TY - JOUR T1 - Estimation of Hamiltonian parameters from thermal states Y1 - 2024 A1 - Luis Pedro García-Pintos A1 - Kishor Bharti A1 - Jacob Bringewatt A1 - Hossein Dehghani A1 - Adam Ehrenberg A1 - Nicole Yunger Halpern A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2401.10343 ER - TY - JOUR T1 - Accelerating Progress Towards Practical Quantum Advantage: The Quantum Technology Demonstration Project Roadmap Y1 - 2023 A1 - Paul Alsing A1 - Phil Battle A1 - Joshua C. Bienfang A1 - Tammie Borders A1 - Tina Brower-Thomas A1 - Lincoln D. Carr A1 - Fred Chong A1 - Siamak Dadras A1 - Brian DeMarco A1 - Ivan Deutsch A1 - Eden Figueroa A1 - Danna Freedman A1 - Henry Everitt A1 - Daniel Gauthier A1 - Ezekiel Johnston-Halperin A1 - Jungsang Kim A1 - Mackillo Kira A1 - Prem Kumar A1 - Paul Kwiat A1 - John Lekki A1 - Anjul Loiacono A1 - Marko Lončar A1 - John R. Lowell A1 - Mikhail Lukin A1 - Celia Merzbacher A1 - Aaron Miller A1 - Christopher Monroe A1 - Johannes Pollanen A1 - David Pappas A1 - Michael Raymer A1 - Ronald Reano A1 - Brandon Rodenburg A1 - Martin Savage A1 - Thomas Searles A1 - Jun Ye AB -

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

UR - https://arxiv.org/abs/2210.14757 ER - TY - JOUR T1 - Accurate and Honest Approximation of Correlated Qubit Noise Y1 - 2023 A1 - F. Setiawan A1 - Alexander V. Gramolin A1 - Elisha S. Matekole A1 - Hari Krovi A1 - Jacob M. Taylor AB -

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

UR - https://arxiv.org/abs/2311.09305 ER - TY - JOUR T1 - Advantages and limitations of quantum routing JF - PRX Quantum Y1 - 2023 A1 - Bapat, Aniruddha A1 - Andrew M. Childs A1 - Alexey V. Gorshkov A1 - Schoute, Eddie KW - Data Structures and Algorithms (cs.DS) KW - FOS: Computer and information sciences KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

VL - 4 UR - https://arxiv.org/abs/2206.01766 CP - 010313 U5 - https://doi.org/10.1103/PRXQuantum.4.010313 ER - TY - JOUR T1 - Bell sampling from quantum circuits Y1 - 2023 A1 - Dominik Hangleiter A1 - Michael J. Gullans AB -

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

UR - https://arxiv.org/abs/2306.00083 ER - TY - JOUR T1 - Bell sampling from quantum circuits Y1 - 2023 A1 - Dominik Hangleiter A1 - Michael J. Gullans AB -

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

UR - https://arxiv.org/abs/2306.00083 ER - TY - JOUR T1 - Bounds on Autonomous Quantum Error Correction Y1 - 2023 A1 - Oles Shtanko A1 - Yu-Jie Liu A1 - Simon Lieu A1 - Alexey V. Gorshkov A1 - Victor V. Albert AB -

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

UR - https://arxiv.org/abs/2308.16233 ER - TY - JOUR T1 - Candidate for a passively protected quantum memory in two dimensions Y1 - 2023 A1 - Simon Lieu A1 - Yu-Jie Liu A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2205.09767 ER - TY - JOUR T1 - Complexity and order in approximate quantum error-correcting codes Y1 - 2023 A1 - Jinmin Yi A1 - Weicheng Ye A1 - Daniel Gottesman A1 - Zi-Wen Liu AB -

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

UR - https://arxiv.org/abs/2310.04710 ER - TY - JOUR T1 - Compressed gate characterization for quantum devices with time-correlated noise Y1 - 2023 A1 - M. J. Gullans A1 - M. Caranti A1 - A. R. Mills A1 - J. R. Petta AB -

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

UR - https://arxiv.org/abs/2307.14432 ER - TY - JOUR T1 - Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits JF - Physical Review B Y1 - 2023 A1 - Shayan Majidy A1 - Utkarsh Agrawal A1 - Sarang Gopalakrishnan A1 - Andrew C. Potter A1 - Romain Vasseur A1 - Nicole Yunger Halpern AB -

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

VL - 108 UR - https://arxiv.org/abs/2305.13356 U5 - 10.1103/physrevb.108.054307 ER - TY - RPRT T1 - Data Needs and Challenges of Quantum Dot Devices Automation: Workshop Report Y1 - 2023 A1 - Justyna P. Zwolak A1 - Jacob M. Taylor A1 - Reed Andrews A1 - Jared Benson A1 - Garnett Bryant A1 - Donovan Buterakos A1 - Anasua Chatterjee A1 - Sankar Das Sarma A1 - Mark A. Eriksson A1 - Eliška Greplová A1 - Michael J. Gullans A1 - Fabian Hader A1 - Tyler J. Kovach A1 - Pranav S. Mundada A1 - Mick Ramsey A1 - Torbjoern Rasmussen A1 - Brandon Severin A1 - Anthony Sigillito A1 - Brennan Undseth A1 - Brian Weber AB -

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

UR - https://arxiv.org/abs/2312.14322 U5 - https://doi.org/10.48550/arXiv.2312.14322 ER - TY - JOUR T1 - DiVincenzo-like criteria for autonomous quantum machines Y1 - 2023 A1 - José Antonio Marín Guzmán A1 - Paul Erker A1 - Simone Gasparinetti A1 - Marcus Huber A1 - Nicole Yunger Halpern AB -

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

UR - https://arxiv.org/abs/2307.08739 ER - TY - JOUR T1 - Effect of non-unital noise on random circuit sampling Y1 - 2023 A1 - Bill Fefferman A1 - Soumik Ghosh A1 - Michael Gullans A1 - Kohdai Kuroiwa A1 - Kunal Sharma AB -

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

UR - https://arxiv.org/abs/2306.16659 ER - TY - JOUR T1 - Error Mitigation Thresholds in Noisy Quantum Circuits Y1 - 2023 A1 - Pradeep Niroula A1 - Sarang Gopalakrishnan A1 - Michael J. Gullans AB -

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

UR - https://arxiv.org/abs/2302.04278 ER - TY - JOUR T1 - Fault-tolerant hyperbolic Floquet quantum error correcting codes Y1 - 2023 A1 - Ali Fahimniya A1 - Hossein Dehghani A1 - Kishor Bharti A1 - Sheryl Mathew A1 - Alicia J. Kollár A1 - Alexey V. Gorshkov A1 - Michael J. Gullans AB -

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

UR - https://arxiv.org/abs/2309.10033 ER - TY - JOUR T1 - Fault-Tolerant Quantum Memory using Low-Depth Random Circuit Codes Y1 - 2023 A1 - Jon Nelson A1 - Gregory Bentsen A1 - Steven T. Flammia A1 - Michael J. Gullans AB -

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

UR - https://arxiv.org/abs/2311.17985 ER - TY - CONF T1 - Fixing and Mechanizing the Security Proof of Fiat-Shamir with Aborts and Dilithium T2 - Advances in Cryptology – CRYPTO 2023 Y1 - 2023 A1 - Barbosa, Manuel A1 - Barthe, Gilles A1 - Doczkal, Christian A1 - Don, Jelle A1 - Fehr, Serge A1 - Grégoire, Benjamin A1 - Huang, Yu-Hsuan A1 - Hülsing, Andreas A1 - Lee, Yi A1 - Wu, Xiaodi ED - Handschuh, Helena ED - Lysyanskaya, Anna AB -

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

JA - Advances in Cryptology – CRYPTO 2023 PB - Springer Nature Switzerland CY - Cham SN - 978-3-031-38554-4 ER - TY - JOUR T1 - A general approach to backaction-evading receivers with magnetomechanical and electromechanical sensors Y1 - 2023 A1 - Brittany Richman A1 - Sohitri Ghosh A1 - Daniel Carney A1 - Gerard Higgins A1 - Peter Shawhan A1 - C. J. Lobb A1 - Jacob M. Taylor AB -

