordinate. It is much more efficient than the previous method based on a radial basis set and allows many more spin channels to be included. This is particularly important in the vicinity of avoided crossings between bound states. We characterize a number of different avoided crossings in Cs_2 and compare our converged calculations with experimental results. Small but significant discrepancies are observed in both crossing strengths and level positions, especially for levels with l symmetry (rotational angular momentum L=8). The discrepancies should allow the development of improved potential models in the future. }, doi = {10.1103/PhysRevA.78.052703}, url = {http://arxiv.org/abs/0806.2583v1}, author = {Jeremy M. Hutson and Eite Tiesinga and Paul S. Julienne} } @article {1355, title = {Coherence of an optically illuminated single nuclear spin qubit}, journal = {Physical Review Letters}, volume = {100}, year = {2008}, month = {2008/2/19}, abstract = {We investigate the coherence properties of individual nuclear spin quantum bits in diamond [Dutt et al., Science, 316, 1312 (2007)] when a proximal electronic spin associated with a nitrogen-vacancy (NV) center is being interrogated by optical radiation. The resulting nuclear spin dynamics are governed by time-dependent hyperfine interaction associated with rapid electronic transitions, which can be described by a spin-fluctuator model. We show that due to a process analogous to motional averaging in nuclear magnetic resonance, the nuclear spin coherence can be preserved after a large number of optical excitation cycles. Our theoretical analysis is in good agreement with experimental results. It indicates a novel approach that could potentially isolate the nuclear spin system completely from the electronic environment. }, doi = {10.1103/PhysRevLett.100.073001}, url = {http://arxiv.org/abs/0707.1341v2}, author = {Liang Jiang and M. V. Gurudev Dutt and Emre Togan and Lily Childress and Paola Cappellaro and J. M. Taylor and Mikhail D. Lukin} } @article {1173, title = {Coherent Quantum Optical Control with Subwavelength Resolution}, journal = {Physical Review Letters}, volume = {100}, year = {2008}, month = {2008/3/7}, abstract = { We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed. }, doi = {10.1103/PhysRevLett.100.093005}, url = {http://arxiv.org/abs/0706.3879v2}, author = {Alexey V. Gorshkov and Liang Jiang and Markus Greiner and Peter Zoller and Mikhail D. Lukin} } @article {1483, title = {Efficient scheme for one-way quantum computing in thermal cavities}, journal = {International Journal of Theoretical Physics}, volume = {47}, year = {2008}, month = {2008/4/12}, pages = {2997 - 3004}, abstract = { We propose a practical scheme for one-way quantum computing based on efficient generation of 2D cluster state in thermal cavities. We achieve a controlled-phase gate that is neither sensitive to cavity decay nor to thermal field by adding a strong classical field to the two-level atoms. We show that a 2D cluster state can be generated directly by making every two atoms collide in an array of cavities, with numerically calculated parameters and appropriate operation sequence that can be easily achieved in practical Cavity QED experiments. Based on a generated cluster state in Box$^{(4)}$ configuration, we then implement Grover{\textquoteright}s search algorithm for four database elements in a very simple way as an example of one-way quantum computing. }, doi = {10.1007/s10773-008-9734-x}, url = {http://arxiv.org/abs/0704.2297v1}, author = {Wen-Xing Yang and Zhe-Xuan Gong} } @article {1382, title = {Estimating Jones polynomials is a complete problem for one clean qubit}, journal = {Quantum Information \& Computation}, volume = {8}, year = {2008}, month = {2008/09/01}, pages = {681-714}, abstract = {

It is known that evaluating a certain approximation to the Jones polynomial for the plat closure of a braid is a BQP-complete problem. That is, this problem exactly captures the power of the quantum circuit model. The one clean qubit model is a model of quantum computation in which all but one qubit starts in the maximally mixed state. One clean qubit computers are believed to be strictly weaker than standard quantum computers, but still capable of solving some classically intractable problems. Here we show that evaluating a certain approximation to the Jones polynomial at a fifth root of unity for the trace closure of a braid is a complete problem for the one clean qubit complexity class. That is, a one clean qubit computer can approximate these Jones polynomials in time polynomial in both the number of strands and number of crossings, and the problem of simulating a one clean qubit computer is reducible to approximating the Jones polynomial of the trace closure of a braid.

}, url = {http://dl.acm.org/citation.cfm?id=2017011.2017012}, author = {Peter W. Shor and Stephen P. Jordan} } @article {1453, title = {Existence of Universal Entangler}, journal = {Journal of Mathematical Physics}, volume = {49}, year = {2008}, month = {2008/01/01}, pages = {012103}, abstract = { A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open. }, doi = {10.1063/1.2829895}, url = {http://arxiv.org/abs/0704.1473v2}, author = {Jianxin Chen and Runyao Duan and Zhengfeng Ji and Mingsheng Ying and Jun Yu} } @article {1379, title = {Fast quantum algorithms for approximating some irreducible representations of groups }, year = {2008}, month = {2008/11/04}, abstract = { We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this problem. Furthermore, quantum Schur transforms yield efficient solutions for certain irreducible representations of the unitary group. Beyond this, we obtain poly(n)-time quantum algorithms for approximating matrix elements from all the irreducible representations of the alternating group A_n, and all the irreducible representations of polynomial highest weight of U(n), SU(n), and SO(n). These quantum algorithms offer exponential speedup in worst case complexity over the fastest known classical algorithms. On the other hand, we show that average case instances are classically easy, and that the techniques analyzed here do not offer a speedup over classical computation for the estimation of group characters. }, url = {http://arxiv.org/abs/0811.0562v2}, author = {Stephen P. Jordan} } @article {1354, title = {High-sensitivity diamond magnetometer with nanoscale resolution}, journal = {Nature Physics}, volume = {4}, year = {2008}, month = {2008/9/14}, pages = {810 - 816}, abstract = {We present a novel approach to the detection of weak magnetic fields that takes advantage of recently developed techniques for the coherent control of solid-state electron spin quantum bits. Specifically, we investigate a magnetic sensor based on Nitrogen-Vacancy centers in room-temperature diamond. We discuss two important applications of this technique: a nanoscale magnetometer that could potentially detect precession of single nuclear spins and an optical magnetic field imager combining spatial resolution ranging from micrometers to millimeters with a sensitivity approaching few femtotesla/Hz$^{1/2}$. }, doi = {10.1038/nphys1075}, url = {http://arxiv.org/abs/0805.1367v1}, author = {J. M. Taylor and P. Cappellaro and L. Childress and L. Jiang and D. Budker and P. R. Hemmer and A. Yacoby and R. Walsworth and M. D. Lukin} } @article {1305, title = {Multilevel effects in the Rabi oscillations of a Josephson phase qubit}, journal = {Physical Review B}, volume = {78}, year = {2008}, month = {2008/9/15}, abstract = { We present Rabi oscillation measurements of a Nb/AlOx/Nb dc superconducting quantum interference device (SQUID) phase qubit with a 100 um^2 area junction acquired over a range of microwave drive power and frequency detuning. Given the slightly anharmonic level structure of the device, several excited states play an important role in the qubit dynamics, particularly at high power. To investigate the effects of these levels, multiphoton Rabi oscillations were monitored by measuring the tunneling escape rate of the device to the voltage state, which is particularly sensitive to excited state population. We compare the observed oscillation frequencies with a simplified model constructed from the full phase qubit Hamiltonian and also compare time-dependent escape rate measurements with a more complete density-matrix simulation. Good quantitative agreement is found between the data and simulations, allowing us to identify a shift in resonance (analogous to the ac Stark effect), a suppression of the Rabi frequency, and leakage to the higher excited states. }, doi = {10.1103/PhysRevB.78.104510}, url = {http://arxiv.org/abs/0806.4711v2}, author = {S. K. Dutta and Frederick W. Strauch and R. M. Lewis and Kaushik Mitra and Hanhee Paik and T. A. Palomaki and Eite Tiesinga and J. R. Anderson and Alex J. Dragt and C. J. Lobb and F. C. Wellstood} } @article {1164, title = {Optimal light storage in atomic vapor}, journal = {Physical Review A}, volume = {78}, year = {2008}, month = {2008/8/1}, abstract = { We study procedures for the optimization of efficiency of light storage and retrieval based on the dynamic form of electromagnetically induced transparency (EIT) in warm Rb vapor. We present a detailed analysis of two recently demonstrated optimization protocols: a time-reversal-based iteration procedure, which finds the optimal input signal pulse shape for any given control field, and a procedure based on the calculation of an optimal control field for any given signal pulse shape. We verify that the two procedures are consistent with each other, and that they both independently achieve the maximum memory efficiency for any given optical depth. We observe good agreement with theoretical predictions for moderate optical depths (<25), while at higher optical depths the experimental efficiency falls below the theoretically predicted values. We identify possible effects responsible for this reduction in memory efficiency. }, doi = {10.1103/PhysRevA.78.023801}, url = {http://arxiv.org/abs/0805.3348v1}, author = {Nathaniel B. Phillips and Alexey V. Gorshkov and Irina Novikova} } @article {1163, title = {Optimal light storage with full pulse shape control}, journal = {Physical Review A}, volume = {78}, year = {2008}, month = {2008/8/20}, abstract = { We experimentally demonstrate optimal storage and retrieval of light pulses of arbitrary shape in atomic ensembles. By shaping auxiliary control pulses, we attain efficiencies approaching the fundamental limit and achieve precise retrieval into any predetermined temporal profile. Our techniques, demonstrated in warm Rb vapor, are applicable to a wide range of systems and protocols. As an example, we present their potential application to the creation of optical time-bin qubits and to controlled partial retrieval. }, doi = {10.1103/PhysRevA.78.021802}, url = {http://arxiv.org/abs/0805.1927v1}, author = {Irina Novikova and Nathaniel B. Phillips and Alexey V. Gorshkov} } @article {1853, title = {Optimal light storage with full pulse-shape control}, journal = {Phys. Rev. A}, volume = {78}, year = {2008}, pages = {021802(R)}, url = {http://link.aps.org/abstract/PRA/v78/e021802/}, author = {Novikova, I and Phillips, N B and Alexey V. Gorshkov} } @article {1854, title = {Optimizing Slow and Stored Light for Multidisciplinary Applications}, journal = {Proc. SPIE}, volume = {6904}, year = {2008}, pages = {69040C}, url = {http://spie.org/x648.xml?product_id=772216\&Search_Origin=QuickSearch\&Search_Results_URL=http://spie.org/x1636.xml\&Alternate_URL=http://spie.org/x18509.xml\&Alternate_URL_Name=timeframe\&Alternate_URL_Value=Exhibitors\&UseJavascript=1\&Please_Wait_URL=http://s}, author = {Klein, M and Xiao, Y and Alexey V. Gorshkov and M Hohensee and C D Leung and M R Browning and Phillips, D F and Novikova, I and Walsworth, R L} } @article {1383, title = {Perturbative Gadgets at Arbitrary Orders}, journal = {Physical Review A}, volume = {77}, year = {2008}, month = {2008/6/19}, abstract = { Adiabatic quantum algorithms are often most easily formulated using many-body interactions. However, experimentally available interactions are generally two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which arbitrary three-body effective interactions can be obtained using Hamiltonians consisting only of two-body interactions. These three-body effective interactions arise from the third order in perturbation theory. Since their introduction, perturbative gadgets have become a standard tool in the theory of quantum computation. Here we construct generalized gadgets so that one can directly obtain arbitrary k-body effective interactions from two-body Hamiltonians. These effective interactions arise from the kth order in perturbation theory. }, doi = {10.1103/PhysRevA.77.062329}, url = {http://arxiv.org/abs/0802.1874v4}, author = {Stephen P. Jordan and Edward Farhi} } @article {1169, title = {Photon storage in Lambda-type optically dense atomic media. IV. Optimal control using gradient ascent }, journal = {Physical Review A}, volume = {77}, year = {2008}, month = {2008/4/4}, abstract = { We use the numerical gradient ascent method from optimal control theory to extend efficient photon storage in Lambda-type media to previously inaccessible regimes and to provide simple intuitive explanations for our optimization techniques. In particular, by using gradient ascent to shape classical control pulses used to mediate photon storage, we open up the possibility of high efficiency photon storage in the non-adiabatic limit, in which analytical solutions to the equations of motion do not exist. This control shaping technique enables an order-of-magnitude increase in the bandwidth of the memory. We also demonstrate that the often discussed connection between time reversal and optimality in photon storage follows naturally from gradient ascent. Finally, we discuss the optimization of controlled reversible inhomogeneous broadening. }, doi = {10.1103/PhysRevA.77.043806}, url = {http://arxiv.org/abs/0710.2698v2}, author = {Alexey V. Gorshkov and Tommaso Calarco and Mikhail D. Lukin and Anders S. Sorensen} } @article {1399, title = {Polynomial-time quantum algorithm for the simulation of chemical dynamics }, journal = {Proceedings of the National Academy of Sciences}, volume = {105}, year = {2008}, month = {2008/11/24}, pages = {18681 - 18686}, abstract = { The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and inter-electronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born-Oppenheimer approximation, but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wavefunction is propagated on a grid with appropriately short timesteps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as state-to-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with one hundred qubits. }, doi = {10.1073/pnas.0808245105}, url = {http://arxiv.org/abs/0801.2986v3}, author = {Ivan Kassal and Stephen P. Jordan and Peter J. Love and Masoud Mohseni and Al{\'a}n Aspuru-Guzik} } @article {1465, title = {The Power of Unentanglement}, year = {2008}, month = {2008/04/04}, abstract = { The class QMA(k), introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give any evidence that k quantum proofs are more powerful than one? Does QMA(k)=QMA(2) for k>=2? Can QMA(k) protocols be amplified to exponentially small error? In this paper, we make progress on all of the above questions. First, we give a protocol by which a verifier can be convinced that a 3SAT formula of size n is satisfiable, with constant soundness, given ~O(sqrt(n)) unentangled quantum witnesses with O(log n) qubits each. Our protocol relies on the existence of very short PCPs. Second, we show that assuming a weak version of the Additivity Conjecture from quantum information theory, any QMA(2) protocol can be amplified to exponentially small error, and QMA(k)=QMA(2) for all k>=2. Third, we prove the nonexistence of "perfect disentanglers" for simulating multiple Merlins with one. }, url = {http://arxiv.org/abs/0804.0802v2}, author = {Scott Aaronson and Salman Beigi and Andrew Drucker and Bill Fefferman and Peter Shor} } @article {1300, title = {Quantum behavior of the dc SQUID phase qubit}, journal = {Physical Review B}, volume = {77}, year = {2008}, month = {2008/6/13}, abstract = { We analyze the behavior of a dc Superconducting Quantum Interference Device (SQUID) phase qubit in which one junction acts as a phase qubit and the rest of the device provides isolation from dissipation and noise in the bias leads. Ignoring dissipation, we find the two-dimensional Hamiltonian of the system and use numerical methods and a cubic approximation to solve Schrodinger{\textquoteright}s equation for the eigenstates, energy levels, tunneling rates, and expectation value of the currents in the junctions. Using these results, we investigate how well this design provides isolation while preserving the characteristics of a phase qubit. In addition, we show that the expectation value of current flowing through the isolation junction depends on the state of the qubit and can be used for non-destructive read out of the qubit state. }, doi = {10.1103/PhysRevB.77.214512}, url = {http://arxiv.org/abs/0805.3680v1}, author = {Kaushik Mitra and F. W. Strauch and C. J. Lobb and J. R. Anderson and F. C. Wellstood and Eite Tiesinga} } @article {1378, title = {Quantum Computation Beyond the Circuit Model}, year = {2008}, month = {2008/09/13}, abstract = { The quantum circuit model is the most widely used model of quantum computation. It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers. However, several other models of quantum computation exist which provide useful alternative frameworks for both discovering new quantum algorithms and devising new physical implementations of quantum computers. In this thesis, I first present necessary background material for a general physics audience and discuss existing models of quantum computation. Then, I present three results relating to various models of quantum computation: a scheme for improving the intrinsic fault tolerance of adiabatic quantum computers using quantum error detecting codes, a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity class, and a generalization of perturbative gadgets which allows k-body interactions to be directly simulated using 2-body interactions. Lastly, I discuss general principles regarding quantum computation that I learned in the course of my research, and using these principles I propose directions for future research. }, url = {http://arxiv.org/abs/0809.2307v1}, author = {Stephen P. Jordan} } @article {1855, title = {Suppression of Inelastic Collisions Between Polar Molecules With a Repulsive Shield}, journal = {Phys. Rev. Lett.}, volume = {101}, year = {2008}, pages = {073201}, url = {http://link.aps.org/abstract/PRL/v101/e073201/}, author = {Alexey V. Gorshkov and Rabl, P and Pupillo, G and Micheli, A and Zoller, P and Lukin, M D and B{\"u}chler, H P} } @article {1404, title = {Theoretical analysis of perfect quantum state transfer with superconducting qubits }, journal = {Physical Review B}, volume = {78}, year = {2008}, month = {2008/9/24}, abstract = { Superconducting quantum circuits, fabricated with multiple layers, are proposed to implement perfect quantum state transfer between nodes of a hypercube network. For tunable devices such as the phase qubit, each node can transmit quantum information to any other node at a constant rate independent of the distance between qubits. The physical limits of quantum state transfer in this network are theoretically analyzed, including the effects of disorder, decoherence, and higher-order couplings. }, doi = {10.1103/PhysRevB.78.094516}, url = {http://arxiv.org/abs/0708.0577v3}, author = {Frederick W. Strauch and Carl J. Williams} } @article {1292, title = {Tunneling phase gate for neutral atoms in a double-well lattice}, journal = {Physical Review A}, volume = {77}, year = {2008}, month = {2008/5/12}, abstract = { We propose a new two--qubit phase gate for ultra--cold atoms confined in an experimentally realized tilted double--well optical lattice [Sebby--Strabley et al., Phys. Rev. A {\bf 73} 033605 (2006)]. Such a lattice is capable of confining pairs of atoms in a two--dimensional array of double--well potentials where control can be exercised over the barrier height and the energy difference of the minima of the two wells (known as the {\textquoteleft}{\textquoteleft}tilt{\textquoteright}{\textquoteright}). The four lowest single--particle motional states consist of two pairs of motional states in which each pair is localized on one side of the central barrier, allowing for two atoms confined in such a lattice to be spatially separated qubits. We present a time--dependent scheme to manipulate the tilt to induce tunneling oscillations which produce a collisional phase gate. Numerical simulations demonstrate that this gate can be performed with high fidelity. }, doi = {10.1103/PhysRevA.77.050304}, url = {http://arxiv.org/abs/0712.1856v1}, author = {Frederick W. Strauch and Mark Edwards and Eite Tiesinga and Carl J. Williams and Charles W. Clark} } @article {1276, title = {Two-body transients in coupled atomic-molecular BECs}, journal = {Physical Review Letters}, volume = {100}, year = {2008}, month = {2008/3/3}, abstract = { We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of atoms are converted into molecules by single-color photoassociation. Three main regimes are found and it is shown that they can be understood on the basis of time-dependent two-body theory. In particular, the so-called rogue dissociation regime [Phys. Rev. Lett., 88, 090403 (2002)], which has a density-dependent limit on the photoassociation rate, is identified with a transient regime of the two-atom dynamics exhibiting universal properties. Finally, we illustrate how these regimes could be explored by photoassociating condensates of alkaline-earth atoms. }, doi = {10.1103/PhysRevLett.100.093001}, url = {http://arxiv.org/abs/0707.2963v2}, author = {Pascal Naidon and Eite Tiesinga and Paul S. Julienne} } @article {2615, title = {Uncertainty principles for compact groups}, journal = {Illinois J. Math. }, volume = {52}, year = {2008}, pages = {1315-1324}, abstract = {

