@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 {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 {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 {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 {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 {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 {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 {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 {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 {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 {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 {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 {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 {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 {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} } @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 {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 {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<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 {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 {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 {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 {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} }