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

UR - https://arxiv.org/abs/2311.09587 ER - TY - JOUR T1 - Generalized Hybrid Search and Applications to Blockchain and Hash Function Security Y1 - 2023 A1 - Alexandru Cojocaru A1 - Juan Garay A1 - Fang Song AB -

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

UR - arXiv:2311.03723 ER - TY - JOUR T1 - High-Energy Collision of Quarks and Hadrons in the Schwinger Model: From Tensor Networks to Circuit QED Y1 - 2023 A1 - Ron Belyansky A1 - Seth Whitsitt A1 - Niklas Mueller A1 - Ali Fahimniya A1 - Elizabeth R. Bennewitz A1 - Zohreh Davoudi A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2307.02522 ER - TY - JOUR T1 - Improved Digital Quantum Simulation by Non-Unitary Channels Y1 - 2023 A1 - W. Gong A1 - Yaroslav Kharkov A1 - Minh C. Tran A1 - Przemyslaw Bienias A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2307.13028 ER - TY - JOUR T1 - Ion Trap with In-Vacuum High Numerical Aperture Imaging for a Dual-Species Modular Quantum Computer Y1 - 2023 A1 - Allison L. Carter A1 - Jameson O'Reilly A1 - George Toh A1 - Sagnik Saha A1 - Mikhail Shalaev A1 - Isabella Goetting A1 - Christopher Monroe AB -

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

UR - https://arxiv.org/abs/2310.07058 ER - TY - JOUR T1 - Logical quantum processor based on reconfigurable atom arrays JF - Nature Y1 - 2023 A1 - Bluvstein, Dolev A1 - Evered, Simon J. A1 - Geim, Alexandra A. A1 - Li, Sophie H. A1 - Zhou, Hengyun A1 - Manovitz, Tom A1 - Ebadi, Sepehr A1 - Cain, Madelyn A1 - Kalinowski, Marcin A1 - Hangleiter, Dominik A1 - Ataides, J. Pablo Bonilla A1 - Maskara, Nishad A1 - Cong, Iris A1 - Gao, Xun A1 - Rodriguez, Pedro Sales A1 - Karolyshyn, Thomas A1 - Semeghini, Giulia A1 - Gullans, Michael J. A1 - Greiner, Markus A1 - Vuletic, Vladan A1 - Lukin, Mikhail D. UR - https://arxiv.org/abs/2312.03982 U5 - 10.1038/s41586-023-06927-3 ER - TY - JOUR T1 - Lower Bounds on Quantum Annealing Times JF - Phys. Rev. Lett. Y1 - 2023 A1 - García-Pintos, Luis Pedro A1 - Brady, Lucas T. A1 - Bringewatt, Jacob A1 - Liu, Yi-Kai KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

VL - 130 UR - https://arxiv.org/abs/2210.15687 CP - 140601 U5 - https://doi.org/10.1103/PhysRevLett.130.140601 ER - TY - JOUR T1 - The maximum refractive index of an atomic crystal - from quantum optics to quantum chemistry Y1 - 2023 A1 - Francesco Andreoli A1 - Bennet Windt A1 - Stefano Grava A1 - Gian Marcello Andolina A1 - Michael J. Gullans A1 - Alexander A. High A1 - Darrick E. Chang AB -

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

UR - https://arxiv.org/abs/2303.10998 ER - TY - JOUR T1 - Minimum-entanglement protocols for function estimation JF - Physical Review Research Y1 - 2023 A1 - Adam Ehrenberg A1 - Jacob Bringewatt A1 - Alexey V. Gorshkov AB -

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

VL - 5 UR - https://arxiv.org/abs/2110.07613 U5 - 10.1103/physrevresearch.5.033228 ER - TY - JOUR T1 - Non-equilibrium critical scaling and universality in a quantum simulator Y1 - 2023 A1 - A. De A1 - P. Cook A1 - K. Collins A1 - W. Morong A1 - D. Paz A1 - P. Titum A1 - G. Pagano A1 - A. V. Gorshkov A1 - M. Maghrebi A1 - C. Monroe AB -

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

UR - https://arxiv.org/abs/2309.10856 ER - TY - JOUR T1 - Observation of a finite-energy phase transition in a one-dimensional quantum simulator Y1 - 2023 A1 - Alexander Schuckert A1 - Or Katz A1 - Lei Feng A1 - Eleanor Crane A1 - Arinjoy De A1 - Mohammad Hafezi A1 - Alexey V. Gorshkov A1 - Christopher Monroe AB -

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

UR - https://arxiv.org/abs/2310.19869 ER - TY - JOUR T1 - Page curves and typical entanglement in linear optics JF - Quantum Y1 - 2023 A1 - Joseph T. Iosue A1 - Adam Ehrenberg A1 - Dominik Hangleiter A1 - Abhinav Deshpande A1 - Alexey V. Gorshkov AB -

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 Rényi-2 Page curve (the average Rényi-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 Rényi-2 entropy by studying its variance. Using the aforementioned results for the Rényi-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.

VL - 7 U4 - 1017 UR - https://arxiv.org/abs/2209.06838 U5 - 10.22331/q-2023-05-23-1017 ER - TY - JOUR T1 - Partial Syndrome Measurement for Hypergraph Product Codes Y1 - 2023 A1 - Noah Berthusen A1 - Daniel Gottesman AB -

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.

UR - https://arxiv.org/abs/2306.17122 ER - TY - JOUR T1 - Precision Bounds on Continuous-Variable State Tomography using Classical Shadows Y1 - 2023 A1 - Srilekha Gandhari A1 - Victor V. Albert A1 - Thomas Gerrits A1 - Jacob M. Taylor A1 - Michael J. Gullans AB -

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 (PNR), and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with a high probability, we show that homodyne detection requires an order O(N4+1/3) measurements in the worst case, whereas PNR and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental homodyne tomography significantly outperforms our bounds, exhibiting a more typical scaling of the number of measurements that is close to linear in N. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements.

UR - https://arxiv.org/abs/2211.05149 ER - TY - JOUR T1 - Projective toric designs, difference sets, and quantum state designs Y1 - 2023 A1 - Joseph T. Iosue A1 - T. C. Mooney A1 - Adam Ehrenberg A1 - Alexey V. Gorshkov AB -

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.

UR - https://arxiv.org/abs/2311.13479 ER - TY - JOUR T1 - Quantum Algorithms and the Power of Forgetting JF - 14th Innovations in Theoretical Computer Science Conference (ITCS 2023) Y1 - 2023 A1 - Andrew M. Childs A1 - Coudron, Matthew A1 - Gilani, Amin Shiraz ED - Tauman Kalai, Yael AB -

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

VL - 251 U4 - 37:1--37:22 SN - 978-3-95977-263-1 UR - https://drops.dagstuhl.de/opus/volltexte/2023/17540 U5 - 10.4230/LIPIcs.ITCS.2023.37 ER - TY - JOUR T1 - Quantum Algorithms for Simulating Nuclear Effective Field Theories Y1 - 2023 A1 - James D. Watson A1 - Jacob Bringewatt A1 - Alexander F. Shaw A1 - Andrew M. Childs A1 - Alexey V. Gorshkov A1 - Zohreh Davoudi AB -

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

UR - https://arxiv.org/abs/2312.05344 ER - TY - JOUR T1 - Quantum Lego Expansion Pack: Enumerators from Tensor Networks Y1 - 2023 A1 - ChunJun Cao A1 - Michael J. Gullans A1 - Brad Lackey A1 - Zitao Wang AB -