We establish an uncertainty principle over arbitrary compact groups, generalizing several previous results. Specifically, we show that if P and R are operators on L2(G) such that P commutes with projection onto every measurable subset of G and R commutes with left-multiplication by elements of G, then ||PR||\≤||P\⋅χG||2||R||2, where χG:g↦1 is the characteristic function of G. As a consequence, we show that every nonzero function f in L2(G) satisfies μ(suppf)\⋅\∑ρ\∈G^dρrankf^(ρ)\≥1.

}, doi = {doi:10.1215/ijm/1258554365}, url = {http://projecteuclid.org/euclid.ijm/1258554365}, author = {Gorjan Alagic and Alexander Russell} } @article {1357, title = {Wigner crystals of ions as quantum hard drives}, journal = {Physical Review A}, volume = {78}, year = {2008}, month = {2008/12/18}, abstract = {Atomic systems in regular lattices are intriguing systems for implementing ideas in quantum simulation and information processing. Focusing on laser cooled ions forming Wigner crystals in Penning traps, we find a robust and simple approach to engineering non-trivial 2-body interactions sufficient for universal quantum computation. We then consider extensions of our approach to the fast generation of large cluster states, and a non-local architecture using an asymmetric entanglement generation procedure between a Penning trap system and well-established linear Paul trap designs. }, doi = {10.1103/PhysRevA.78.062331}, url = {http://arxiv.org/abs/0706.1951v1}, author = {J. M. Taylor and T. Calarco} } @article {1277, title = {Coherent, adiabatic and dissociation regimes in coupled atomic-molecular Bose-Einstein condensates }, year = {2007}, month = {2007/11/02}, abstract = { We discuss the dynamics of a Bose-Einstein condensate of atoms which is suddenly coupled to a condensate of molecules by an optical or magnetic Feshbach resonance. Three limiting regimes are found and can be understood from the transient dynamics occuring for each pair of atoms. This transient dynamics can be summarised into a time-dependent shift and broadening of the molecular state. A simple Gross-Pitaevskii picture including this shift and broadening is proposed to describe the system in the three regimes. Finally, we suggest how to explore these regimes experimentally. }, url = {http://arxiv.org/abs/0711.0397v2}, author = {Pascal Naidon and Eite Tiesinga and Paul S. Julienne} } @article {1424, title = {The Complexity of the Consistency and N-representability Problems for Quantum States}, year = {2007}, month = {2007/12/18}, type = {PhD Thesis, Univ. of California, San Diego}, abstract = { QMA (Quantum Merlin-Arthur) is the quantum analogue of the class NP. There are a few QMA-complete problems, most notably the {\textquoteleft}{\textquoteleft}Local Hamiltonian{\textquoteright}{\textquoteright} problem introduced by Kitaev. In this dissertation we show some new QMA-complete problems. The first one is {\textquoteleft}{\textquoteleft}Consistency of Local Density Matrices{\textquoteright}{\textquoteright}: given several density matrices describing different (constant-size) subsets of an n-qubit system, decide whether these are consistent with a single global state. This problem was first suggested by Aharonov. We show that it is QMA-complete, via an oracle reduction from Local Hamiltonian. This uses algorithms for convex optimization with a membership oracle, due to Yudin and Nemirovskii. Next we show that two problems from quantum chemistry, {\textquoteleft}{\textquoteleft}Fermionic Local Hamiltonian{\textquoteright}{\textquoteright} and {\textquoteleft}{\textquoteleft}N-representability,{\textquoteright}{\textquoteright} are QMA-complete. These problems arise in calculating the ground state energies of molecular systems. N-representability is a key component in recently developed numerical methods using the contracted Schrodinger equation. Although these problems have been studied since the 1960{\textquoteright}s, it is only recently that the theory of quantum computation has allowed us to properly characterize their complexity. Finally, we study some special cases of the Consistency problem, pertaining to 1-dimensional and {\textquoteleft}{\textquoteleft}stoquastic{\textquoteright}{\textquoteright} systems. We also give an alternative proof of a result due to Jaynes: whenever local density matrices are consistent, they are consistent with a Gibbs state. }, url = {http://arxiv.org/abs/0712.3041v1}, author = {Yi-Kai Liu} } @article {1291, title = {Effective-range description of a Bose gas under strong one- or two-dimensional confinement }, journal = {New Journal of Physics}, volume = {9}, year = {2007}, month = {2007/01/29}, pages = {19 - 19}, abstract = { We point out that theories describing s-wave collisions of bosonic atoms confined in one- or two-dimensional geometries can be extended to much tighter confinements than previously thought. This is achieved by replacing the scattering length by an energy-dependent scattering length which was already introduced for the calculation of energy levels under 3D confinement. This replacement accurately predicts the position of confinement-induced resonances in strongly confined geometries. }, doi = {10.1088/1367-2630/9/1/019}, url = {http://arxiv.org/abs/physics/0607140v2}, author = {Pascal Naidon and Eite Tiesinga and William F. Mitchell and Paul S. Julienne} } @article {1255, title = {Every NAND formula of size N can be evaluated in time N^{1/2+o(1)} on a quantum computer }, year = {2007}, month = {2007/03/02}, abstract = { For every NAND formula of size N, there is a bounded-error N^{1/2+o(1)}-time quantum algorithm, based on a coined quantum walk, that evaluates this formula on a black-box input. Balanced, or {\textquoteleft}{\textquoteleft}approximately balanced,{\textquoteright}{\textquoteright} NAND formulas can be evaluated in O(sqrt{N}) queries, which is optimal. It follows that the (2-o(1))-th power of the quantum query complexity is a lower bound on the formula size, almost solving in the positive an open problem posed by Laplante, Lee and Szegedy. }, url = {http://arxiv.org/abs/quant-ph/0703015v3}, author = {Andrew M. Childs and Ben W. Reichardt and Robert Spalek and Shengyu Zhang} } @article {1358, title = {A fast and robust approach to long-distance quantum communication with atomic ensembles}, journal = {Physical Review A}, volume = {76}, year = {2007}, month = {2007/7/2}, abstract = {Quantum repeaters create long-distance entanglement between quantum systems while overcoming difficulties such as the attenuation of single photons in a fiber. Recently, an implementation of a repeater protocol based on single qubits in atomic ensembles and linear optics has been proposed [Nature 414, 413 (2001)]. Motivated by rapid experimental progress towards implementing that protocol, here we develop a more efficient scheme compatible with active purification of arbitrary errors. Using similar resources as the earlier protocol, our approach intrinsically purifies leakage out of the logical subspace and all errors within the logical subspace, leading to greatly improved performance in the presence of experimental inefficiencies. Our analysis indicates that our scheme could generate approximately one pair per 3 minutes over 1280 km distance with fidelity (F>78\%) sufficient to violate Bell{\textquoteright}s inequality. }, doi = {10.1103/PhysRevA.76.012301}, url = {http://arxiv.org/abs/quant-ph/0609236v3}, author = {L. Jiang and J. M. Taylor and M. D. Lukin} } @article {1253, title = {Improved quantum algorithms for the ordered search problem via semidefinite programming }, journal = {Physical Review A}, volume = {75}, year = {2007}, month = {2007/3/26}, abstract = { One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find new quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm. }, doi = {10.1103/PhysRevA.75.032335}, url = {http://arxiv.org/abs/quant-ph/0608161v1}, author = {Andrew M. Childs and Andrew J. Landahl and Pablo A. Parrilo} } @article {1214, title = {The limitations of nice mutually unbiased bases}, journal = {Journal of Algebraic Combinatorics}, volume = {25}, year = {2007}, month = {2006/7/11}, pages = {111 - 123}, abstract = { Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets. }, doi = {10.1007/s10801-006-0002-y}, url = {http://arxiv.org/abs/quant-ph/0412066v1}, author = {Michael Aschbacher and Andrew M. Childs and Pawel Wocjan} } @article {1423, title = {The Local Consistency Problem for Stoquastic and 1-D Quantum Systems}, year = {2007}, month = {2007/12/10}, abstract = { The Local Hamiltonian problem (finding the ground state energy of a quantum system) is known to be QMA-complete. The Local Consistency problem (deciding whether descriptions of small pieces of a quantum system are consistent) is also known to be QMA-complete. Here we consider special cases of Local Hamiltonian, for {\textquoteleft}{\textquoteleft}stoquastic{\textquoteright}{\textquoteright} and 1-dimensional systems, that seem to be strictly easier than QMA. We show that there exist analogous special cases of Local Consistency, that have equivalent complexity (up to poly-time oracle reductions). Our main technical tool is a new reduction from Local Consistency to Local Hamiltonian, using SDP duality. }, url = {http://arxiv.org/abs/0712.1388v2}, author = {Yi-Kai Liu} } @article {1441, title = {The LU-LC conjecture is false}, year = {2007}, month = {2007/09/09}, abstract = { The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false. }, url = {http://arxiv.org/abs/0709.1266v2}, author = {Zhengfeng Ji and Jianxin Chen and Zhaohui Wei and Mingsheng Ying} } @article {1856, title = {Multi-photon Entanglement: From Quantum Curiosity to Quantum Computing and Quantum Repeaters}, journal = {Proc. SPIE}, volume = {6664}, year = {2007}, pages = {66640G}, url = {http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PSISDG00666400000166640G000001\&idtype=cvips\&gifs=Yes\&bproc=volrange\&scode=6600\%20-\%206699}, author = {Walther, P and Eisaman, M D and Nemiroski, A and Alexey V. Gorshkov and Zibrov, A S and Zeilinger, A and Lukin, M D} } @article {1588, title = {N-representability is QMA-complete}, journal = {Phys. Rev. Lett.}, volume = {98}, year = {2007}, month = {2007/03/16}, abstract = {We study the computational complexity of the N-representability problem in quantum chemistry. We show that this problem is quantum Merlin-Arthur complete, which is the quantum generalization of nondeterministic polynomial time complete. Our proof uses a simple mapping from spin systems to fermionic systems, as well as a convex optimization technique that reduces the problem of finding ground states to N representability.}, doi = {10.1103/PhysRevLett.98.110503}, url = {http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.98.110503}, author = {Yi-Kai Liu and Matthias Christandl and F. Verstraete} } @article {1203, title = {Optimal control of light pulse storage and retrieval}, journal = {Physical Review Letters}, volume = {98}, year = {2007}, month = {2007/6/15}, abstract = { We demonstrate experimentally a procedure to obtain the maximum efficiency for the storage and retrieval of light pulses in atomic media. The procedure uses time reversal to obtain optimal input signal pulse-shapes. Experimental results in warm Rb vapor are in good agreement with theoretical predictions and demonstrate a substantial improvement of efficiency. This optimization procedure is applicable to a wide range of systems. }, doi = {10.1103/PhysRevLett.98.243602}, url = {http://arxiv.org/abs/quant-ph/0702266v1}, author = {Irina Novikova and Alexey V. Gorshkov and David F. Phillips and Anders S. Sorensen and Mikhail D. Lukin and Ronald L. Walsworth} } @article {1217, title = {Optimal quantum adversary lower bounds for ordered search}, year = {2007}, month = {2007/08/24}, abstract = { The goal of the ordered search problem is to find a particular item in an ordered list of n items. Using the adversary method, Hoyer, Neerbek, and Shi proved a quantum lower bound for this problem of (1/pi) ln n + Theta(1). Here, we find the exact value of the best possible quantum adversary lower bound for a symmetrized version of ordered search (whose query complexity differs from that of the original problem by at most 1). Thus we show that the best lower bound for ordered search that can be proved by the adversary method is (1/pi) ln n + O(1). Furthermore, we show that this remains true for the generalized adversary method allowing negative weights. }, doi = {10.1007/978-3-540-70575-8_71}, url = {http://arxiv.org/abs/0708.3396v1}, author = {Andrew M. Childs and Troy Lee} } @article {1857, title = {Optimization of slow and stored light in atomic vapor}, journal = {Proc. SPIE}, volume = {6482}, year = {2007}, pages = {64820M}, url = {http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PSISDG00648200000164820M000001\&idtype=cvips\&gifs=Yes\&bproc=volrange\&scode=6400\%20-\%206499}, author = {Novikova, I and Alexey V. Gorshkov and Phillips, D F and Xiao, Y and Klein, M and Walsworth, R L} } @article {1166, title = {Photon storage in Lambda-type optically dense atomic media. I. Cavity model }, journal = {Physical Review A}, volume = {76}, year = {2007}, month = {2007/9/7}, abstract = { In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in Lambda-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we perform the same analysis for the cavity model. In particular, we show that the retrieval efficiency is equal to C/(1+C) independent of the retrieval technique, where C is the cooperativity parameter. We also derive the optimal strategy for storage and, in particular, demonstrate that at any detuning one can store, with the optimal efficiency of C/(1+C), any smooth input mode satisfying T C gamma >> 1 and a certain class of resonant input modes satisfying T C gamma ~ 1, where T is the duration of the input mode and 2 gamma is the transition linewidth. In the two subsequent papers of the series, we present the full analysis of the free-space model and discuss the effects of inhomogeneous broadening on photon storage. }, doi = {10.1103/PhysRevA.76.033804}, url = {http://arxiv.org/abs/quant-ph/0612082v2}, author = {Alexey V. Gorshkov and Axel Andre and Mikhail D. Lukin and Anders S. Sorensen} } @article {1167, title = {Photon storage in Lambda-type optically dense atomic media. II. Free-space model }, journal = {Physical Review A}, volume = {76}, year = {2007}, month = {2007/9/7}, abstract = { In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we presented a universal physical picture for describing a wide range of techniques for storage and retrieval of photon wave packets in Lambda-type atomic media in free space, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo based techniques. This universal picture produced an optimal control strategy for photon storage and retrieval applicable to all approaches and yielded identical maximum efficiencies for all of them. In the present paper, we present the full details of this analysis as well some of its extensions, including the discussion of the effects of non-degeneracy of the two lower levels of the Lambda system. The analysis in the present paper is based on the intuition obtained from the study of photon storage in the cavity model in the preceding paper [Gorshkov et al., Phys. Rev. A 76, 033804 (2007)]. }, doi = {10.1103/PhysRevA.76.033805}, url = {http://arxiv.org/abs/quant-ph/0612083v2}, author = {Alexey V. Gorshkov and Axel Andre and Mikhail D. Lukin and Anders S. Sorensen} } @article {1168, title = {Photon storage in Lambda-type optically dense atomic media. III. Effects of inhomogeneous broadening }, journal = {Physical Review A}, volume = {76}, year = {2007}, month = {2007/9/7}, abstract = { In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)] and in the two preceding papers [Gorshkov et al., Phys. Rev. A 76, 033804 (2007); 76, 033805 (2007)], we used a universal physical picture to optimize and demonstrate equivalence between a wide range of techniques for storage and retrieval of photon wave packets in homogeneously broadened Lambda-type atomic media, including the adiabatic reduction of the photon group velocity, pulse-propagation control via off-resonant Raman techniques, and photon-echo-based techniques. In the present paper, we generalize this treatment to include inhomogeneous broadening. In particular, we consider the case of Doppler-broadened atoms and assume that there is a negligible difference between the Doppler shifts of the two optical transitions. In this situation, we show that, at high enough optical depth, all atoms contribute coherently to the storage process as if the medium were homogeneously broadened. We also discuss the effects of inhomogeneous broadening in solid state samples. In this context, we discuss the advantages and limitations of reversing the inhomogeneous broadening during the storage time, as well as suggest a way for achieving high efficiencies with a nonreversible inhomogeneous profile. }, doi = {10.1103/PhysRevA.76.033806}, url = {http://arxiv.org/abs/quant-ph/0612084v2}, author = {Alexey V. Gorshkov and Axel Andre and Mikhail D. Lukin and Anders S. Sorensen} } @article {1482, title = {Practical scheme for quantum dense coding between three parties using microwave radiation in trapped ions }, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, volume = {40}, year = {2007}, month = {2007/03/28}, pages = {1245 - 1252}, abstract = { We propose a practical scheme for implementing two-dimension quantum dense coding (QDC) between three parties through manipulating three ions confined in microtraps addressed by microwaves and assisted by a magnetic field gradient. The ions in our scheme are not required to be strictly cooled to the vibrational ground state because single-qubit and multi-qubit operations are made via Ising terms, in which the vibrational modes of the ions remain unchanged throughout the scheme, rendering our scheme robust to the heating of the ions. We also present the detailed steps and parameters for implementing the three-party QDC experimentally and show that the proposed scheme is within the current techniques of ion-trap experiments. }, doi = {10.1088/0953-4075/40/6/014}, url = {http://arxiv.org/abs/quant-ph/0702062v1}, author = {Wen-Xing Yang and Zhe-Xuan Gong} } @article {1257, title = {Quantum algorithms for hidden nonlinear structures}, year = {2007}, month = {2007/05/21}, abstract = { Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor{\textquoteright}s factoring algorithm. We suggest an alternative generalization, namely to problems of finding hidden nonlinear structures over finite fields. We give examples of two such problems that can be solved efficiently by a quantum computer, but not by a classical computer. We also give some positive results on the quantum query complexity of finding hidden nonlinear structures. }, doi = {10.1109/FOCS.2007.18}, url = {http://arxiv.org/abs/0705.2784v1}, author = {Andrew M. Childs and Leonard J. Schulman and Umesh V. Vazirani} } @article {2613, title = {Quantum Algorithms for Simon{\textquoteright}s Problem over General Groups}, journal = {SODA {\textquoteright}07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms}, year = {2007}, month = {1/25/2007}, pages = {1217{\textendash}1224}, abstract = {