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

UR - https://arxiv.org/abs/2308.05152 ER - TY - JOUR T1 - Quantum Sensing with Erasure Qubits Y1 - 2023 A1 - Pradeep Niroula A1 - Jack Dolde A1 - Xin Zheng A1 - Jacob Bringewatt A1 - Adam Ehrenberg A1 - Kevin C. Cox A1 - Jeff Thompson A1 - Michael J. Gullans A1 - Shimon Kolkowitz A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2310.01512 ER - TY - JOUR T1 - Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions Y1 - 2023 A1 - Yuri Alexeev A1 - Maximilian Amsler A1 - Paul Baity A1 - Marco Antonio Barroca A1 - Sanzio Bassini A1 - Torey Battelle A1 - Daan Camps A1 - David Casanova A1 - Young jai Choi A1 - Frederic T. Chong A1 - Charles Chung A1 - Chris Codella A1 - Antonio D. Corcoles A1 - James Cruise A1 - Alberto Di Meglio A1 - Jonathan Dubois A1 - Ivan Duran A1 - Thomas Eckl A1 - Sophia Economou A1 - Stephan Eidenbenz A1 - Bruce Elmegreen A1 - Clyde Fare A1 - Ismael Faro A1 - Cristina Sanz Fernández A1 - Rodrigo Neumann Barros Ferreira A1 - Keisuke Fuji A1 - Bryce Fuller A1 - Laura Gagliardi A1 - Giulia Galli A1 - Jennifer R. Glick A1 - Isacco Gobbi A1 - Pranav Gokhale A1 - Salvador de la Puente Gonzalez A1 - Johannes Greiner A1 - Bill Gropp A1 - Michele Grossi A1 - Emmanuel Gull A1 - Burns Healy A1 - Benchen Huang A1 - Travis S. Humble A1 - Nobuyasu Ito A1 - Artur F. Izmaylov A1 - Ali Javadi-Abhari A1 - Douglas Jennewein A1 - Shantenu Jha A1 - Liang Jiang A1 - Barbara Jones A1 - Wibe Albert de Jong A1 - Petar Jurcevic A1 - William Kirby A1 - Stefan Kister A1 - Masahiro Kitagawa A1 - Joel Klassen A1 - Katherine Klymko A1 - Kwangwon Koh A1 - Masaaki Kondo A1 - Doga Murat Kurkcuoglu A1 - Krzysztof Kurowski A1 - Teodoro Laino A1 - Ryan Landfield A1 - Matt Leininger A1 - Vicente Leyton-Ortega A1 - Ang Li A1 - Meifeng Lin A1 - Junyu Liu A1 - Nicolas Lorente A1 - Andre Luckow A1 - Simon Martiel A1 - Francisco Martin-Fernandez A1 - Margaret Martonosi A1 - Claire Marvinney A1 - Arcesio Castaneda Medina A1 - Dirk Merten A1 - Antonio Mezzacapo A1 - Kristel Michielsen A1 - Abhishek Mitra A1 - Tushar Mittal A1 - Kyungsun Moon A1 - Joel Moore A1 - Mario Motta A1 - Young-Hye Na A1 - Yunseong Nam A1 - Prineha Narang A1 - Yu-ya Ohnishi A1 - Daniele Ottaviani A1 - Matthew Otten A1 - Scott Pakin A1 - Vincent R. Pascuzzi A1 - Ed Penault A1 - Tomasz Piontek A1 - Jed Pitera A1 - Patrick Rall A1 - Gokul Subramanian Ravi A1 - Niall Robertson A1 - Matteo Rossi A1 - Piotr Rydlichowski A1 - Hoon Ryu A1 - Georgy Samsonidze A1 - Mitsuhisa Sato A1 - Nishant Saurabh A1 - Vidushi Sharma A1 - Kunal Sharma A1 - Soyoung Shin A1 - George Slessman A1 - Mathias Steiner A1 - Iskandar Sitdikov A1 - In-Saeng Suh A1 - Eric Switzer A1 - Wei Tang A1 - Joel Thompson A1 - Synge Todo A1 - Minh Tran A1 - Dimitar Trenev A1 - Christian Trott A1 - Huan-Hsin Tseng A1 - Esin Tureci A1 - David García Valinas A1 - Sofia Vallecorsa A1 - Christopher Wever A1 - Konrad Wojciechowski A1 - Xiaodi Wu A1 - Shinjae Yoo A1 - Nobuyuki Yoshioka A1 - Victor Wen-zhe Yu A1 - Seiji Yunoki A1 - Sergiy Zhuk A1 - Dmitry Zubarev AB -

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

UR - https://arxiv.org/abs/2312.09733 ER - TY - JOUR T1 - Realization of 1D Anyons with Arbitrary Statistical Phase Y1 - 2023 A1 - Joyce Kwan A1 - Perrin Segura A1 - Yanfei Li A1 - Sooshin Kim A1 - Alexey V. Gorshkov A1 - André Eckardt A1 - Brice Bakkali-Hassani A1 - Markus Greiner AB -

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

UR - https://arxiv.org/abs/2306.01737 ER - TY - JOUR T1 - Self-dual quasiperiodic percolation JF - Phys. Rev. E Y1 - 2023 A1 - Sommers, Grace M. A1 - Gullans, Michael J. A1 - Huse, David A. AB -

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

VL - 107 U4 - 024137 UR - https://arxiv.org/abs/2206.11290 U5 - 10.1103/PhysRevE.107.024137 ER - TY - JOUR T1 - A sharp phase transition in linear cross-entropy benchmarking Y1 - 2023 A1 - Brayden Ware A1 - Abhinav Deshpande A1 - Dominik Hangleiter A1 - Pradeep Niroula A1 - Bill Fefferman A1 - Alexey V. Gorshkov A1 - Michael J. Gullans AB -

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

UR - https://arxiv.org/abs/2305.04954 ER - TY - JOUR T1 - Thermally driven quantum refrigerator autonomously resets superconducting qubit Y1 - 2023 A1 - Mohammed Ali Aamir A1 - Paul Jamet Suria A1 - José Antonio Marín Guzmán A1 - Claudia Castillo-Moreno A1 - Jeffrey M. Epstein A1 - Nicole Yunger Halpern A1 - Simone Gasparinetti AB -

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

UR - https://arxiv.org/abs/2305.16710 ER - TY - JOUR T1 - Thresholds in the Robustness of Error Mitigation in Noisy Quantum Dynamics Y1 - 2023 A1 - Pradeep Niroula A1 - Sarang Gopalakrishnan A1 - Michael J. Gullans AB -

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

UR - https://arxiv.org/abs/2302.04278 ER - TY - JOUR T1 - Transition of Anticoncentration in Gaussian Boson Sampling Y1 - 2023 A1 - Adam Ehrenberg A1 - Joseph T. Iosue A1 - Abhinav Deshpande A1 - Dominik Hangleiter A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2312.08433 ER - TY - JOUR T1 - A Watermark for Large Language Models Y1 - 2023 A1 - John Kirchenbauer A1 - Jonas Geiping A1 - Yuxin Wen A1 - Jonathan Katz A1 - Ian Miers A1 - Tom Goldstein AB -

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

UR - https://arxiv.org/abs/2301.10226 ER - TY - JOUR T1 - Accurate and Efficient Quantum Computations of Molecular Properties Using Daubechies Wavelet Molecular Orbitals: A Benchmark Study against Experimental Data JF - PRX Quantum Y1 - 2022 A1 - Cheng-Lin Hong A1 - Ting Tsai A1 - Jyh-Pin Chou A1 - Peng-Jen Chen A1 - Pei-Kai Tsai A1 - Yu-Cheng Chen A1 - En-Jui Kuo A1 - David Srolovitz A1 - Alice Hu A1 - Yuan-Chung Cheng A1 - Hsi-Sheng Goan AB -

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

VL - 3 U4 - 020360 UR - https://arxiv.org/abs/2205.14476 U5 - https://doi.org/10.1103/PRXQuantum.3.020360 ER - TY - JOUR T1 - Boson Sampling for Generalized Bosons Y1 - 2022 A1 - En-Jui Kuo A1 - Yijia Xu A1 - Dominik Hangleiter A1 - Andrey Grankin A1 - Mohammad Hafezi AB -

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

UR - https://arxiv.org/abs/2204.08389 ER - TY - JOUR T1 - Bosonic Qiskit Y1 - 2022 A1 - Stavenger, Timothy J A1 - Crane, Eleanor A1 - Smith, Kevin A1 - Kang, Christopher T A1 - Girvin, Steven M A1 - Wiebe, Nathan KW - Emerging Technologies (cs.ET) KW - FOS: Computer and information sciences KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2209.11153 U5 - 10.48550/ARXIV.2209.11153 ER - TY - JOUR T1 - Bounding the Minimum Time of a Quantum Measurement Y1 - 2022 A1 - Shettell, Nathan A1 - Centrone, Federico A1 - García-Pintos, Luis Pedro KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2209.06248 U5 - 10.48550/ARXIV.2209.06248 ER - TY - JOUR T1 - Candidate for a self-correcting quantum memory in two dimensions Y1 - 2022 A1 - Simon Lieu A1 - Yu-Jie Liu A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2205.09767 ER - TY - JOUR T1 - Clifford-deformed Surface Codes Y1 - 2022 A1 - Dua, Arpit A1 - Kubica, Aleksander A1 - Jiang, Liang A1 - Flammia, Steven T. A1 - Michael Gullans KW - Disordered Systems and Neural Networks (cond-mat.dis-nn) KW - FOS: Physical sciences KW - Mesoscale and Nanoscale Physics (cond-mat.mes-hall) KW - Quantum Physics (quant-ph) KW - Statistical Mechanics (cond-mat.stat-mech) AB -

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

UR - https://arxiv.org/abs/2201.07802 U5 - 10.48550/ARXIV.2201.07802 ER - TY - JOUR T1 - Closing the Locality and Detection Loopholes in Multiparticle Entanglement Self-Testing JF - Physical Review Letters Y1 - 2022 A1 - Dian Wu A1 - Qi Zhao A1 - Can Wang A1 - Liang Huang A1 - Yang-Fan Jiang A1 - Bing Bai A1 - You Zhou A1 - Xue-Mei Gu A1 - Feng-Ming Liu A1 - Ying-Qiu Mao A1 - Qi-Chao Sun A1 - Ming-Cheng Chen A1 - Jun Zhang A1 - Cheng-Zhi Peng A1 - Xiao-Bo Zhu A1 - Qiang Zhang A1 - Chao-Yang Lu A1 - Jian-Wei Pan AB -

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

VL - 128 U4 - 250401 UR - https://www.researchgate.net/profile/Dian-Wu/publication/361497881_Closing_the_Locality_and_Detection_Loopholes_in_Multiparticle_Entanglement_Self-Testing/links/62b55a8c1010dc02cc57530c/Closing-the-Locality-and-Detection-Loopholes-in-Multiparticle-Entangl CP - 25 U5 - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.128.250401 ER - TY - JOUR T1 - Combining machine learning with physics: A framework for tracking and sorting multiple dark solitons JF - Phys. Rev. Research Y1 - 2022 A1 - Shangjie Guo A1 - Sophia M. Koh A1 - Amilson R. Fritsch A1 - I. B. Spielman A1 - Justyna P. Zwolak AB -

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

VL - 4 U4 - 023163 UR - https://arxiv.org/abs/2111.04881 U5 - https://doi.org/10.1103/PhysRevResearch.4.023163 ER - TY - JOUR T1 - Continuous Symmetry Breaking in a Trapped-Ion Spin Chain Y1 - 2022 A1 - Feng, Lei A1 - Katz, Or A1 - Haack, Casey A1 - Maghrebi, Mohammad A1 - Gorshkov, Alexey V. A1 - Gong, Zhexuan A1 - Cetina, Marko A1 - Monroe, Christopher KW - FOS: Physical sciences KW - Quantum Gases (cond-mat.quant-gas) KW - Quantum Physics (quant-ph) KW - Statistical Mechanics (cond-mat.stat-mech) KW - Strongly Correlated Electrons (cond-mat.str-el) AB -

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

UR - https://arxiv.org/abs/2211.01275 U5 - 10.48550/ARXIV.2211.01275 ER - TY - JOUR T1 - Continuous-variable quantum state designs: theory and applications Y1 - 2022 A1 - Iosue, Joseph T. A1 - Sharma, Kunal A1 - Gullans, Michael J. A1 - Victor V. Albert KW - FOS: Physical sciences KW - Mathematical Physics (math-ph) KW - Optics (physics.optics) KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2211.05127 U5 - 10.48550/ARXIV.2211.05127 ER - TY - JOUR T1 - Continuous-Variable Shadow Tomography Y1 - 2022 A1 - Gandhari, Srilekha A1 - Victor V. Albert A1 - Gerrits, Thomas A1 - Taylor, Jacob M. A1 - Gullans, Michael J. KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2211.05149 U5 - 10.48550/ARXIV.2211.05149 ER - TY - JOUR T1 - CoVault: A Secure Analytics Platform Y1 - 2022 A1 - De Viti, Roberta A1 - Sheff, Isaac A1 - Glaeser, Noemi A1 - Dinis, Baltasar A1 - Rodrigues, Rodrigo A1 - Katz, Jonathan A1 - Bhattacharjee, Bobby A1 - Hithnawi, Anwar A1 - Garg, Deepak A1 - Druschel, Peter KW - and Cluster Computing (cs.DC) KW - Cryptography and Security (cs.CR) KW - Distributed KW - FOS: Computer and information sciences KW - Parallel AB -

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

UR - https://arxiv.org/abs/2208.03784 U5 - 10.48550/ARXIV.2208.03784 ER - TY - JOUR T1 - Dark Solitons in Bose-Einstein Condensates: A Dataset for Many-body Physics Research Y1 - 2022 A1 - Amilson R. Fritsch A1 - Shangjie Guo A1 - Sophia M. Koh A1 - I. B. Spielman A1 - Justyna P. Zwolak AB -

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

UR - https://arxiv.org/abs/2205.09114 ER - TY - JOUR T1 - Disordered Lieb-Robinson bounds in one dimension Y1 - 2022 A1 - Baldwin, Christopher L. A1 - Ehrenberg, Adam A1 - Guo, Andrew Y. A1 - Alexey V. Gorshkov KW - Disordered Systems and Neural Networks (cond-mat.dis-nn) KW - FOS: Physical sciences KW - Mathematical Physics (math-ph) KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2208.05509 U5 - 10.48550/ARXIV.2208.05509 ER - TY - JOUR T1 - Error-correcting codes for fermionic quantum simulation Y1 - 2022 A1 - Chen, Yu-An A1 - Alexey V. Gorshkov A1 - Xu, Yijia KW - FOS: Mathematics KW - FOS: Physical sciences KW - Mathematical Physics (math-ph) KW - Quantum Algebra (math.QA) KW - Quantum Physics (quant-ph) KW - Strongly Correlated Electrons (cond-mat.str-el) AB -

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

UR - https://arxiv.org/abs/2210.08411 U5 - 10.48550/ARXIV.2210.08411 ER - TY - JOUR T1 - Experimental Implementation of an Efficient Test of Quantumness Y1 - 2022 A1 - Lewis, Laura A1 - Zhu, Daiwei A1 - Gheorghiu, Alexandru A1 - Noel, Crystal A1 - Katz, Or A1 - Harraz, Bahaa A1 - Wang, Qingfeng A1 - Risinger, Andrew A1 - Feng, Lei A1 - Biswas, Debopriyo A1 - Egan, Laird A1 - Vidick, Thomas A1 - Cetina, Marko A1 - Monroe, Christopher KW - FOS: Physical sciences KW - Other Condensed Matter (cond-mat.other) KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2209.14316 U5 - 10.48550/ARXIV.2209.14316 ER - TY - JOUR T1 - FIPS Compliant Quantum Secure Communication using Quantum Permutation Pad Y1 - 2022 A1 - He, Alex A1 - Lou, Dafu A1 - She, Eric A1 - Guo, Shangjie A1 - Watson, Hareesh A1 - Weng, Sibyl A1 - Perepechaenko, Maria A1 - Kuang, Rand KW - Cryptography and Security (cs.CR) KW - FOS: Computer and information sciences KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2301.00062 U5 - 10.48550/ARXIV.2301.00062 ER - TY - JOUR T1 - Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions JF - Phys. Rev. Research Y1 - 2022 A1 - Andrew Y. Guo A1 - Abhinav Deshpande A1 - Su-Kuan Chu A1 - Zachary Eldredge A1 - Przemyslaw Bienias A1 - Dhruv Devulapalli A1 - Yuan Su A1 - Andrew M. Childs A1 - Alexey V. Gorshkov AB -

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

VL - 4 UR - https://arxiv.org/abs/2007.00662 CP - L042016 U5 - https://doi.org/10.1103/PhysRevResearch.4.L042016 ER - TY - JOUR T1 - Importance of the Spectral gap in Estimating Ground-State Energies JF - PRX Quantum Y1 - 2022 A1 - Abhinav Deshpande A1 - Alexey V. Gorshkov A1 - Bill Fefferman AB -