Daniel Simon\&$\#$39;s 1994 discovery of an efficient quantum algorithm for solving the hidden subgroup problem (HSP) over Zn2 provided one of the first algebraic problems for which quantum computers are exponentially faster than their classical counterparts. In this paper, we study the generalization of Simon\&$\#$39;s problem to arbitrary groups. Fixing a finite group G, this is the problem of recovering an involution m = (m1,...,mn) ε Gn from an oracle f with the property that f(x) = f(x \· y) \⇔ y ε {1, m}. In the current parlance, this is the hidden subgroup problem (HSP) over groups of the form Gn, where G is a nonabelian group of constant size, and where the hidden subgroup is either trivial or has order two.

Although groups of the form Gn have a simple product structure, they share important representation-theoretic properties with the symmetric groups Sn, where a solution to the HSP would yield a quantum algorithm for Graph Isomorphism. In particular, solving their HSP with the so-called \"standard method\" requires highly entangled measurements on the tensor product of many coset states.

Here we give quantum algorithms with time complexity 2O(\√n log n) that recover hidden involutions m = (m1,..., mn) ε Gn where, as in Simon\&$\#$39;s problem, each mi is either the identity or the conjugate of a known element m and there is a character X of G for which X(m) = - X(1). Our approach combines the general idea behind Kuperberg\&$\#$39;s sieve for dihedral groups with the \"missing harmonic\" approach of Moore and Russell. These are the first nontrivial hidden subgroup algorithms for group families that require highly entangled multiregister Fourier sampling.

}, doi = {https://dl.acm.org/doi/10.5555/1283383.1283514}, url = {https://arxiv.org/abs/quant-ph/0603251}, author = {Gorjan Alagic and Cristopher Moore and Alexander Russell} } @article {2614, title = {Quantum Computing and the Hunt for Hidden Symmetry}, journal = {Bulletin of the EATCS}, volume = {93}, year = {2007}, pages = {53-75}, abstract = {

In 1994, Peter Shor gave e cient quantum algorithms for factoring integers and extracting discrete logarithms [20]. If we believe that nature will permit us to faithfully implement our current model of quantum computation, then these algorithms dramatically contradict the Strong Church-Turing thesis. The e ect is heightened by the fact that these algorithms solve computational problems with long histories of attention by the computational and mathematical communities alike. In this article we discuss the branch of quantum algorithms research arising from attempts to generalize the core quantum algorithmic aspects of Shor\&$\#$39;s algorithms. Roughly, this can be viewed as the problem of generalizing algorithms of Simon [21] and Shor [20], which work over abelian groups, to general nonabelian groups. The article is meant to be self-contained, assuming no knowledge of quantum computing or the representation theory of nite groups. We begin in earnest in Section 2, describing the problem of symmetry nding : given a function f : G \→ S on a group G, this is the problem of determining {g \∈ G | \∀x, f(x) = f(gx)}, the set of symmetries of f . We switch gears in Section 3, giving a short introduction to the circuit model of quantum computation. The connection between these two sections is eventually established in Section 4, where we discuss the representation theory of nite groups and the quantum Fourier transform a unitary transformation speci cally tuned to the symmetries of the underlying group. Section 4.2 is devoted to Fourier