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

VL - 3 UR - https://arxiv.org/abs/2007.11582 U5 - 10.1103/prxquantum.3.040327 ER - TY - JOUR T1 - Infinite-randomness criticality in monitored quantum dynamics with static disorder Y1 - 2022 A1 - Aidan Zabalo A1 - Justin H. Wilson A1 - Michael J. Gullans A1 - Romain Vasseur A1 - Sarang Gopalakrishnan A1 - David A. Huse A1 - J. H. Pixley AB -

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

UR - https://arxiv.org/abs/2205.14002 ER - TY - JOUR T1 - Kramers' degeneracy for open systems in thermal equilibrium JF - Phys. Rev. B Y1 - 2022 A1 - Simon Lieu A1 - Max McGinley A1 - Oles Shtanko A1 - Nigel R. Cooper A1 - Alexey V. Gorshkov VL - 105 U4 - L121104 UR - https://arxiv.org/abs/2105.02888 CP - 12 U5 - https://doi.org/10.1103/PhysRevB.105.L121104 ER - TY - JOUR T1 - Many-Body Quantum Teleportation via Operator Spreading in the Traversable Wormhole Protocol JF - Physical Review X Y1 - 2022 A1 - Thomas Schuster A1 - Bryce Kobrin A1 - Ping Gao A1 - Iris Cong A1 - Emil T. Khabiboulline A1 - Norbert M. Linke A1 - Mikhail D. Lukin A1 - Christopher Monroe A1 - Beni Yoshida A1 - Norman Y. Yao AB -

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

VL - 12 UR - https://arxiv.org/abs/2102.00010 U5 - 10.1103/physrevx.12.031013 ER - TY - JOUR T1 - Monitoring-induced Entanglement Entropy and Sampling Complexity Y1 - 2022 A1 - Van Regemortel, Mathias A1 - Shtanko, Oles A1 - García-Pintos, Luis Pedro A1 - Deshpande, Abhinav A1 - Dehghani, Hossein A1 - Alexey V. Gorshkov A1 - Hafezi, Mohammad KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2201.12672 U5 - 10.48550/ARXIV.2201.12672 ER - TY - JOUR T1 - Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions JF - Physical Review Letters Y1 - 2022 A1 - Aidan Zabalo A1 - Michael Gullans A1 - Justin H. Wilson A1 - Romain Vasseur A1 - Andreas W. W. Ludwig A1 - Sarang Gopalakrishnan A1 - David A. Huse A1 - J. H. Pixley AB -

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

VL - 128 UR - https://arxiv.org/abs/2107.03393 U5 - 10.1103/physrevlett.128.050602 ER - TY - JOUR T1 - Opportunities and Challenges in Fault-Tolerant Quantum Computation Y1 - 2022 A1 - Daniel Gottesman KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2210.15844 U5 - 10.48550/ARXIV.2210.15844 ER - TY - JOUR T1 - Quantum Depth in the Random Oracle Model Y1 - 2022 A1 - Arora, Atul Singh A1 - Coladangelo, Andrea A1 - Coudron, Matthew A1 - Gheorghiu, Alexandru A1 - Singh, Uttam A1 - Waldner, Hendrik KW - Computational Complexity (cs.CC) KW - Cryptography and Security (cs.CR) KW - FOS: Computer and information sciences KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2210.06454 U5 - 10.48550/ARXIV.2210.06454 ER - TY - JOUR T1 - Quantum Many-Body Scars from Einstein-Podolsky-Rosen States in Bilayer Systems Y1 - 2022 A1 - Wildeboer, Julia A1 - Langlett, Christopher M. A1 - Yang, Zhi-Cheng A1 - Alexey V. Gorshkov A1 - Iadecola, Thomas A1 - Xu, Shenglong KW - FOS: Physical sciences KW - Strongly Correlated Electrons (cond-mat.str-el) AB -

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

UR - https://arxiv.org/abs/2209.05527 U5 - 10.48550/ARXIV.2209.05527 ER - TY - JOUR T1 - Quantum Routing with Teleportation Y1 - 2022 A1 - Devulapalli, Dhruv A1 - Schoute, Eddie A1 - Bapat, Aniruddha A1 - Andrew M. Childs A1 - Alexey V. Gorshkov KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2204.04185 U5 - 10.48550/ARXIV.2204.04185 ER - TY - JOUR T1 - Quantum Simulation for High Energy Physics Y1 - 2022 A1 - Bauer, Christian W. A1 - Davoudi, Zohreh A1 - Balantekin, A. Baha A1 - Bhattacharya, Tanmoy A1 - Carena, Marcela A1 - de Jong, Wibe A. A1 - Draper, Patrick A1 - El-Khadra, Aida A1 - Gemelke, Nate A1 - Hanada, Masanori A1 - Kharzeev, Dmitri A1 - Lamm, Henry A1 - Li, Ying-Ying A1 - Liu, Junyu A1 - Lukin, Mikhail A1 - Meurice, Yannick A1 - Monroe, Christopher A1 - Nachman, Benjamin A1 - Pagano, Guido A1 - Preskill, John A1 - Rinaldi, Enrico A1 - Roggero, Alessandro A1 - Santiago, David I. A1 - Savage, Martin J. A1 - Siddiqi, Irfan A1 - Siopsis, George A1 - Van Zanten, David A1 - Wiebe, Nathan A1 - Yamauchi, Yukari A1 - Yeter-Aydeniz, Kübra A1 - Zorzetti, Silvia KW - FOS: Physical sciences KW - High Energy Physics - Lattice (hep-lat) KW - High Energy Physics - Phenomenology (hep-ph) KW - High Energy Physics - Theory (hep-th) KW - Nuclear Theory (nucl-th) KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2204.03381 U5 - 10.48550/ARXIV.2204.03381 ER - TY - JOUR T1 - Sample-optimal classical shadows for pure states Y1 - 2022 A1 - Grier, Daniel A1 - Pashayan, Hakop A1 - Schaeffer, Luke KW - FOS: Computer and information sciences KW - FOS: Physical sciences KW - Information Theory (cs.IT) KW - Machine Learning (cs.LG) KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2211.11810 U5 - 10.48550/ARXIV.2211.11810 ER - TY - JOUR T1 - Self-Testing of a Single Quantum System: Theory and Experiment Y1 - 2022 A1 - Hu, Xiao-Min A1 - Xie, Yi A1 - Arora, Atul Singh A1 - Ai, Ming-Zhong A1 - Bharti, Kishor A1 - Zhang, Jie A1 - Wu, Wei A1 - Chen, Ping-Xing A1 - Cui, Jin-Ming A1 - Liu, Bi-Heng A1 - Huang, Yun-Feng A1 - Li, Chuan-Feng A1 - Guo, Guang-Can A1 - Roland, Jérémie A1 - Cabello, Adán A1 - Kwek, Leong-Chuan KW - Atomic Physics (physics.atom-ph) KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2203.09003 U5 - https://doi.org/10.48550/arXiv.2203.09003 ER - TY - JOUR T1 - Sharp complexity phase transitions generated by entanglement Y1 - 2022 A1 - Ghosh, Soumik A1 - Deshpande, Abhinav A1 - Hangleiter, Dominik A1 - Gorshkov, Alexey V. A1 - Fefferman, Bill KW - Computational Complexity (cs.CC) KW - FOS: Computer and information sciences KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2212.10582 U5 - 10.48550/ARXIV.2212.10582 ER - TY - JOUR T1 - Simulation Complexity of Many-Body Localized Systems Y1 - 2022 A1 - Adam Ehrenberg A1 - Abhinav Deshpande A1 - Christopher L. Baldwin A1 - Dmitry A. Abanin A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2205.12967 ER - TY - JOUR T1 - Snowmass 2021 White Paper: Tabletop experiments for infrared quantum gravity Y1 - 2022 A1 - Carney, Daniel A1 - Chen, Yanbei A1 - Geraci, Andrew A1 - Müller, Holger A1 - Panda, Cristian D. A1 - Stamp, Philip C. E. A1 - Taylor, Jacob M. KW - FOS: Physical sciences KW - General Relativity and Quantum Cosmology (gr-qc) KW - High Energy Physics - Phenomenology (hep-ph) KW - Quantum Physics (quant-ph) AB -

Progress in the quantum readout and control of mechanical devices from single atoms to large masses may enable a first generation of experiments probing the gravitational interaction in the quantum regime, conceivably within the next decade. In this Snowmass whitepaper, we briefly outline the possibilities and challenges facing the realization of these experiments. In particular, we emphasize the need for detailed theories of modifications to the usual effective QFT of gravitons in the infrared regime E/L3≪mPl/ℓ3Pl in which these experiments operate, and relations to possible UV completions.