}, url = {https://pdfs.semanticscholar.org/08f7/abc04ca0bd38c1351ee1179139d8b0fc172b.pdf?_ga=2.210619804.800377824.1595266095-1152452310.1595266095}, author = {Gorjan Alagic and Alexander Russell} } @article {1356, title = {A quantum dot implementation of the quantum NAND algorithm}, year = {2007}, month = {2007/08/10}, abstract = {We propose a physical implementation of the quantum NAND tree evaluation algorithm. Our approach, based on continuous time quantum walks, uses the wave interference of a single electron in a heirarchical set of tunnel coupled quantum dots. We find that the query complexity of the NAND tree evaluation does not suffer strongly from disorder and dephasing, nor is it directly limited by temperature or restricted dimensionality for 2-d structures. Finally, we suggest a potential application of this algorithm to the efficient determination of high-order correlation functions of complex quantum systems. }, url = {http://arxiv.org/abs/0708.1484v1}, author = {J. M. Taylor} } @article {1359, title = {Relaxation, dephasing, and quantum control of electron spins in double quantum dots}, journal = {Physical Review B}, volume = {76}, year = {2007}, month = {2007/7/13}, abstract = {Recent experiments have demonstrated quantum manipulation of two-electron spin states in double quantum dots using electrically controlled exchange interactions. Here, we present a detailed theory for electron spin dynamics in two-electron double dot systems that was used to guide these experiments and analyze experimental results. The theory treats both charge and spin degrees of freedom on an equal basis. Specifically, we analyze the relaxation and dephasing mechanisms that are relevant to experiments and discuss practical approaches for quantum control of two-electron system. We show that both charge and spin dephasing play important roles in the dynamics of the two-spin system, but neither represents a fundamental limit for electrical control of spin degrees of freedom in semiconductor quantum bits. }, doi = {10.1103/PhysRevB.76.035315}, url = {http://arxiv.org/abs/cond-mat/0602470v2}, author = {J. M. Taylor and J. R. Petta and A. C. Johnson and A. Yacoby and C. M. Marcus and M. D. Lukin} } @article {1194, title = {Signatures of incoherence in a quantum information processor}, year = {2007}, month = {2007/05/24}, abstract = { Incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. While many incoherent processes appear decoherent, there are important differences. The distribution functions underlying incoherent processes are either static or slowly varying with respect to control operations and so the errors introduced by these distributions are refocusable. The observation and control of incoherence in small Hilbert spaces is well known. Here we explore incoherence during an entangling operation, such as is relevant in quantum information processing. As expected, it is more difficult to separate incoherence and decoherence over such processes. However, by studying the fidelity decay under a cyclic entangling map we are able to identify distinctive experimental signatures of incoherence. This result is demonstrated both through numerical simulations and experimentally in a three qubit nuclear magnetic resonance implementation. }, url = {http://arxiv.org/abs/0705.3666v2}, author = {Michael K. Henry and Alexey V. Gorshkov and Yaakov S. Weinstein and Paola Cappellaro and Joseph Emerson and Nicolas Boulant and Jonathan S. Hodges and Chandrasekhar Ramanathan and Timothy F. Havel and Rudy Martinez and David G. Cory} } @article {1487, title = {Simple scheme for implementing the Deutsch-Jozsa algorithm in thermal cavity }, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {40}, year = {2007}, month = {2007/01/05}, pages = {155 - 161}, abstract = { We present a simple scheme to implement the Deutsch-Jozsa algorithm based on two-atom interaction in a thermal cavity. The photon-number-dependent parts in the evolution operator are canceled with the strong resonant classical field added. As a result, our scheme is immune to thermal field, and does not require the cavity to remain in the vacuum state throughout the procedure. Besides, large detuning between the atoms and the cavity is not necessary neither, leading to potential speed up of quantum operation. Finally, we show by numerical simulation that the proposed scheme is equal to demonstrate the Deutsch-Jozsa algorithm with high fidelity. }, doi = {10.1088/1751-8113/40/1/009}, url = {http://arxiv.org/abs/quant-ph/0611225v2}, author = {Wen-Xing Yang and Zhe-Xuan Gong} } @article {1323, title = {Two dogmas about quantum mechanics}, year = {2007}, month = {2007/12/27}, abstract = { We argue that the intractable part of the measurement problem -- the {\textquoteright}big{\textquoteright} measurement problem -- is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell{\textquoteright}s assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the {\textquoteright}truthmaker{\textquoteright} for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. We show how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the {\textquoteright}big{\textquoteright} measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, we accept that measurements have definite outcomes. By contrast with the Bohmians and the GRW {\textquoteright}collapse{\textquoteright} theorists who add structure to the theory and propose dynamical solutions to the {\textquoteright}big{\textquoteright} measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events. }, url = {http://arxiv.org/abs/0712.4258v2}, author = {Jeffrey Bub and Itamar Pitowsky} } @article {1180, title = {Universal Approach to Optimal Photon Storage in Atomic Media}, journal = {Physical Review Letters}, volume = {98}, year = {2007}, month = {2007/3/19}, abstract = { We present a universal physical picture for describing storage and retrieval of photon wave packets in a Lambda-type atomic medium. This physical picture encompasses a variety of different approaches to pulse storage ranging from adiabatic reduction of the photon group velocity and pulse-propagation control via off-resonant Raman fields to photon-echo based techniques. Furthermore, we derive an optimal control strategy for storage and retrieval of a photon wave packet of any given shape. All these approaches, when optimized, yield identical maximum efficiencies, which only depend on the optical depth of the medium. }, doi = {10.1103/PhysRevLett.98.123601}, url = {http://arxiv.org/abs/quant-ph/0604037v3}, author = {Alexey V. Gorshkov and Axel Andre and Michael Fleischhauer and Anders S. Sorensen and Mikhail D. Lukin} } @article {1589, title = {On Bounded Distance Decoding for General Lattices}, journal = {Proc. RANDOM}, year = {2006}, month = {2006/01/01}, pages = {450-461}, abstract = {A central problem in the algorithmic study of lattices is the closest vector problem: given a lattice L represented by some basis, and a target point y⃗ , find the lattice point closest to y⃗ . Bounded Distance Decoding is a variant of this problem in which the target is guaranteed to be close to the lattice, relative to the minimum distance λ1(L) of the lattice. Specifically, in the α-Bounded Distance Decoding problem (α-BDD), we are given a lattice L and a vector y⃗ (within distance α.λ1(L) from the lattice), and we are asked to find a lattice point x⃗ ∈L within distance α.λ1(L) from the target. In coding theory, the lattice points correspond to codewords, and the target points correspond to lattice points being perturbed by noise vectors. Since in coding theory the lattice is usually fixed, we may {\textquotedblleft}pre-process{\textquotedblright} it before receiving any targets, to make the subsequent decoding faster. This leads us to consider α-BDD with pre-processing. We show how a recent technique of Aharonov and Regev [2] can be used to solve α-BDD with pre-processing in polynomial time for α=O((logn)/n-------√). This improves upon the previously best known algorithm due to Klein [13] which solved the problem for α=O(1/n). We also establish hardness results for α-BDD and α-BDD with pre-processing, as well as generalize our results to other l p norms.}, url = {http://link.springer.com/chapter/10.1007/11830924_41$\#$page-1}, author = {Yi-Kai Liu and Vadim Lyubashevsky and Daniele Micciancio} } @article {1360, title = {Cavity quantum electrodynamics with semiconductor double-dot molecules on a chip}, year = {2006}, month = {2006/05/05}, abstract = {We describe a coherent control technique for coupling electron spin states associated with semiconductor double-dot molecule to a microwave stripline resonator on a chip. We identify a novel regime of operation in which strong interaction between a molecule and a resonator can be achieved with minimal decoherence, reaching the so-called strong coupling regime of cavity QED. We describe potential applications of such a system, including low-noise coherent electrical control, fast QND measurements of spin states, and long-range spin coupling. }, url = {http://arxiv.org/abs/cond-mat/0605144v1}, author = {J. M. Taylor and M. D. Lukin} } @article {1422, title = {Consistency of Local Density Matrices is QMA-complete}, journal = {Proc. RANDOM }, year = {2006}, month = {2006/04/21}, pages = {438-449}, abstract = { Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes a subset C_i of the qubits. We say that the rho_i are {\textquoteleft}{\textquoteleft}consistent{\textquoteright}{\textquoteright} if there exists some global state sigma (on all n qubits) that matches each of the rho_i on the subsets C_i. This generalizes the classical notion of the consistency of marginal probability distributions. We show that deciding the consistency of local density matrices is QMA-complete (where QMA is the quantum analogue of NP). This gives an interesting example of a hard problem in QMA. Our proof is somewhat unusual: we give a Turing reduction from Local Hamiltonian, using a convex optimization algorithm by Bertsimas and Vempala, which is based on random sampling. Unlike in the classical case, simple mapping reductions do not seem to work here. }, url = {http://arxiv.org/abs/quant-ph/0604166v3}, author = {Yi-Kai Liu} } @article {1481, title = {Effective error-suppression scheme for reversible quantum computer}, year = {2006}, month = {2006/08/20}, abstract = { We construct a new error-suppression scheme that makes use of the adjoint of reversible quantum algorithms. For decoherence induced errors such as depolarization, it is presented that provided the depolarization error probability is less than 1, our scheme can exponentially reduce the final output error rate to zero using a number of cycles, and the output state can be coherently sent to another stage of quantum computation process. Besides, experimental set-ups via optical approach have been proposed using Grover{\textquoteright}s search algorithm as an example. Some further discussion on the benefits and limitations of the scheme is given in the end. }, url = {http://arxiv.org/abs/quant-ph/0608152v4}, author = {Zhe-Xuan Gong} } @article {1405, title = {Effects of finite temperature on the Mott insulator state}, journal = {Physical Review A}, volume = {73}, year = {2006}, month = {2006/1/20}, abstract = { We investigate the effects of finite temperature on ultracold Bose atoms confined in an optical lattice plus a parabolic potential in the Mott insulator state. In particular, we analyze the temperature dependence of the density distribution of atomic pairs in the lattice, by means of exact Monte-Carlo simulations. We introduce a simple model that quantitatively accounts for the computed pair density distributions at low enough temperatures. We suggest that the temperature dependence of the atomic pair statistics may be used to estimate the system{\textquoteright}s temperature at energies of the order of the atoms{\textquoteright} interaction energy. }, doi = {10.1103/PhysRevA.73.013408}, url = {http://arxiv.org/abs/cond-mat/0407075v3}, author = {Guido Pupillo and Carl J. Williams and Nikolay V. Prokof{\textquoteright}ev} } @article {1394, title = {Error correcting codes for adiabatic quantum computation}, journal = {Physical Review A}, volume = {74}, year = {2006}, month = {2006/11/14}, abstract = { Recently, there has been growing interest in using adiabatic quantum computation as an architecture for experimentally realizable quantum computers. One of the reasons for this is the idea that the energy gap should provide some inherent resistance to noise. It is now known that universal quantum computation can be achieved adiabatically using 2-local Hamiltonians. The energy gap in these Hamiltonians scales as an inverse polynomial in the problem size. Here we present stabilizer codes which can be used to produce a constant energy gap against 1-local and 2-local noise. The corresponding fault-tolerant universal Hamiltonians are 4-local and 6-local respectively, which is the optimal result achievable within this framework. }, doi = {10.1103/PhysRevA.74.052322}, url = {http://arxiv.org/abs/quant-ph/0512170v3}, author = {Stephen P. Jordan and Edward Farhi and Peter W. Shor} } @article {1364, title = {Fault-tolerant Quantum Communication with Minimal Physical Requirements}, journal = {Physical Review Letters}, volume = {96}, year = {2006}, month = {2006/2/23}, abstract = {We describe a novel protocol for a quantum repeater which enables long distance quantum communication through realistic, lossy photonic channels. Contrary to previous proposals, our protocol incorporates active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station. Because of these minimal physical requirements, the present protocol can be realized in simple physical systems such as solid-state single photon emitters. As an example, we show how nitrogen vacancy color centers in diamond can be used to implement the protocol, using the nuclear and electronic spin to form the two qubits. }, doi = {10.1103/PhysRevLett.96.070504}, url = {http://arxiv.org/abs/quant-ph/0410123v3}, author = {L. Childress and J. M. Taylor and A. S. Sorensen and M. D. Lukin} } @article {1421, title = {Gibbs States and the Consistency of Local Density Matrices}, year = {2006}, month = {2006/03/02}, abstract = { Suppose we have an n-qubit system, and we are given a collection of local density matrices rho_1,...,rho_m, where each rho_i describes some subset of the qubits. We say that rho_1,...,rho_m are "consistent" if there exists a global state sigma (on all n qubits) whose reduced density matrices match rho_1,...,rho_m. We prove the following result: if rho_1,...,rho_m are consistent with some state sigma > 0, then they are also consistent with a state sigma{\textquoteright} of the form sigma{\textquoteright} = (1/Z) exp(M_1+...+M_m), where each M_i is a Hermitian matrix acting on the same qubits as rho_i, and Z is a normalizing factor. (This is known as a Gibbs state.) Actually, we show a more general result, on the consistency of a set of expectation values ,...,, where the observables T_1,...,T_r need not commute. This result was previously proved by Jaynes (1957) in the context of the maximum-entropy principle; here we provide a somewhat different proof, using properties of the partition function. }, url = {http://arxiv.org/abs/quant-ph/0603012v1}, author = {Yi-Kai Liu} } @article {1416, title = {Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice }, journal = {Physical Review A}, volume = {73}, year = {2006}, month = {2006/1/9}, abstract = { We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. We expect this irregular motion to result from the well-known dynamical instability exhibited by the mean-field theory for these systems. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally-observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices. }, doi = {10.1103/PhysRevA.73.013605}, url = {http://arxiv.org/abs/cond-mat/0410677v4}, author = {Julio Gea-Banacloche and Ana Maria Rey and Guido Pupillo and Carl J. Williams and Charles W. Clark} } @article {1375, title = {Parallelism for Quantum Computation with Qudits}, journal = {Physical Review A}, volume = {74}, year = {2006}, month = {2006/9/28}, abstract = { Robust quantum computation with d-level quantum systems (qudits) poses two requirements: fast, parallel quantum gates and high fidelity two-qudit gates. We first describe how to implement parallel single qudit operations. It is by now well known that any single-qudit unitary can be decomposed into a sequence of Givens rotations on two-dimensional subspaces of the qudit state space. Using a coupling graph to represent physically allowed couplings between pairs of qudit states, we then show that the logical depth of the parallel gate sequence is equal to the height of an associated tree. The implementation of a given unitary can then optimize the tradeoff between gate time and resources used. These ideas are illustrated for qudits encoded in the ground hyperfine states of the atomic alkalies $^{87}$Rb and $^{133}$Cs. Second, we provide a protocol for implementing parallelized non-local two-qudit gates using the assistance of entangled qubit pairs. Because the entangled qubits can be prepared non-deterministically, this offers the possibility of high fidelity two-qudit gates. }, doi = {10.1103/PhysRevA.74.032334}, url = {http://arxiv.org/abs/quant-ph/0603081v1}, author = {Dianne P. O{\textquoteright}Leary and Gavin K. Brennen and Stephen S. Bullock} } @article {1410, title = {Pseudo-fermionization of 1-D bosons in optical lattices}, journal = {New Journal of Physics}, volume = {8}, year = {2006}, month = {2006/08/30}, pages = {161 - 161}, abstract = { We present a model that generalizes the Bose-Fermi mapping for strongly correlated 1D bosons in an optical lattice, to cases in which the average number of atoms per site is larger than one. This model gives an accurate account of equilibrium properties of such systems, in parameter regimes relevant to current experiments. The application of this model to non-equilibrium phenomena is explored by a study of the dynamics of an atom cloud subject to a sudden displacement of the confining potential. Good agreement is found with results of recent experiments. The simplicity and intuitive appeal of this model make it attractive as a general tool for understanding bosonic systems in the strongly correlated regime. }, doi = {10.1088/1367-2630/8/8/161}, url = {http://arxiv.org/abs/cond-mat/0505325v2}, author = {Guido Pupillo and Ana Maria Rey and Carl J. Williams and Charles W. Clark} } @article {1314, title = {Quantum computation from a quantum logical perspective}, year = {2006}, month = {2006/05/29}, abstract = { It is well-known that Shor{\textquoteright}s factorization algorithm, Simon{\textquoteright}s period-finding algorithm, and Deutsch{\textquoteright}s original XOR algorithm can all be formulated as solutions to a hidden subgroup problem. Here the salient features of the information-processing in the three algorithms are presented from a different perspective, in terms of the way in which the algorithms exploit the non-Boolean quantum logic represented by the projective geometry of Hilbert space. From this quantum logical perspective, the XOR algorithm appears directly as a special case of Simon{\textquoteright}s algorithm, and all three algorithms can be seen as exploiting the non-Boolean logic represented by the subspace structure of Hilbert space in a similar way. Essentially, a global property of a function (such as a period, or a disjunctive property) is encoded as a subspace in Hilbert space representing a quantum proposition, which can then be efficiently distinguished from alternative propositions, corresponding to alternative global properties, by a measurement (or sequence of measurements) that identifies the target proposition as the proposition represented by the subspace containing the final state produced by the algorithm. }, url = {http://arxiv.org/abs/quant-ph/0605243v2}, author = {Jeffrey Bub} } @article {1252, title = {Two-way quantum communication channels}, journal = {International Journal of Quantum Information}, volume = {04}, year = {2006}, month = {2006/02/01}, pages = {63 - 83}, abstract = { We consider communication between two parties using a bipartite quantum operation, which constitutes the most general quantum mechanical model of two-party communication. We primarily focus on the simultaneous forward and backward communication of classical messages. For the case in which the two parties share unlimited prior entanglement, we give inner and outer bounds on the achievable rate region that generalize classical results due to Shannon. In particular, using a protocol of Bennett, Harrow, Leung, and Smolin, we give a one-shot expression in terms of the Holevo information for the entanglement-assisted one-way capacity of a two-way quantum channel. As applications, we rederive two known additivity results for one-way channel capacities: the entanglement-assisted capacity of a general one-way channel, and the unassisted capacity of an entanglement-breaking one-way channel. }, doi = {10.1142/S0219749906001621}, url = {http://arxiv.org/abs/quant-ph/0506039v1}, author = {Andrew M. Childs and Debbie W. Leung and Hoi-Kwong Lo} } @article {1241, title = {Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem }, year = {2006}, month = {2006/09/14}, abstract = { Schur duality decomposes many copies of a quantum state into subspaces labeled by partitions, a decomposition with applications throughout quantum information theory. Here we consider applying Schur duality to the problem of distinguishing coset states in the standard approach to the hidden subgroup problem. We observe that simply measuring the partition (a procedure we call weak Schur sampling) provides very little information about the hidden subgroup. Furthermore, we show that under quite general assumptions, even a combination of weak Fourier sampling and weak Schur sampling fails to identify the hidden subgroup. We also prove tight bounds on how many coset states are required to solve the hidden subgroup problem by weak Schur sampling, and we relate this question to a quantum version of the collision problem. }, doi = {10.1007/978-3-540-70918-3_51}, url = {http://arxiv.org/abs/quant-ph/0609110v1}, author = {Andrew M. Childs and Aram W. Harrow and Pawel Wocjan} } @article {1373, title = {Asymptotically Optimal Quantum Circuits for d-level Systems}, journal = {Physical Review Letters}, volume = {94}, year = {2005}, month = {2005/6/14}, abstract = { As a qubit is a two-level quantum system whose state space is spanned by |0>, |1>, so a qudit is a d-level quantum system whose state space is spanned by |0>,...,|d-1>. Quantum computation has stimulated much recent interest in algorithms factoring unitary evolutions of an n-qubit state space into component two-particle unitary evolutions. In the absence of symmetry, Shende, Markov and Bullock use Sard{\textquoteright}s theorem to prove that at least C 4^n two-qubit unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa (VMS) use the QR matrix factorization and Gray codes in an optimal order construction involving two-particle evolutions. In this work, we note that Sard{\textquoteright}s theorem demands C d^{2n} two-qudit unitary evolutions to construct a generic (symmetry-less) n-qudit evolution. However, the VMS result applied to virtual-qubits only recovers optimal order in the case that d is a power of two. We further construct a QR decomposition for d-multi-level quantum logics, proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing the complexity question for all d-level systems (d finite.) Gray codes are not required, and the optimal Theta(d^{2n}) asymptotic also applies to gate libraries where two-qudit interactions are restricted by a choice of certain architectures. }, doi = {10.1103/PhysRevLett.94.230502}, url = {http://arxiv.org/abs/quant-ph/0410116v2}, author = {Stephen S. Bullock and Dianne P. O{\textquoteright}Leary and Gavin K. Brennen} } @article {1415, title = {Bragg Spectroscopy of ultracold atoms loaded in an optical lattice}, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/8/12}, abstract = { We study Bragg spectroscopy of ultra-cold atoms in one-dimensional optical lattices as a method for probing the excitation spectrum in the Mott insulator phase, in particular the one particle-hole excitation band. Within the framework of perturbation theory we obtain an analytical expression for the dynamic structure factor $S(q,\omega)$ and use it to calculate the imparted energy which has shown to be a relevant observable in recent experiments. We test the accuracy of our approximations by comparing them with numerically exact solutions of the Bose-Hubbard model in restricted cases and establish the limits of validity of our linear response analysis. Finally we show that when the system is deep in the Mott insulator regime, its response to the Bragg perturbation is temperature dependent. We suggest that this dependence might be used as a tool to probe temperatures of order of the Mott gap. }, doi = {10.1103/PhysRevA.72.023407}, url = {http://arxiv.org/abs/cond-mat/0406552v2}, author = {Ana Maria Rey and P. Blair Blakie and Guido Pupillo and Carl J. Williams and Charles W. Clark} } @article {1322, title = {Conditionalizing and commutativity: a note on Malley}, year = {2005}, month = {2005/06/19}, abstract = { This paper has been withdrawn. }, url = {http://arxiv.org/abs/quant-ph/0506159v2}, author = {Allen Stairs and Jeffrey Bub} } @article {1372, title = {Criteria for Exact Qudit Universality}, journal = {Physical Review A}, volume = {71}, year = {2005}, month = {2005/5/16}, abstract = { We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states |0>, |1>,... |d-1>. An important earlier work of Mathukrishnan and Stroud [1] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. Their technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H_{jk}^x=\hbar\Omega (|k>k iff H_{jk}^{x,y} are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian H=-\hbar\Omega |d-1,d-1>We study a natural notion of decoherence on quantum random walks over the hypercube. We prove that in this model there is a decoherence threshold beneath which the essential properties of the hypercubic quantum walk, such as linear mixing times, are preserved. Beyond the threshold, we prove that the walks behave like their classical counterparts.