UR - https://arxiv.org/abs/2203.11846 U5 - 10.48550/ARXIV.2203.11846 ER - TY - JOUR T1 - Snowmass 2021 White Paper: The Windchime Project Y1 - 2022 A1 - The Windchime Collaboration A1 - Attanasio, Alaina A1 - Bhave, Sunil A. A1 - Blanco, Carlos A1 - Carney, Daniel A1 - Demarteau, Marcel A1 - Elshimy, Bahaa A1 - Febbraro, Michael A1 - Feldman, Matthew A. A1 - Ghosh, Sohitri A1 - Hickin, Abby A1 - Hong, Seongjin A1 - Lang, Rafael F. A1 - Lawrie, Benjamin A1 - Li, Shengchao A1 - Liu, Zhen A1 - Maldonado, Juan P. A. A1 - Marvinney, Claire A1 - Oo, Hein Zay Yar A1 - Pai, Yun-Yi A1 - Pooser, Raphael A1 - Qin, Juehang A1 - Sparmann, Tobias J. A1 - Taylor, Jacob M. A1 - Tian, Hao A1 - Tunnell, Christopher KW - Cosmology and Nongalactic Astrophysics (astro-ph.CO) KW - FOS: Physical sciences KW - High Energy Physics - Experiment (hep-ex) KW - High Energy Physics - Phenomenology (hep-ph) AB -

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

UR - https://arxiv.org/abs/2203.07242 U5 - 10.48550/ARXIV.2203.07242 ER - TY - JOUR T1 - Spectral Form Factor of a Quantum Spin Glass Y1 - 2022 A1 - Winer, Michael A1 - Barney, Richard A1 - Christopher L. Baldwin A1 - Galitski, Victor A1 - Swingle, Brian KW - Disordered Systems and Neural Networks (cond-mat.dis-nn) KW - FOS: Physical sciences KW - High Energy Physics - Theory (hep-th) KW - Statistical Mechanics (cond-mat.stat-mech) KW - Strongly Correlated Electrons (cond-mat.str-el) AB -

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

UR - https://arxiv.org/abs/2203.12753 U5 - https://doi.org/10.48550/arXiv.2203.12753 ER - TY - JOUR T1 - Ultrastrong light-matter interaction in a photonic crystal Y1 - 2022 A1 - Vrajitoarea, Andrei A1 - Belyansky, Ron A1 - Lundgren, Rex A1 - Whitsitt, Seth A1 - Alexey V. Gorshkov A1 - Houck, Andrew A. KW - FOS: Physical sciences KW - Quantum Gases (cond-mat.quant-gas) KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2209.14972 U5 - 10.48550/ARXIV.2209.14972 ER - TY - JOUR T1 - Universal scattering with general dispersion relations JF - Phys. Rev. Research Y1 - 2022 A1 - Wang, Yidan A1 - Michael Gullans A1 - Na, Xuesen A1 - Whitsitt, Seth A1 - Alexey V. Gorshkov KW - FOS: Physical sciences KW - Mathematical Physics (math-ph) KW - Quantum Physics (quant-ph) AB -

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

VL - 4 UR - https://arxiv.org/abs/2103.09830 U5 - https://doi.org/10.1103/PhysRevResearch.4.023014 ER - TY - JOUR T1 - Universality in one-dimensional scattering with general dispersion relations JF - Phys. Rev. Res. Y1 - 2022 A1 - Yidan Wang A1 - Michael Gullans A1 - Xuesen Na A1 - Alexey V. Gorshkov AB -

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

VL - 4 UR - https://arxiv.org/abs/2103.09830 U5 - https://doi.org/10.48550/arXiv.2103.09830 ER - TY - JOUR T1 - Unlimited non-causal correlations and their relation to non-locality JF - Quantum Y1 - 2022 A1 - Ämin Baumeler A1 - Amin Shiraz Gilani A1 - Jibran Rashid AB -

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

VL - 6 U4 - 673 UR - https://arxiv.org/abs/2104.06234 U5 - https://doi.org/10.22331%2Fq-2022-03-29-673 ER - TY - JOUR T1 - Behavior of Analog Quantum Algorithms Y1 - 2021 A1 - Lucas T. Brady A1 - Lucas Kocia A1 - Przemyslaw Bienias A1 - Aniruddha Bapat A1 - Yaroslav Kharkov A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2107.01218 ER - TY - JOUR T1 - Can you sign a quantum state? JF - v4: version for publication in Quantum, v5: CC license Y1 - 2021 A1 - Gorjan Alagic A1 - Tommaso Gagliardoni A1 - Christian Majenz AB -

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

UR - https://arxiv.org/abs/1811.11858 ER - TY - JOUR T1 - Chiral transport of hot carriers in graphene in the quantum Hall regime Y1 - 2021 A1 - Bin Cao A1 - Tobias Grass A1 - Olivier Gazzano A1 - Kishan Ashokbhai Patel A1 - Jiuning Hu A1 - Markus Müller A1 - Tobias Huber A1 - Luca Anzi A1 - Kenji Watanabe A1 - Takashi Taniguchi A1 - David Newell A1 - Michael Gullans A1 - Roman Sordan A1 - Mohammad Hafezi A1 - Glenn Solomon AB -

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

UR - https://arxiv.org/abs/2110.01079 ER - TY - JOUR T1 - Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models Y1 - 2021 A1 - Przemyslaw Bienias A1 - Igor Boettcher A1 - Ron Belyansky A1 - Alicia J. Kollár A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2105.06490 ER - TY - JOUR T1 - Clustering of steady-state correlations in open systems with long-range interactions Y1 - 2021 A1 - Andrew Y. Guo A1 - Simon Lieu A1 - Minh C. Tran A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2110.15368 ER - TY - JOUR T1 - Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing JF - PRX Quantum Y1 - 2021 A1 - Shtanko, Oles A1 - Deshpande, Abhinav A1 - Julienne, Paul S. A1 - Alexey V. Gorshkov AB -

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

VL - 2 UR - http://dx.doi.org/10.1103/PRXQuantum.2.030350 U5 - 10.1103/prxquantum.2.030350 ER - TY - JOUR T1 - Constructing quantum many-body scar Hamiltonians from Floquet automata Y1 - 2021 A1 - Pierre-Gabriel Rozon A1 - Michael Gullans A1 - Kartiek Agarwal AB -

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

UR - https://arxiv.org/abs/2112.12153 ER - TY - JOUR T1 - Cross-Platform Comparison of Arbitrary Quantum Computations Y1 - 2021 A1 - Daiwei Zhu A1 - Ze-Pei Cian A1 - Crystal Noel A1 - Andrew Risinger A1 - Debopriyo Biswas A1 - Laird Egan A1 - Yingyue Zhu A1 - Alaina M. Green A1 - Cinthia Huerta Alderete A1 - Nhung H. Nguyen A1 - Qingfeng Wang A1 - Andrii Maksymov A1 - Yunseong Nam A1 - Marko Cetina A1 - Norbert M. Linke A1 - Mohammad Hafezi A1 - Christopher Monroe AB -

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

UR - https://arxiv.org/abs/2107.11387 ER - TY - JOUR T1 - Crystallography of Hyperbolic Lattices Y1 - 2021 A1 - Igor Boettcher A1 - Alexey V. Gorshkov A1 - Alicia J. Kollár A1 - Joseph Maciejko A1 - Steven Rayan A1 - Ronny Thomale AB -

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

UR - https://arxiv.org/abs/2105.01087 ER - TY - JOUR T1 - Discovering hydrodynamic equations of many-body quantum systems Y1 - 2021 A1 - Yaroslav Kharkov A1 - Oles Shtanko A1 - Alireza Seif A1 - Przemyslaw Bienias A1 - Mathias Van Regemortel A1 - Mohammad Hafezi A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2111.02385 ER - TY - JOUR T1 - EasyPQC: Verifying Post-Quantum Cryptography JF - ACM CCS 2021 Y1 - 2021 A1 - Manuel Barbosa A1 - Gilles Barthe A1 - Xiong Fan A1 - Benjamin Grégoire A1 - Shih-Han Hung A1 - Jonathan Katz A1 - Pierre-Yves Strub A1 - Xiaodi Wu A1 - Li Zhou AB -