}, doi = {https://doi.org/10.1103/PhysRevA.72.062304}, url = {https://arxiv.org/abs/quant-ph/0501169}, author = {Gorjan Alagic and Alexander Russell} } @article {1361, title = {Dephasing of quantum bits by a quasi-static mesoscopic environment}, year = {2005}, month = {2005/12/07}, abstract = {We examine coherent processes in a two-state quantum system that is strongly coupled to a mesoscopic spin bath and weakly coupled to other environmental degrees of freedom. Our analysis is specifically aimed at understanding the quantum dynamics of solid-state quantum bits such as electron spins in semiconductor structures and superconducting islands. The role of mesoscopic degrees of freedom with long correlation times (local degrees of freedom such as nuclear spins and charge traps) in qubit-related dephasing is discussed in terms of a quasi-static bath. A mathemat- ical framework simultaneously describing coupling to the slow mesoscopic bath and a Markovian environment is developed and the dephasing and decoherence properties of the total system are investigated. The model is applied to several specific examples with direct relevance to current ex- periments. Comparisons to experiments suggests that such quasi-static degrees of freedom play an important role in current qubit implementations. Several methods of mitigating the bath-induced error are considered. }, url = {http://arxiv.org/abs/quant-ph/0512059v2}, author = {J. M. Taylor and M. D. Lukin} } @article {1590, title = {Designing Incentives for Peer-to-Peer Routing}, journal = {Proc. INFOCOM}, year = {2005}, month = {2005/03/13}, pages = {374-385}, abstract = {In a peer-to-peer network, nodes are typically required to route packets for each other. This leads to a problem of {\textquotedblleft}free-loaders,{\textquotedblright} nodes that use the network but refuse to route other nodes{\textquoteright} packets. In this paper we study ways of designing incentives to discourage free-loading. We model the interactions between nodes as a {\textquotedblleft}random matching game,{\textquotedblright} and describe a simple reputation system that provides incentives for good behavior. Under certain assumptions, we obtain a stable subgame-perfect equilibrium. We use simulations to investigate the robustness of this scheme in the presence of noise and malicious nodes, and we examine some of the design trade-offs. We also evaluate some possible adversarial strategies, and discuss how our results might apply to real peer-to-peer systems.}, url = {http://cseweb.ucsd.edu/~vahdat/papers/infocom05.pdf}, author = {Alberto Blanc and Yi-Kai Liu and Amin Vahda} } @article {1869, title = {Exponential iterated integrals and the relative solvable completion of the fundamental group of a manifold}, journal = {Topology}, volume = {44}, year = {2005}, month = {2005/03/01}, pages = {351 - 373}, abstract = {

We develop a class of integrals on a manifold\ M\ called\ exponential iterated integrals \ , an extension of K.T. Chen\&$\#$39;s iterated integrals. It is shown that the matrix entries of any upper triangular representation of\ π1(M,x)\ can be expressed via these new integrals. The ring of exponential iterated integrals contains the coordinate rings for a class of universal representations, called the\ relative solvable completions \ \ of\ π1(M,x). We consider exponential iterated integrals in the particular case of fibered knot complements, where the fundamental group always has a faithful relative solvable completion.

}, issn = {00409383}, doi = {10.1016/j.top.2004.10.005}, url = {http://www.sciencedirect.com/science/article/pii/S0040938304000795}, author = {Carl Miller} } @article {1377, title = {Fast quantum algorithm for numerical gradient estimation}, journal = {Physical Review Letters}, volume = {95}, year = {2005}, month = {2005/7/28}, abstract = { Given a blackbox for f, a smooth real scalar function of d real variables, one wants to estimate the gradient of f at a given point with n bits of precision. On a classical computer this requires a minimum of d+1 blackbox queries, whereas on a quantum computer it requires only one query regardless of d. The number of bits of precision to which f must be evaluated matches the classical requirement in the limit of large n. }, doi = {10.1103/PhysRevLett.95.050501}, url = {http://arxiv.org/abs/quant-ph/0405146v2}, author = {Stephen P. Jordan} } @article {1363, title = {Fault-tolerant quantum repeaters with minimal physical resources, and implementations based on single photon emitters}, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/11/28}, abstract = {We analyze a novel method that uses fixed, minimal physical resources to achieve generation and nested purification of quantum entanglement for quantum communication over arbitrarily long distances, and discuss its implementation using realistic photon emitters and photonic channels. In this method, we use single photon emitters with two internal degrees of freedom formed by an electron spin and a nuclear spin to build intermediate nodes in a quantum channel. State-selective fluorescence is used for probabilistic entanglement generation between electron spins in adjacent nodes. We analyze in detail several approaches which are applicable to realistic, homogeneously broadened single photon emitters. Furthermore, the coupled electron and nuclear spins can be used to efficiently implement entanglement swapping and purification. We show that these techniques can be combined to generate high-fidelity entanglement over arbitrarily long distances. We present a specific protocol that functions in polynomial time and tolerates percent-level errors in entanglement fidelity and local operations. The scheme has the lowest requirements on physical resources of any current scheme for fully fault-tolerant quantum repeaters. }, doi = {10.1103/PhysRevA.72.052330}, url = {http://arxiv.org/abs/quant-ph/0502112v1}, author = {L. I. Childress and J. M. Taylor and A. S. Sorensen and M. D. Lukin} } @article {1240, title = {From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups }, year = {2005}, month = {2005/04/11}, abstract = { We approach the hidden subgroup problem by performing the so-called pretty good measurement on hidden subgroup states. For various groups that can be expressed as the semidirect product of an abelian group and a cyclic group, we show that the pretty good measurement is optimal and that its probability of success and unitary implementation are closely related to an average-case algebraic problem. By solving this problem, we find efficient quantum algorithms for a number of nonabelian hidden subgroup problems, including some for which no efficient algorithm was previously known: certain metacyclic groups as well as all groups of the form (Z_p)^r X| Z_p for fixed r (including the Heisenberg group, r=2). In particular, our results show that entangled measurements across multiple copies of hidden subgroup states can be useful for efficiently solving the nonabelian HSP. }, doi = {10.1109/SFCS.2005.38}, url = {http://arxiv.org/abs/quant-ph/0504083v2}, author = {Dave Bacon and Andrew M. Childs and Wim van Dam} } @article {1290, title = {Multichannel quantum-defect theory for slow atomic collisions}, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/10/28}, abstract = { We present a multichannel quantum-defect theory for slow atomic collisions that takes advantages of the analytic solutions for the long-range potential, and both the energy and the angular-momentum insensitivities of the short-range parameters. The theory provides an accurate and complete account of scattering processes, including shape and Feshbach resonances, in terms of a few parameters such as the singlet and the triplet scattering lengths. As an example, results for $^{23}$Na-$^{23}$Na scattering are presented and compared close-coupling calculations. }, doi = {10.1103/PhysRevA.72.042719}, url = {http://arxiv.org/abs/physics/0508060v1}, author = {Bo Gao and Eite Tiesinga and Carl J. Williams and Paul S. Julienne} } @article {1239, title = {Optimal measurements for the dihedral hidden subgroup problem}, year = {2005}, month = {2005/01/10}, abstract = { We consider the dihedral hidden subgroup problem as the problem of distinguishing hidden subgroup states. We show that the optimal measurement for solving this problem is the so-called pretty good measurement. We then prove that the success probability of this measurement exhibits a sharp threshold as a function of the density nu=k/log N, where k is the number of copies of the hidden subgroup state and 2N is the order of the dihedral group. In particular, for nu<1 the optimal measurement (and hence any measurement) identifies the hidden subgroup with a probability that is exponentially small in log N, while for nu>1 the optimal measurement identifies the hidden subgroup with a probability of order unity. Thus the dihedral group provides an example of a group G for which Omega(log|G|) hidden subgroup states are necessary to solve the hidden subgroup problem. We also consider the optimal measurement for determining a single bit of the answer, and show that it exhibits the same threshold. Finally, we consider implementing the optimal measurement by a quantum circuit, and thereby establish further connections between the dihedral hidden subgroup problem and average case subset sum problems. In particular, we show that an efficient quantum algorithm for a restricted version of the optimal measurement would imply an efficient quantum algorithm for the subset sum problem, and conversely, that the ability to quantum sample from subset sum solutions allows one to implement the optimal measurement. }, url = {http://arxiv.org/abs/quant-ph/0501044v2}, author = {Dave Bacon and Andrew M. Childs and Wim van Dam} } @article {1567, title = {QR Factorizations Using a Restricted Set of Rotations}, journal = {Electronic Transactions on Numerical Analysis}, volume = {21}, year = {2005}, month = {2005/07/11}, pages = {20-27}, abstract = {Any matrix A of dimension m {\texttimes} n (m >= n) can be reduced to upper triangular form by multiplying by a sequence of mn - n(n + 1)/2 appropriately chosen rotation matrices. In this work, we address the question of whether such a factorization exists when the set of allowed rotation planes is restricted. We introduce the rotation graph as a tool to devise elimination orderings in QR factorizations. Properties of this graph characterize sets of rotation planes that are sufficient (or sufficient under permutation) and identify rotation planes to add to complete a deficient set. We also devise a constructive way to determine all feasible rotation sequences for performing the QR factorization using a restricted set of rotation planes. We present applications to quantum circuit design and parallel QR factorization.}, issn = {1068-9613}, url = {http://www.emis.ams.org/journals/ETNA/vol.21.2005/pp20-27.dir/pp20-27.pdf}, author = {Dianne P. O{\textquoteright}Leary and Stephen S. Bullock} } @article {1215, title = {Quantum algorithm for a generalized hidden shift problem}, year = {2005}, month = {2005/07/19}, abstract = { Consider the following generalized hidden shift problem: given a function f on {0,...,M-1} x Z_N satisfying f(b,x)=f(b+1,x+s) for b=0,1,...,M-2, find the unknown shift s in Z_N. For M=N, this problem is an instance of the abelian hidden subgroup problem, which can be solved efficiently on a quantum computer, whereas for M=2, it is equivalent to the dihedral hidden subgroup problem, for which no efficient algorithm is known. For any fixed positive epsilon, we give an efficient (i.e., poly(log N)) quantum algorithm for this problem provided M > N^epsilon. The algorithm is based on the "pretty good measurement" and uses H. Lenstra{\textquoteright}s (classical) algorithm for integer programming as a subroutine. }, url = {http://arxiv.org/abs/quant-ph/0507190v1}, author = {Andrew M. Childs and Wim van Dam} } @article {1216, title = {On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems }, year = {2005}, month = {2005/10/25}, abstract = { We consider an approach to deciding isomorphism of rigid n-vertex graphs (and related isomorphism problems) by solving a nonabelian hidden shift problem on a quantum computer using the standard method. Such an approach is arguably more natural than viewing the problem as a hidden subgroup problem. We prove that the hidden shift approach to rigid graph isomorphism is hard in two senses. First, we prove that Omega(n) copies of the hidden shift states are necessary to solve the problem (whereas O(n log n) copies are sufficient). Second, we prove that if one is restricted to single-register measurements, an exponential number of hidden shift states are required. }, url = {http://arxiv.org/abs/quant-ph/0510185v1}, author = {Andrew M. Childs and Pawel Wocjan} } @article {1313, title = {Quantum information and computation}, year = {2005}, month = {2005/12/15}, abstract = { This article deals with theoretical developments in the subject of quantum information and quantum computation, and includes an overview of classical information and some relevant quantum mechanics. The discussion covers topics in quantum communication, quantum cryptography, and quantum computation, and concludes by considering whether a perspective in terms of quantum information sheds new light on the conceptual problems of quantum mechanics. }, url = {http://arxiv.org/abs/quant-ph/0512125v2}, author = {Jeffrey Bub} } @article {1312, title = {Quantum mechanics is about quantum information}, journal = {Foundations of Physics}, volume = {35}, year = {2005}, month = {2005/04/01}, pages = {541 - 560}, abstract = { I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of quantum information is to be understood as a new physical primitive -- just as, following Einstein{\textquoteright}s special theory of relativity, a field is no longer regarded as the physical manifestation of vibrations in a mechanical medium, but recognized as a new physical primitive in its own right. }, doi = {10.1007/s10701-004-2010-x}, url = {http://arxiv.org/abs/quant-ph/0408020v2}, author = {Jeffrey Bub} } @article {1418, title = {Scalable register initialization for quantum computing in an optical lattice }, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, volume = {38}, year = {2005}, month = {2005/06/14}, pages = {1687 - 1694}, abstract = { The Mott insulator state created by loading an atomic Bose-Einstein condensate (BEC) into an optical lattice may be used as a means to prepare a register of atomic qubits in a quantum computer. Such architecture requires a lattice commensurately filled with atoms, which corresponds to the insulator state only in the limit of zero inter-well tunneling. We show that a lattice with spatial inhomogeneity created by a quadratic magnetic trapping potential can be used to isolate a subspace in the center which is impervious to hole-hoping. Components of the wavefunction with more than one atom in any well can be projected out by selective measurement on a molecular photo-associative transition. Maintaining the molecular coupling induces a quantum Zeno effect that can sustain a commensurately filled register for the duration of a quantum computation. }, doi = {10.1088/0953-4075/38/11/010}, url = {http://arxiv.org/abs/quant-ph/0312069v1}, author = {Gavin K. Brennen and Guido Pupillo and Ana Maria Rey and Charles W. Clark and Carl J. Williams} } @article {1297, title = {Sodium Bose-Einstein Condensates in an Optical Lattice}, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/10/10}, abstract = { The phase transition from a superfluid to a Mott insulator has been observed in a $^{23}$Na Bose-Einstein condensate. A dye laser detuned $\approx 5$nm red of the Na $3^2$S$ \to 3^2$P$_{1/2}$ transition was used to form the three dimensional optical lattice. The heating effects of the small detuning as well as the three-body decay processes constrained the timescale of the experiment. Certain lattice detunings were found to induce a large loss of atoms. These loss features were shown to be due to photoassociation of atoms to vibrational levels in the Na$_2$ $(1) ^3\Sigma_g^+$ state. }, doi = {10.1103/PhysRevA.72.043604}, url = {http://arxiv.org/abs/cond-mat/0507288v1}, author = {K. Xu and Y. Liu and J. R. Abo-Shaeer and T. Mukaiyama and J. K. Chin and D. E. Miller and W. Ketterle and Kevin M. Jones and Eite Tiesinga} } @article {1362, title = {Solid-state circuit for spin entanglement generation and purification}, journal = {Physical Review Letters}, volume = {94}, year = {2005}, month = {2005/6/15}, abstract = {We show how realistic charge manipulation and measurement techniques, combined with the exchange interaction, allow for the robust generation and purification of four-particle spin entangled states in electrically controlled semiconductor quantum dots. The generated states are immunized to the dominant sources of noise via a dynamical decoherence-free subspace; all additional errors are corrected by a purification protocol. This approach may find application in quantum computation, communication, and metrology. }, doi = {10.1103/PhysRevLett.94.236803}, url = {http://arxiv.org/abs/cond-mat/0503255v2}, author = {J. M. Taylor and W. D{\"u}r and P. Zoller and A. Yacoby and C. M. Marcus and M. D. Lukin} } @article {1275, title = {Spontaneous dissociation of long-range Feshbach molecules}, journal = {Physical Review Letters}, volume = {94}, year = {2005}, month = {2005/1/18}, abstract = { We study the spontaneous dissociation of diatomic molecules produced in cold atomic gases via magnetically tunable Feshbach resonances. We provide a universal formula for the lifetime of these molecules that relates their decay to the scattering length and the loss rate constant for inelastic spin relaxation. Our universal treatment as well as our exact coupled channels calculations for $^{85}$Rb dimers predict a suppression of the decay over several orders of magnitude when the scattering length is increased. Our predictions are in good agreement with recent measurements of the lifetime of $^{85}$Rb$_2$. }, doi = {10.1103/PhysRevLett.94.020402}, url = {http://arxiv.org/abs/cond-mat/0408387v2}, author = {Thorsten Koehler and Eite Tiesinga and Paul S. Julienne} } @article {2611, title = {Strong Fourier Sampling Fails over Gn}, year = {2005}, month = {11/7/2005}, abstract = {