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

U5 - https://dx.doi.org/10.1145/3460120.3484567 ER - TY - JOUR T1 - Efficient quantum programming using EASE gates on a trapped-ion quantum computer Y1 - 2021 A1 - Nikodem Grzesiak A1 - Andrii Maksymov A1 - Pradeep Niroula A1 - Yunseong Nam AB -

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

UR - https://arxiv.org/abs/2107.07591 ER - TY - JOUR T1 - Energy storage and coherence in closed and open quantum batteries JF - Quantum Y1 - 2021 A1 - Francesco Caravelli A1 - Bin Yan A1 - Luis Pedro García-Pintos A1 - Alioscia Hamma AB -

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

VL - 5 U4 - 505 UR - https://arxiv.org/abs/2012.15026 U5 - https://doi.org/10.22331/q-2021-07-15-505 ER - TY - JOUR T1 - Entanglement and purification transitions in non-Hermitian quantum mechanics JF - Phys. Rev. Lett., in press Y1 - 2021 A1 - Sarang Gopalakrishnan A1 - Michael Gullans AB -

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

UR - https://arxiv.org/abs/2012.01435 ER - TY - JOUR T1 - Entanglement Phase Transitions in Measurement-Only Dynamics JF - Physical Review X Y1 - 2021 A1 - Ippoliti, Matteo A1 - Michael Gullans A1 - Gopalakrishnan, Sarang A1 - Huse, David A. A1 - Khemani, Vedika AB -

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

VL - 11 UR - https://arxiv.org/abs/2004.09560 CP - 1 J1 - Phys. Rev. X U5 - 10.1103/PhysRevX.11.011030 ER - TY - CONF T1 - Expanding the VOQC Toolkit T2 - The Second International Workshop on Programming Languages for Quantum Computing (PLanQC 2021) Y1 - 2021 A1 - Kesha Hietala A1 - Liyi Li A1 - Akshaj Gaur A1 - Aaron Green A1 - Robert Rand A1 - Xiaodi Wu A1 - Michael Hicks AB -

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

JA - The Second International Workshop on Programming Languages for Quantum Computing (PLanQC 2021) UR - http://rand.cs.uchicago.edu/files/planqc_2021c.pdf ER - TY - JOUR T1 - Feedback-stabilized dynamical steady states in the Bose-Hubbard model JF - Phys. Rev. Research Y1 - 2021 A1 - Jeremy T. Young A1 - Alexey V. Gorshkov A1 - I. B. Spielman AB -

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

VL - 3 U4 - 043075 UR - https://arxiv.org/abs/2106.09744 CP - 4 U5 - https://doi.org/10.1103/PhysRevResearch.3.043075 ER - TY - JOUR T1 - Frustration-induced anomalous transport and strong photon decay in waveguide QED JF - Phys. Rev. Research Y1 - 2021 A1 - Ron Belyansky A1 - Seth Whitsitt A1 - Rex Lundgren A1 - Yidan Wang A1 - Andrei Vrajitoarea A1 - Andrew A. Houck A1 - Alexey V. Gorshkov AB -

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

VL - 3 UR - https://arxiv.org/abs/2007.03690 CP - 032058 U5 - https://doi.org/10.1103/PhysRevResearch.3.L032058 ER - TY - JOUR T1 - García-Pintos, Hamma, and del Campo Reply JF - Phys. Rev. Lett. Y1 - 2021 A1 - Luis Pedro García-Pintos A1 - Alioscia Hamma A1 - Adolfo del Campo AB -

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

VL - 127 U4 - 028902 U5 - 10.1103/PhysRevLett.127.028902 ER - TY - JOUR T1 - Interactive Protocols for Classically-Verifiable Quantum Advantage Y1 - 2021 A1 - Daiwei Zhu A1 - Gregory D. Kahanamoku-Meyer A1 - Laura Lewis A1 - Crystal Noel A1 - Or Katz A1 - Bahaa Harraz A1 - Qingfeng Wang A1 - Andrew Risinger A1 - Lei Feng A1 - Debopriyo Biswas A1 - Laird Egan A1 - Alexandru Gheorghiu A1 - Yunseong Nam A1 - Thomas Vidick A1 - Umesh Vazirani A1 - Norman Y. Yao A1 - Marko Cetina A1 - Christopher Monroe AB -

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

UR - https://arxiv.org/abs/2112.05156 ER - TY - JOUR T1 - The Lieb-Robinson light cone for power-law interactions Y1 - 2021 A1 - Minh C. Tran A1 - Andrew Y. Guo A1 - Christopher L. Baldwin A1 - Adam Ehrenberg A1 - Alexey V. Gorshkov A1 - Andrew Lucas AB -

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

UR - https://arxiv.org/abs/2103.15828 ER - TY - JOUR T1 - Limits to Perception by Quantum Monitoring with Finite Efficiency JF - Entropy Y1 - 2021 A1 - García-Pintos, Luis Pedro A1 - del Campo, Adolfo AB -

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

VL - 23 U4 - 1527 UR - https://www.mdpi.com/1099-4300/23/11/1527 U5 - 10.3390/e23111527 ER - TY - JOUR T1 - Linear and continuous variable spin-wave processing using a cavity-coupled atomic ensemble Y1 - 2021 A1 - Kevin C. Cox A1 - Przemyslaw Bienias A1 - David H. Meyer A1 - Donald P. Fahey A1 - Paul D. Kunz A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2109.15246 ER - TY - JOUR T1 - Machine learning outperforms thermodynamics in measuring how well a many-body system learns a drive JF - Scientific Reports Y1 - 2021 A1 - Zhong, Weishun A1 - Gold, Jacob M. A1 - Marzen, Sarah A1 - England, Jeremy L. A1 - Nicole Yunger Halpern AB -

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

VL - 11 UR - https://arxiv.org/abs/2004.03604 U5 - https://doi.org/10.1038/s41598-021-88311-7 ER - TY - JOUR T1 - Machine-learning enhanced dark soliton detection in Bose-Einstein condensates JF - Mach. Learn.: Sci. Technol. Y1 - 2021 A1 - Shangjie Guo A1 - Amilson R. Fritsch A1 - Craig Greenberg A1 - I. B. Spielman A1 - Justyna P. Zwolak AB -

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

VL - 2 U4 - 035020 UR - https://arxiv.org/abs/2101.05404 U5 - https://doi.org/10.1088/2632-2153/abed1e ER - TY - JOUR T1 - Maximum Refractive Index of an Atomic Medium JF - Physical Review X Y1 - 2021 A1 - Andreoli, Francesco A1 - Michael Gullans A1 - High, Alexander A. A1 - Browaeys, Antoine A1 - Chang, Darrick E. AB -

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

VL - 11 UR - https://arxiv.org/abs/2006.01680 CP - 1 J1 - Phys. Rev. X U5 - 10.1103/PhysRevX.11.011026 ER - TY - JOUR T1 - Observation of measurement-induced quantum phases in a trapped-ion quantum computer Y1 - 2021 A1 - Crystal Noel A1 - Pradeep Niroula A1 - Daiwei Zhu A1 - Andrew Risinger A1 - Laird Egan A1 - Debopriyo Biswas A1 - Marko Cetina A1 - Alexey V. Gorshkov A1 - Michael Gullans A1 - David A. Huse A1 - Christopher Monroe AB -

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

UR - https://arxiv.org/abs/2106.05881 ER - TY - JOUR T1 - Observation of Stark many-body localization without disorder Y1 - 2021 A1 - W. Morong A1 - F. Liu A1 - P. Becker A1 - K. S. Collins A1 - L. Feng A1 - A. Kyprianidis A1 - G. Pagano A1 - T. You A1 - Alexey V. Gorshkov A1 - C. Monroe AB -

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

UR - https://arxiv.org/abs/2102.07250 ER - TY - JOUR T1 - Proposal for gravitational direct detection of dark matter JF - Physical Review D Y1 - 2021 A1 - Carney, Daniel A1 - Ghosh, Sohitri A1 - Krnjaic, Gordan A1 - Taylor, Jacob M. AB -

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.