We present a negative result regarding the hidden subgroup problem on the powers Gn of a fixed group G. Under a condition on the base group G, we prove that strong Fourier sampling cannot distinguish some subgroups of Gn. Since strong sampling is in fact the optimal measurement on a coset state, this shows that we have no hope of efficiently solving the hidden subgroup problem over these groups with separable measurements on coset states (that is, using any polynomial number of single-register coset state experiments). Base groups satisfying our condition include all nonabelian simple groups. We apply our results to show that there exist uniform families of nilpotent groups whose normal series factors have constant size and yet are immune to strong Fourier sampling.

}, url = {https://arxiv.org/abs/quant-ph/0511054}, author = {Gorjan Alagic and Cristopher Moore and Alexander Russell} } @article {1371, title = {Time Reversal and n-qubit Canonical Decompositions}, journal = {Journal of Mathematical Physics}, volume = {46}, year = {2005}, month = {2005/01/01}, pages = {062104}, abstract = { For n an even number of qubits and v a unitary evolution, a matrix decomposition v=k1 a k2 of the unitary group is explicitly computable and allows for study of the dynamics of the concurrence entanglement monotone. The side factors k1 and k2 of this Concurrence Canonical Decomposition (CCD) are concurrence symmetries, so the dynamics reduce to consideration of the a factor. In this work, we provide an explicit numerical algorithm computing v=k1 a k2 for n odd. Further, in the odd case we lift the monotone to a two-argument function, allowing for a theory of concurrence dynamics in odd qubits. The generalization may also be studied using the CCD, leading again to maximal concurrence capacity for most unitaries. The key technique is to consider the spin-flip as a time reversal symmetry operator in Wigner{\textquoteright}s axiomatization; the original CCD derivation may be restated entirely in terms of this time reversal. En route, we observe a Kramers{\textquoteright} nondegeneracy: the existence of a nondegenerate eigenstate of any time reversal symmetric n-qubit Hamiltonian demands (i) n even and (ii) maximal concurrence of said eigenstate. We provide examples of how to apply this work to study the kinematics and dynamics of entanglement in spin chain Hamiltonians. }, doi = {10.1063/1.1900293}, url = {http://arxiv.org/abs/quant-ph/0402051v2}, author = {Stephen S. Bullock and Gavin K. Brennen and Dianne P. O{\textquoteright}Leary} } @article {1409, title = {Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach }, journal = {Physical Review A}, volume = {72}, year = {2005}, month = {2005/9/22}, abstract = { We discuss interacting and non-interacting one dimensional atomic systems trapped in an optical lattice plus a parabolic potential. We show that, in the tight-binding approximation, the non-interacting problem is exactly solvable in terms of Mathieu functions. We use the analytic solutions to study the collective oscillations of ideal bosonic and fermionic ensembles induced by small displacements of the parabolic potential. We treat the interacting boson problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From analysis of the dependence upon lattice depth of the low-energy excitation spectrum of the interacting system, we consider the problems of "fermionization" of a Bose gas, and the superfluid-Mott insulator transition. The spectrum of the noninteracting system turns out to provide a useful guide to understanding the collective oscillations of the interacting system, throughout a large and experimentally relevant parameter regime. }, doi = {10.1103/PhysRevA.72.033616}, url = {http://arxiv.org/abs/cond-mat/0503477v2}, author = {Ana Maria Rey and Guido Pupillo and Charles W. Clark and Carl J. Williams} } @article {1251, title = {Unified derivations of measurement-based schemes for quantum computation}, journal = {Physical Review A}, volume = {71}, year = {2005}, month = {2005/3/17}, abstract = { We present unified, systematic derivations of schemes in the two known measurement-based models of quantum computation. The first model (introduced by Raussendorf and Briegel [Phys. Rev. Lett., 86, 5188 (2001)]) uses a fixed entangled state, adaptive measurements on single qubits, and feedforward of the measurement results. The second model (proposed by Nielsen [Phys. Lett. A, 308, 96 (2003)] and further simplified by Leung [Int. J. Quant. Inf., 2, 33 (2004)]) uses adaptive two-qubit measurements that can be applied to arbitrary pairs of qubits, and feedforward of the measurement results. The underlying principle of our derivations is a variant of teleportation introduced by Zhou, Leung, and Chuang [Phys. Rev. A, 62, 052316 (2000)]. Our derivations unify these two measurement-based models of quantum computation and provide significantly simpler schemes. }, doi = {10.1103/PhysRevA.71.032318}, url = {http://arxiv.org/abs/quant-ph/0404132v2}, author = {Andrew M. Childs and Debbie W. Leung and Michael A. Nielsen} } @article {1288, title = {Adiabatic association of ultracold molecules via magnetic field tunable interactions }, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, volume = {37}, year = {2004}, month = {2004/09/14}, pages = {3457 - 3500}, abstract = { We consider in detail the situation of applying a time dependent external magnetic field to a 87Rb atomic Bose-Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of T. Koehler and K. Burnett [Phys. Rev. A 65, 033601 (2002)] to study the efficiency of the association of molecules in a 87Rb Bose-Einstein condensate during a linear passage of the magnetic field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau-Zener, configuration interaction, and two level mean field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose-Einstein condensed gas, provided that the magnetic field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic field strength, and identify the Landau-Zener coefficient determined by F.H. Mies et al. [Phys. Rev. A 61, 022721 (2000)] as the main parameter that controls the efficiency. }, doi = {10.1088/0953-4075/37/17/006}, url = {http://arxiv.org/abs/cond-mat/0312178v5}, author = {Krzysztof Goral and Thorsten Koehler and Simon A. Gardiner and Eite Tiesinga and Paul S. Julienne} } @article {1411, title = {Advantages of high-speed technique for quantum key distribution; reply to quant-ph/0407050 }, year = {2004}, month = {2004/07/18}, abstract = { We respond to a comment on our high-speed technique for the implementation of free-space quantum key distribution (QKD). The model used in the comment assigns inappropriately high link losses to the technique in question. We show that the use of reasonable loss parameters in the model invalidates the comment{\textquoteright}s main conclusion and highlights the benefits of increased transmission rates. }, url = {http://arxiv.org/abs/quant-ph/0407139v1}, author = {J. C. Bienfang and Charles W. Clark and Carl J. Williams and E. W. Hagley and Jesse Wen} } @article {1365, title = {Quantum information processing using localized ensembles of nuclear spins}, year = {2004}, month = {2004/07/23}, abstract = {We describe a technique for quantum information processing based on localized en sembles of nuclear spins. A qubit is identified as the presence or absence of a collective excitation of a mesoscopic ensemble of nuclear spins surrounding a single quantum dot. All single and two-qubit operations can be effected using hyperfine interactions and single-electron spin rotations, hence the proposed scheme avoids gate errors arising from entanglement between spin and orbital degrees of freedom. Ultra-long coherence times of nuclear spins suggest that this scheme could be particularly well suited for applications where long lived memory is essential. }, url = {http://arxiv.org/abs/cond-mat/0407640v2}, author = {J. M. Taylor and G. Giedke and H. Christ and B. Paredes and J. I. Cirac and P. Zoller and M. D. Lukin and A. Imamoglu} } @article {1420, title = {Quantum key distribution with 1.25 Gbps clock synchronization}, journal = {Optics Express}, volume = {12}, year = {2004}, month = {2004/05/17}, pages = {2011}, abstract = { We have demonstrated the exchange of sifted quantum cryptographic key over a 730 meter free-space link at rates of up to 1.0 Mbps, two orders of magnitude faster than previously reported results. A classical channel at 1550 nm operates in parallel with a quantum channel at 845 nm. Clock recovery techniques on the classical channel at 1.25 Gbps enable quantum transmission at up to the clock rate. System performance is currently limited by the timing resolution of our silicon avalanche photodiode detectors. With improved detector resolution, our technique will yield another order of magnitude increase in performance, with existing technology. }, doi = {10.1364/OPEX.12.002011}, url = {http://arxiv.org/abs/quant-ph/0405097v1}, author = {J. C. Bienfang and A. J. Gross and A. Mink and B. J. Hershman and A. Nakassis and X. Tang and R. Lu and D. H. Su and Charles W Clark and Carl J. Williams and E. W. Hagley and Jesse Wen} } @article {1406, title = {Relativistic many-body calculations of electric-dipole matrix elements, lifetimes and polarizabilities in rubidium }, journal = {Physical Review A}, volume = {69}, year = {2004}, month = {2004/2/27}, abstract = { Electric-dipole matrix elements for ns-n{\textquoteright}p, nd-n{\textquoteright}p, and 6d-4f transitions in Rb are calculated using a relativistic all-order method. A third-order calculation is also carried out for these matrix elements to evaluate the importance of the high-order many-body perturbation theory contributions. The all-order matrix elements are used to evaluate lifetimes of ns and np levels with n=6, 7, 8 and nd levels with n=4, 5, 6 for comparison with experiment and to provide benchmark values for these lifetimes. The dynamic polarizabilities are calculated for ns states of rubidium. The resulting lifetime and polarizability values are compared with available theory and experiment. }, doi = {10.1103/PhysRevA.69.022509}, url = {http://arxiv.org/abs/physics/0307057v1}, author = {M. S. Safronova and Carl J. Williams and Charles W. Clark} } @article {1238, title = {Reversible simulation of bipartite product Hamiltonians}, journal = {IEEE Transactions on Information Theory}, volume = {50}, year = {2004}, month = {2004/06/01}, pages = {1189 - 1197}, abstract = { Consider two quantum systems A and B interacting according to a product Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used to simulate each other reversibly (i.e., without efficiency losses) with the help of local unitary operations and local ancillas. Accordingly, all non-local features of a product Hamiltonian -- including the rate at which it can be used to produce entanglement, transmit classical or quantum information, or simulate other Hamiltonians -- depend only upon a single parameter. We identify this parameter and use it to obtain an explicit expression for the entanglement capacity of all product Hamiltonians. Finally, we show how the notion of simulation leads to a natural formulation of measures of the strength of a nonlocal Hamiltonian. }, doi = {10.1109/TIT.2004.828069}, url = {http://arxiv.org/abs/quant-ph/0303097v1}, author = {Andrew M. Childs and Debbie W. Leung and Guifre Vidal} } @article {1419, title = {Scalable quantum computation in systems with Bose-Hubbard dynamics}, journal = {Journal of Modern Optics}, volume = {51}, year = {2004}, month = {2004/02/15}, pages = {2395 - 2404}, abstract = { Several proposals for quantum computation utilize a lattice type architecture with qubits trapped by a periodic potential. For systems undergoing many body interactions described by the Bose-Hubbard Hamiltonian, the ground state of the system carries number fluctuations that scale with the number of qubits. This process degrades the initialization of the quantum computer register and can introduce errors during error correction. In an earlier manuscript we proposed a solution to this problem tailored to the loading of cold atoms into an optical lattice via the Mott Insulator phase transition. It was shown that by adding an inhomogeneity to the lattice and performing a continuous measurement, the unit filled state suitable for a quantum computer register can be maintained. Here, we give a more rigorous derivation of the register fidelity in homogeneous and inhomogeneous lattices and provide evidence that the protocol is effective in the finite temperature regime. }, doi = {10.1080/09500340408231798}, url = {http://arxiv.org/abs/quant-ph/0403052v2}, author = {Guido Pupillo and Ana Maria Rey and Gavin Brennen and Carl J. Williams and Charles W. Clark} } @article {1213, title = {Spatial search and the Dirac equation}, journal = {Physical Review A}, volume = {70}, year = {2004}, month = {2004/10/19}, abstract = { We consider the problem of searching a d-dimensional lattice of N sites for a single marked location. We present a Hamiltonian that solves this problem in time of order sqrt(N) for d>2 and of order sqrt(N) log(N) in the critical dimension d=2. This improves upon the performance of our previous quantum walk search algorithm (which has a critical dimension of d=4), and matches the performance of a corresponding discrete-time quantum walk algorithm. The improvement uses a lattice version of the Dirac Hamiltonian, and thus requires the introduction of spin (or coin) degrees of freedom. }, doi = {10.1103/PhysRevA.70.042312}, url = {http://arxiv.org/abs/quant-ph/0405120v1}, author = {Andrew M. Childs and Jeffrey Goldstone} } @article {1211, title = {Spatial search by quantum walk}, journal = {Physical Review A}, volume = {70}, year = {2004}, month = {2004/8/23}, abstract = { Grover{\textquoteright}s quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup. }, doi = {10.1103/PhysRevA.70.022314}, url = {http://arxiv.org/abs/quant-ph/0306054v2}, author = {Andrew M. Childs and Jeffrey Goldstone} } @article {1311, title = {Why the quantum?}, year = {2004}, month = {2004/02/20}, abstract = { This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints (Foundations of Physics 33, 1561-1591 (2003); quant-ph/0211089). I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the information-theoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the information-theoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information. }, url = {http://arxiv.org/abs/quant-ph/0402149v1}, author = {Jeffrey Bub} } @article {1414, title = {Bogoliubov approach to superfluidity of atoms in an optical lattice}, journal = {Journal of Physics B: Atomic, Molecular and Optical Physics}, volume = {36}, year = {2003}, month = {2003/03/14}, pages = {825 - 841}, abstract = { We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This enables us to explore the connection between the quantum depletion of the condensate and the quasi-momentum distribution on the one hand and the superfluid fraction on the other. The approach to the insulator phase may be characterized through the filling of the band by quantum depletion, which should be directly observable via the matter wave interference patterns. We complement these findings by self-consistent Hartree-Fock-Bogoliubov-Popov calculations for one-dimensional lattices including the effects of a parabolic trapping potential. }, doi = {10.1088/0953-4075/36/5/304}, url = {http://arxiv.org/abs/cond-mat/0210550v2}, author = {Ana Maria Rey and Keith Burnett and Robert Roth and Mark Edwards and Carl J. Williams and Charles W. Clark} } @article {1321, title = {Can quantum cryptography imply quantum mechanics? Reply to Smolin}, year = {2003}, month = {2003/11/11}, abstract = { Clifton, Bub, and Halvorson (CBH) have argued that quantum mechanics can be derived from three cryptographic, or broadly information-theoretic, axioms. But Smolin disagrees, and he has given a toy theory that he claims is a counterexample. Here we show that Smolin{\textquoteright}s toy theory violates an independence condition for spacelike separated systems that was assumed in the CBH argument. We then argue that any acceptable physical theory should satisfy this independence condition. }, url = {http://arxiv.org/abs/quant-ph/0311065v1}, author = {Hans Halvorson and Jeffrey Bub} } @article {1366, title = {Controlling a mesoscopic spin environment by quantum bit manipulation}, journal = {Physical Review Letters}, volume = {91}, year = {2003}, month = {2003/12/10}, abstract = {We present a unified description of cooling and manipulation of a mesoscopic bath of nuclear spins via coupling to a single quantum system of electronic spin (quantum bit). We show that a bath cooled by the quantum bit rapidly saturates. Although the resulting saturated states of the spin bath ({\textquoteleft}{\textquoteleft}dark states{\textquoteright}{\textquoteright}) generally have low degrees of polarization and purity, their symmetry properties make them a valuable resource for the coherent manipulation of quantum bits. Specifically, we demonstrate that the dark states of nuclear ensembles can be used to coherently control the system-bath interaction and to provide a robust, long-lived quantum memory for qubit states. }, doi = {10.1103/PhysRevLett.91.246802}, url = {http://arxiv.org/abs/cond-mat/0308459v1}, author = {J. M. Taylor and A. Imamoglu and M. D. Lukin} } @conference {1773, title = {Language-reconfigurable universal phone recognition}, booktitle = {Eighth European Conference on Speech Communication and Technology}, year = {2003}, author = {Walker, Brenton D and Lackey, Bradley C and Muller, JS and Schone, Patrick John} } @article {1367, title = {Long-lived memory for mesoscopic quantum bits}, journal = {Physical Review Letters}, volume = {90}, year = {2003}, month = {2003/5/20}, abstract = {We describe a technique to create long-lived quantum memory for quantum bits in mesoscopic systems. Specifically we show that electronic spin coherence can be reversibly mapped onto the collective state of the surrounding nuclei. The coherent transfer can be efficient and fast and it can be used, when combined with standard resonance techniques, to reversibly store coherent superpositions on the time scale of seconds. This method can also allow for {\textquoteleft}{\textquoteleft}engineering{\textquoteright}{\textquoteright} entangled states of nuclear ensembles and efficiently manipulating the stored states. We investigate the feasibility of this method through a detailed analysis of the coherence properties of the system. }, doi = {10.1103/PhysRevLett.90.206803}, url = {http://arxiv.org/abs/cond-mat/0301323v1}, author = {J. M. Taylor and C. M. Marcus and M. D. Lukin} } @article {1250, title = {Lower bounds on the complexity of simulating quantum gates}, journal = {Physical Review A}, volume = {68}, year = {2003}, month = {2003/11/18}, abstract = { We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary n-qubit gates. }, doi = {10.1103/PhysRevA.68.052311}, url = {http://arxiv.org/abs/quant-ph/0307190v1}, author = {Andrew M. Childs and Henry L. Haselgrove and Michael A. Nielsen} } @article {1407, title = {Optimizing the fast Rydberg quantum gate}, journal = {Physical Review A}, volume = {67}, year = {2003}, month = {2003/4/17}, abstract = { The fast phase gate scheme, in which the qubits are atoms confined in sites of an optical lattice, and gate operations are mediated by excitation of Rydberg states, was proposed by Jaksch et al. Phys. Rev. Lett. 85, 2208 (2000). A potential source of decoherence in this system derives from motional heating, which occurs if the ground and Rydberg states of the atom move in different optical lattice potentials. We propose to minimize this effect by choosing the lattice photon frequency \omega so that the ground and Rydberg states have the same frequency-dependent polarizability \alpha(omega). The results are presented for the case of Rb. }, doi = {10.1103/PhysRevA.67.040303}, url = {http://arxiv.org/abs/quant-ph/0212081v1}, author = {M. S. Safronova and Carl J. Williams and Charles W. Clark} } @article {1212, title = {Quantum algorithms for subset finding}, year = {2003}, month = {2003/11/06}, abstract = { Recently, Ambainis gave an O(N^(2/3))-query quantum walk algorithm for element distinctness, and more generally, an O(N^(L/(L+1)))-query algorithm for finding L equal numbers. We point out that this algorithm actually solves a much more general problem, the problem of finding a subset of size L that satisfies any given property. We review the algorithm and give a considerably simplified analysis of its query complexity. We present several applications, including two algorithms for the problem of finding an L-clique in an N-vertex graph. One of these algorithms uses O(N^(2L/(L+1))) edge queries, and the other uses \tilde{O}(N^((5L-2)/(2L+4))), which is an improvement for L <= 5. The latter algorithm generalizes a recent result of Magniez, Santha, and Szegedy, who considered the case L=3 (finding a triangle). We also pose two open problems regarding continuous time quantum walk and lower bounds. }, url = {http://arxiv.org/abs/quant-ph/0311038v2}, author = {Andrew M. Childs and Jason M. Eisenberg} } @article {1408, title = {A Quantum Computer Architecture using Nonlocal Interactions}, journal = {Physical Review A}, volume = {67}, year = {2003}, month = {2003/5/27}, abstract = { Several authors have described the basic requirements essential to build a scalable quantum computer. Because many physical implementation schemes for quantum computing rely on nearest neighbor interactions, there is a hidden quantum communication overhead to connect distant nodes of the computer. In this paper we propose a physical solution to this problem which, together with the key building blocks, provides a pathway to a scalable quantum architecture using nonlocal interactions. Our solution involves the concept of a quantum bus that acts as a refreshable entanglement resource to connect distant memory nodes providing an architectural concept for quantum computers analogous to the von Neumann architecture for classical computers. }, doi = {10.1103/PhysRevA.67.050302}, url = {http://arxiv.org/abs/quant-ph/0301012v2}, author = {Gavin K. Brennen and Daegene Song and Carl J. Williams} } @article {1289, title = {Ultracold collision properties of metastable alkaline-earth atoms}, journal = {Physical Review Letters}, volume = {90}, year = {2003}, month = {2003/2/13}, abstract = { Ultra-cold collisions of spin-polarized 24Mg,40Ca, and 88Sr in the metastable 3P2 excited state are investigated. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The estimates are based on molecular potentials between 3P2 alkaline-earth atoms obtained from ab initio atomic and molecular structure calculations. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive. }, doi = {10.1103/PhysRevLett.90.063002}, url = {http://arxiv.org/abs/physics/0210076v1}, author = {Andrei Derevianko and Sergey G. Porsev and Svetlana Kotochigova and Eite Tiesinga and Paul S. Julienne} } @article {1296, title = {Ultracold Cs$_2$ Feshbach Spectroscopy}, year = {2003}, month = {2003/12/23}, abstract = { We have observed and located more than 60 magnetic field-induced Feshbach resonances in ultracold collisions of ground-state $^{133}$Cs atoms. These resonances are associated with molecular states with up to four units of rotational angular momentum, and are detected through variations in the elastic, inelastic, and radiative collision cross sections. These observations allow us to greatly improve upon the interaction potentials between two cesium atoms and to reproduce the positions of most resonances to accuracies better than 0.5\%. Based on the relevant coupling scheme between the electron spin, nuclear spin, and orbital angular momenta of the nuclei, quantum numbers and energy structure of the molecular states beneath the dissociation continuum are revealed. Finally, we predict the relevant collision properties for cesium Bose-Einstein condensation experiments. }, url = {http://arxiv.org/abs/cond-mat/0312613v2}, author = {Cheng Chin and Vladan Vuletic and Andrew J. Kerman and Steven Chu and Eite Tiesinga and Paul J. Leo and Carl J. Williams} } @article {1210, title = {Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions }, year = {2002}, month = {2002/07/10}, abstract = { We compute the asymptotic entanglement capacity of the Ising interaction ZZ, the anisotropic Heisenberg interaction XX + YY, and more generally, any two-qubit Hamiltonian with canonical form K = a XX + b YY. We also describe an entanglement assisted classical communication protocol using the Hamiltonian K with rate equal to the asymptotic entanglement capacity. }, url = {http://arxiv.org/abs/quant-ph/0207052v2}, author = {Andrew M. Childs and D. W. Leung and F. Verstraete and G. Vidal} } @article {1328, title = {Characterizing quantum theory in terms of information-theoretic constraints}, journal = {Foundations of Physics}, volume = {33}, year = {2002}, month = {2003/11/01}, pages = {1561 - 1591}, abstract = { We show that three fundamental information-theoretic constraints--the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment--suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment. }, doi = {10.1023/A:1026056716397}, url = {http://arxiv.org/abs/quant-ph/0211089v2}, author = {Rob Clifton and Jeffrey Bub and Hans Halvorson} } @article {1263, title = {Exponential algorithmic speedup by quantum walk}, year = {2002}, month = {2002/09/24}, abstract = { We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our oracular setting. We then show how this quantum walk can be used to solve our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve this problem with high probability in subexponential time. }, doi = {10.1145/780542.780552}, url = {http://arxiv.org/abs/quant-ph/0209131v2}, author = {Andrew M. Childs and Richard Cleve and Enrico Deotto and Edward Farhi and Sam Gutmann and Daniel A. Spielman} } @article {1417, title = {{\textquoteleft}Flat Phase{\textquoteright} Loading of a Bose-Einstein Condensate into an Optical Lattice }, journal = {Physical Review A}, volume = {66}, year = {2002}, month = {2002/11/26}, abstract = { It has been proposed that the adiabatic loading of a Bose-Einstein Condensate (BEC) into an optical lattice via the Mott-insulator transition can be used to initialize a quantum computer [D. Jaksch, {\it et al.}, Phys. Rev. Lett. {\bf 81}, 3108 (1998)]. The loading of a BEC into the lattice without causing band excitation is readily achievable; however, unless one switches on an optical lattice very slowly, the optical lattice causes a phase to accumulate across the condensate. We show analytically and numerically that a cancellation of this effect is possible by adjusting the harmonic trap force-constant of the magnetic trap appropriately, thereby facilitating quick loading of an optical lattice for quantum computing purposes. A simple analytical theory is developed for a non-stationary BEC in a harmonic trap. }, doi = {10.1103/PhysRevA.66.053620}, url = {http://arxiv.org/abs/physics/0209071v1}, author = {Shlomo E. Sklarz and Inbal Friedler and David J. Tannor and Yehuda B. Band and Carl J. Williams} } @article {lackey2002gauss, title = {On the Gauss{\textendash}Bonnet Formula in Riemann{\textendash}Finsler Geometry}, journal = {Bulletin of the London Mathematical Society}, volume = {34}, number = {03}, year = {2002}, month = {2002/04/01}, pages = {329{\textendash}340}, publisher = {Cambridge Univ Press}, abstract = {Using Chern{\textquoteright}s method of transgression, the Euler class of a compact orientable Riemann{\textendash}Finsler space is represented by polynomials in the connection and curvature matrices of a torsion-free connection. When using the Chern connection (and hence the Christoffel{\textendash}Levi{\textendash}Civita connection in the Riemannian case), this result extends the Gauss{\textendash}Bonnet formula of Bao and Chern to Finsler spaces whose indicatrices need not have constant volume.}, author = {Brad Lackey} } @article {1310, title = {Maxwell{\textquoteright}s demon and the thermodynamics of computation}, year = {2002}, month = {2002/03/05}, abstract = { It is generally accepted, following Landauer and Bennett, that the process of measurement involves no minimum entropy cost, but the erasure of information in resetting the memory register of a computer to zero requires dissipating heat into the environment. This thesis has been challenged recently in a two-part article by Earman and Norton. I review some relevant observations in the thermodynamics of computation and argue that Earman and Norton are mistaken: there is in principle no entropy cost to the acquisition of information, but the destruction of information does involve an irreducible entropy cost. }, url = {http://arxiv.org/abs/quant-ph/0203017v1}, author = {J. Bub} } @article {1262, title = {Quantum search by measurement}, journal = {Physical Review A}, volume = {66}, year = {2002}, month = {2002/9/23}, abstract = { We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution, in that the goal is to remain in the ground state of a time-varying Hamiltonian. Indeed, we show that the running times of the two algorithms are closely related. We also show how to achieve the quadratic speedup for Grover{\textquoteright}s unstructured search problem with only two measurements. Finally, we discuss some similarities and differences between the adiabatic and measurement algorithms. }, doi = {10.1103/PhysRevA.66.032314}, url = {http://arxiv.org/abs/quant-ph/0204013v1}, author = {Andrew M. Childs and Enrico Deotto and Edward Farhi and Jeffrey Goldstone and Sam Gutmann and Andrew J. Landahl} } @article {1261, title = {Universal simulation of Hamiltonian dynamics for qudits}, journal = {Physical Review A}, volume = {66}, year = {2002}, month = {2002/8/30}, abstract = { What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries. }, doi = {10.1103/PhysRevA.66.022317}, url = {http://arxiv.org/abs/quant-ph/0109064v2}, author = {Michael A. Nielsen and Michael J. Bremner and Jennifer L. Dodd and Andrew M. Childs and Christopher M. Dawson} } @article {1248, title = {Exact sampling from non-attractive distributions using summary states}, journal = {Physical Review E}, volume = {63}, year = {2001}, month = {2001/2/22}, abstract = { Propp and Wilson{\textquoteright}s method of coupling from the past allows one to efficiently generate exact samples from attractive statistical distributions (e.g., the ferromagnetic Ising model). This method may be generalized to non-attractive distributions by the use of summary states, as first described by Huber. Using this method, we present exact samples from a frustrated antiferromagnetic triangular Ising model and the antiferromagnetic q=3 Potts model. We discuss the advantages and limitations of the method of summary states for practical sampling, paying particular attention to the slowing down of the algorithm at low temperature. In particular, we show that such a slowing down can occur in the absence of a physical phase transition. }, doi = {10.1103/PhysRevE.63.036113}, url = {http://arxiv.org/abs/cond-mat/0005132v1}, author = {Andrew M. Childs and Ryan B. Patterson and David J. C. MacKay} } @article {1208, title = {An example of the difference between quantum and classical random walks}, journal = {Quantum Information Processing}, volume = {1}, year = {2001}, month = {2002/04/01}, pages = {35 - 43}, abstract = { In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph, propagation between a particular pair of nodes is exponentially faster in the quantum case. }, doi = {10.1023/A:1019609420309}, url = {http://arxiv.org/abs/quant-ph/0103020v1}, author = {Andrew M. Childs and Edward Farhi and Sam Gutmann} } @article {1249, title = {Realization of quantum process tomography in NMR}, journal = {Physical Review A}, volume = {64}, year = {2001}, month = {2001/6/13}, abstract = { Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic resonance quantum computer. This allows us to measure the fidelity of a controlled-not logic gate and to experimentally investigate the error model for our computer. Based on the latter analysis, we test an important assumption underlying nearly all models of quantum error correction, the independence of errors on different qubits. }, doi = {10.1103/PhysRevA.64.012314}, url = {http://arxiv.org/abs/quant-ph/0012032v1}, author = {Andrew M. Childs and Isaac L. Chuang and Debbie W. Leung} } @article {1209, title = {Robustness of adiabatic quantum computation}, journal = {Physical Review A}, volume = {65}, year = {2001}, month = {2001/12/14}, abstract = { We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic computation against two kinds of errors, unitary control errors and decoherence, and we study this robustness using numerical simulations of the algorithm. }, doi = {10.1103/PhysRevA.65.012322}, url = {http://arxiv.org/abs/quant-ph/0108048v1}, author = {Andrew M. Childs and Edward Farhi and John Preskill} } @article {1204, title = {Secure assisted quantum computation}, year = {2001}, month = {2001/11/07}, abstract = { Suppose Alice wants to perform some computation that could be done quickly on a quantum computer, but she cannot do universal quantum computation. Bob can do universal quantum computation and claims he is willing to help, but Alice wants to be sure that Bob cannot learn her input, the result of her calculation, or perhaps even the function she is trying to compute. We describe a simple, efficient protocol by which Bob can help Alice perform the computation, but there is no way for him to learn anything about it. We also discuss techniques for Alice to detect whether Bob is honestly helping her or if he is introducing errors. }, url = {http://arxiv.org/abs/quant-ph/0111046v2}, author = {Andrew M. Childs} } @article {1308, title = {Secure key distribution via pre- and post-selected quantum states}, journal = {Physical Review A}, volume = {63}, year = {2001}, month = {2001/2/14}, abstract = { A quantum key distribution scheme whose security depends on the features of pre- and post-selected quantum states is described. }, doi = {10.1103/PhysRevA.63.032309}, url = {http://arxiv.org/abs/quant-ph/0006086v3}, author = {J. Bub} } @article {1260, title = {Universal simulation of Markovian quantum dynamics}, journal = {Physical Review A}, volume = {64}, year = {2001}, month = {2001/11/9}, abstract = { Although the conditions for performing arbitrary unitary operations to simulate the dynamics of a closed quantum system are well understood, the same is not true of the more general class of quantum operations (also known as superoperators) corresponding to the dynamics of open quantum systems. We propose a framework for the generation of Markovian quantum dynamics and study the resources needed for universality. For the case of a single qubit, we show that a single nonunitary process is necessary and sufficient to generate all unital Markovian quantum dynamics, whereas a set of processes parametrized by one continuous parameter is needed in general. We also obtain preliminary results for the unital case in higher dimensions. }, doi = {10.1103/PhysRevA.64.062302}, url = {http://arxiv.org/abs/quant-ph/0008070v2}, author = {Dave Bacon and Andrew M. Childs and Isaac L. Chuang and Julia Kempe and Debbie W. Leung and Xinlan Zhou} } @article {1237, title = {Finding cliques by quantum adiabatic evolution}, year = {2000}, month = {2000/12/19}, abstract = { Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph. An n-vertex random graph has each edge included with probability 1/2, and a clique is a completely connected subgraph. There is no known classical algorithm that finds the largest clique in a random graph with high probability and runs in a time polynomial in n. For the small graphs we are able to investigate (n <= 18), the quantum algorithm appears to require only a quadratic run time. }, url = {http://arxiv.org/abs/quant-ph/0012104v1}, author = {Andrew M. Childs and Edward Farhi and Jeffrey Goldstone and Sam Gutmann} } @article {lackey2000metric, title = {Metric Equivalence of Path Spaces}, journal = {Nonlinear Studies}, volume = {7}, number = {2}, year = {2000}, month = {2000/01/01}, abstract = {Local equivalence and the invariants of systems of second order differential equations were studied in a series of papers by Kosambi, Cartan, and Chern. The resulting theory, deemed KCC-theory, is a rich geometric study which in many ways generalizes Riemannian and Finsler geometry. Yet, in many applications one requires a metric structure in addition to the systems of second order differential equations. We pose a geometry which is equipped with both of these structures, and solve the problem of local equivalence and thus determining a preferred connection and finding a generating set for all the invariants of the theory.}, author = {Brad Lackey} } @article {1309, title = {The quantum bit commitment theorem}, year = {2000}, month = {2000/07/25}, abstract = { Unconditionally secure two-party bit commitment based solely on the principles of quantum mechanics (without exploiting special relativistic signalling constraints, or principles of general relativity or thermodynamics) has been shown to be impossible, but the claim is repeatedly challenged. The quantum bit commitment theorem is reviewed here and the central conceptual point, that an {\textquoteleft}Einstein-Podolsky-Rosen{\textquoteright} attack or cheating strategy can always be applied, is clarified. The question of whether following such a cheating strategy can ever be disadvantageous to the cheater is considered and answered in the negative. There is, indeed, no loophole in the theorem. }, url = {http://arxiv.org/abs/quant-ph/0007090v4}, author = {Jeffrey Bub} } @article {1236, title = {Quantum information and precision measurement}, journal = {Journal of Modern Optics}, volume = {47}, year = {2000}, month = {1999/04/07}, pages = {155 - 176}, abstract = { We describe some applications of quantum information theory to the analysis of quantum limits on measurement sensitivity. A measurement of a weak force acting on a quantum system is a determination of a classical parameter appearing in the master equation that governs the evolution of the system; limitations on measurement accuracy arise because it is not possible to distinguish perfectly among the different possible values of this parameter. Tools developed in the study of quantum information and computation can be exploited to improve the precision of physics experiments; examples include superdense coding, fast database search, and the quantum Fourier transform. }, doi = {10.1080/09500340008244034}, url = {http://arxiv.org/abs/quant-ph/9904021v2}, author = {Andrew M. Childs and John Preskill and Joseph Renes} } @article {1207, title = {Universal quantum computation with two-level trapped ions}, journal = {Physical Review A}, volume = {63}, year = {2000}, month = {2000/12/11}, abstract = { Although the initial proposal for ion trap quantum computation made use of an auxiliary internal level to perform logic between ions, this resource is not necessary in principle. Instead, one may perform such operations directly using sideband laser pulses, operating with an arbitrary (sufficiently small) Lamb-Dicke parameter. We explore the potential of this technique, showing how to perform logical operations between the internal state of an ion and the collective motional state and giving explicit constructions for a controlled-not gate between ions. }, doi = {10.1103/PhysRevA.63.012306}, url = {http://arxiv.org/abs/quant-ph/0008065v1}, author = {Andrew M. Childs and Isaac L. Chuang} } @article {1266, title = {On Galilean connections and the first jet bundle}, year = {1999}, month = {1999/09/24}, abstract = { We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as geometries associated to systems of second order ordinary differential equations. We show these Cartan connections admit a form of normal coordinates, and that in these normal coordinates the geodesic equations of the connection are second order ordinary differential equations. We then classify such connections by some of their torsions, extending a classical theorem of Chern involving the geometry associated to a system of second order differential equations. }, url = {http://arxiv.org/abs/math/9909148v1}, author = {James D. E. Grant and Brad Lackey} } @article {lackey1999model, title = {A model of trophodynamics}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {35}, number = {1}, year = {1999}, month = {1999/01/01}, pages = {37{\textendash}57}, publisher = {Pergamon}, doi = {10.1016/S0362-546X(98)00097-2}, author = {Brad Lackey} } @article {1307, title = {Quantum Mechanics as a Principle Theory}, year = {1999}, month = {1999/10/22}, abstract = { I show how quantum mechanics, like the theory of relativity, can be understood as a {\textquoteright}principle theory{\textquoteright} in Einstein{\textquoteright}s sense, and I use this notion to explore the approach to the problem of interpretation developed in my book Interpreting the Quantum World (Cambridge: Cambridge University Press, 1999). }, url = {http://arxiv.org/abs/quant-ph/9910096v1}, author = {Jeffrey Bub} } @article {1775, title = {Randers surfaces whose Laplacians have completely positive symbol}, journal = {Nonlinear Analysis: Theory, Methods \& Applications}, volume = {38}, year = {1999}, pages = {27{\textendash}40}, author = {Bao, David and Lackey, Brad} } @article {1327, title = {Revised Proof of the Uniqueness Theorem for {\textquoteright}No Collapse{\textquoteright} Interpretations of Quantum Mechanics }, year = {1999}, month = {1999/10/22}, abstract = { We show that the Bub-Clifton uniqueness theorem for {\textquoteright}no collapse{\textquoteright} interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the {\textquoteright}weak separability{\textquoteright} assumption. }, url = {http://arxiv.org/abs/quant-ph/9910097v1}, author = {Jeffrey Bub and Rob Clifton and Sheldon Goldstein} } @inbook {1778, title = {A Bochner Vanishing Theorem for Elliptic Complexes}, booktitle = {The Theory of Finslerian Laplacians and Applications}, year = {1998}, pages = {199{\textendash}226}, publisher = {Springer}, organization = {Springer}, author = {Lackey, Brad} } @inbook {1776, title = {A geometric inequality and a Weitzenboeck formula for Finsler surfaces}, booktitle = {The Theory of Finslerian Laplacians and Applications}, year = {1998}, pages = {245{\textendash}275}, publisher = {Springer}, organization = {Springer}, author = {Bao, David and Lackey, Brad} } @inbook {1777, title = {A Lichnerowicz Vanishing Theorem for Finsler Spaces}, booktitle = {The Theory of Finslerian Laplacians and Applications}, year = {1998}, pages = {227{\textendash}243}, publisher = {Springer}, organization = {Springer}, author = {Lackey, Brad} } @article {bao1996hodge, title = {A Hodge decomposition theorem for Finsler spaces}, journal = {Comptes rendus de l{\textquoteright}Acad{\'e}mie des sciences. S{\'e}rie 1, Math{\'e}matique}, volume = {323}, number = {1}, year = {1996}, month = {1996/01/01}, pages = {51{\textendash}56}, publisher = {Elsevier}, abstract = {Soit (M,F) une vari\e{\textquoteright}t{\'e} finsl{\'e}rienne compacte sans bord. On donne une condition n{\'e}cessaire et suffisante, portant sur le tenseur fondamental, afin q{\textquoteright}une forme diff{\'e}rentielle ext{\'e}rieure de M soit harmonique. On introduit aussi le laplacien sur M et on d{\'e}montre l{\textquoteright}analoque du th{\'e}or{\`e}me de Hodge dans le cas finsl{\'e}rien.}, author = {Bao, David and Brad Lackey} } @article {1779, title = {Special eigenforms on the sphere bundle of a Finsler manifold}, journal = {Contemporary Mathematics}, volume = {196}, year = {1996}, pages = {67{\textendash}78}, author = {Bao, David and Lackey, Brad} }