VL - 102 UR - https://arxiv.org/abs/1903.00492 U5 - https://doi.org/10.1103/PhysRevD.102.072003 ER - TY - JOUR T1 - Protocols for estimating multiple functions with quantum sensor networks: Geometry and performance JF - Physical Review Research Y1 - 2021 A1 - Jacob Bringewatt A1 - Boettcher, Igor A1 - Niroula, Pradeep A1 - Bienias, Przemyslaw A1 - Alexey V. Gorshkov AB -

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.

VL - 3 UR - https://arxiv.org/abs/2104.09540 U5 - 10.1103/physrevresearch.3.033011 ER - TY - JOUR T1 - Quantum routing with fast reversals JF - Quantum Y1 - 2021 A1 - Aniruddha Bapat A1 - Andrew M. Childs A1 - Alexey V. Gorshkov A1 - Samuel King A1 - Eddie Schoute A1 - Hrishee Shastri AB -

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

VL - 5 UR - https://arxiv.org/abs/2103.03264 U5 - https://doi.org/10.22331/q-2021-08-31-533 ER - TY - JOUR T1 - Quench Dynamics of a Fermi Gas with Strong Long-Range Interactions JF - Phys. Rev. X Y1 - 2021 A1 - Elmer Guardado-Sanchez A1 - Benjamin M. Spar A1 - Peter Schauss A1 - Ron Belyansky A1 - Jeremy T. Young A1 - Przemyslaw Bienias A1 - Alexey V. Gorshkov A1 - Thomas Iadecola A1 - Waseem S. Bakr AB -

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

VL - 11 UR - https://arxiv.org/abs/2010.05871 U5 - https://doi.org/10.1103/PhysRevX.11.021036 ER - TY - JOUR T1 - Rainbow Scars: From Area to Volume Law Y1 - 2021 A1 - Christopher M. Langlett A1 - Zhi-Cheng Yang A1 - Julia Wildeboer A1 - Alexey V. Gorshkov A1 - Thomas Iadecola A1 - Shenglong Xu AB -

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

UR - https://arxiv.org/abs/2107.03416 ER - TY - JOUR T1 - Relaxation of non-integrable systems and correlation functions Y1 - 2021 A1 - Riddell, Jonathon A1 - García-Pintos, Luis Pedro A1 - Alhambra, Álvaro M. KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) KW - Statistical Mechanics (cond-mat.stat-mech) KW - Strongly Correlated Electrons (cond-mat.str-el) AB -

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

UR - https://arxiv.org/abs/2112.09475 U5 - 10.48550/ARXIV.2112.09475 ER - TY - JOUR T1 - Robust Self-Testing of Multiparticle Entanglement JF - Phys. Rev. Lett. Y1 - 2021 A1 - Dian Wu A1 - Qi Zhao A1 - Xue-Mei Gu A1 - Han-Sen Zhong A1 - You Zhou A1 - Li-Chao Peng A1 - Jian Qin A1 - Yi-Han Luo A1 - Kai Chen A1 - Li Li A1 - Nai-Le Liu A1 - Chao-Yang Lu A1 - Jian-Wei Pan AB -

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

VL - 127 U4 - 230503 UR - https://arxiv.org/abs/2105.10298 U5 - https://doi.org/10.1103/PhysRevLett.127.230503 ER - TY - JOUR T1 - Singularities in nearly-uniform 1D condensates due to quantum diffusion Y1 - 2021 A1 - Christopher L. Baldwin A1 - P. Bienias A1 - Alexey V. Gorshkov A1 - Michael Gullans A1 - M. Maghrebi AB -

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

UR - https://arxiv.org/abs/2103.06293 ER - TY - JOUR T1 - Spin-Wave Quantum Computing with Atoms in a Single-Mode Cavity Y1 - 2021 A1 - Kevin C. Cox A1 - Przemyslaw Bienias A1 - David H. Meyer A1 - Paul D. Kunz A1 - Donald P. Fahey A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2109.15252 ER - TY - JOUR T1 - Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains Y1 - 2021 A1 - Jacopo De Nardis A1 - Sarang Gopalakrishnan A1 - Romain Vasseur A1 - Brayden Ware AB -

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

UR - https://arxiv.org/abs/2109.13251 ER - TY - JOUR T1 - Tight bounds on the convergence of noisy random circuits to uniform Y1 - 2021 A1 - Abhinav Deshpande A1 - Bill Fefferman A1 - Alexey V. Gorshkov A1 - Michael Gullans A1 - Pradeep Niroula A1 - Oles Shtanko AB -

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

UR - https://arxiv.org/abs/2112.00716 ER - TY - JOUR T1 - Tunable three-body loss in a nonlinear Rydberg medium JF - Phys. Rev. Lett., in press Y1 - 2021 A1 - Dalia P. Ornelas Huerta A1 - Przemyslaw Bienias A1 - Alexander N. Craddock A1 - Michael Gullans A1 - Andrew J. Hachtel A1 - Marcin Kalinowski A1 - Mary E. Lyon A1 - Alexey V. Gorshkov A1 - Steven L. Rolston A1 - J. V. Porto AB -

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

UR - https://arxiv.org/abs/2009.13599 ER - TY - JOUR T1 - Unifying Quantum and Classical Speed Limits on Observables Y1 - 2021 A1 - Luis Pedro García-Pintos A1 - Schuyler Nicholson A1 - Jason R. Green A1 - Adolfo del Campo A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2108.04261 ER - TY - JOUR T1 - Asymmetric blockade and multi-qubit gates via dipole-dipole interactions Y1 - 2020 A1 - Jeremy T. Young A1 - Przemyslaw Bienias A1 - Ron Belyansky A1 - Adam M. Kaufman A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2006.02486 ER - TY - JOUR T1 - Back-action evading impulse measurement with mechanical quantum sensors JF - Phys. Rev. A Y1 - 2020 A1 - Sohitri Ghosh A1 - Daniel Carney A1 - Peter Shawhan A1 - J. M. Taylor AB -

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

VL - 102 UR - https://arxiv.org/pdf/1910.11892.pdf CP - 023525 U5 - https://doi.org/10.1103/PhysRevA.102.023525 ER - TY - JOUR T1 - Circuit Complexity across a Topological Phase Transition JF - Physical Review Research Y1 - 2020 A1 - Fangli Liu A1 - Rex Lundgren A1 - Paraj Titum A1 - James R. Garrison A1 - Alexey V. Gorshkov AB -

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

VL - 2 U4 - 013323 UR - https://arxiv.org/abs/1902.10720 CP - 1 U5 - https://doi.org/10.1103/PhysRevResearch.2.013323 ER - TY - JOUR T1 - Classical Models of Entanglement in Monitored Random Circuits Y1 - 2020 A1 - Oles Shtanko A1 - Yaroslav A. Kharkov A1 - Luis Pedro García-Pintos A1 - Alexey V. Gorshkov AB -

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

UR - https://arxiv.org/abs/2004.06736 ER - TY - JOUR T1 - Coherent transport of spin by adiabatic passage in quantum dot arrays JF - Physical Review B Y1 - 2020 A1 - Michael Gullans A1 - Petta, J. R. AB -

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

VL - 102 UR - https://arxiv.org/abs/2007.10582 CP - 15 J1 - Phys. Rev. B U5 - 10.1103/PhysRevB.102.155404 ER - TY - JOUR T1 - Coherent transport of spin by adiabatic passage in quantum dot arrays JF - Phys. Rev. B Y1 - 2020 A1 - Michael Gullans A1 - J. R. Petta AB -

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

VL - 102 UR - https://arxiv.org/abs/2007.10582 CP - 155404 U5 - https://doi.org/10.1103/PhysRevB.102.155404 ER - TY - JOUR T1 - Critical Theory for the Breakdown of Photon Blockade Y1 - 2020 A1 - Jonathan B. Curtis A1 - Igor Boettcher A1 - Jeremy T. Young A1 - Mohammad F. Maghrebi A1 - Howard Carmichael A1 - Alexey V. Gorshkov A1 - Michael Foss-Feig AB -

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

UR - https://arxiv.org/abs/2006.05593 ER - TY - JOUR T1 - Destructive Error Interference in Product-Formula Lattice Simulation JF - Phys. Rev. Lett. Y1 - 2020 A1 - Minh C. Tran A1 - Su-Kuan Chu A1 - Yuan Su A1 - Andrew M. Childs A1 - Alexey V. Gorshkov AB -

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

VL - 124 UR - https://arxiv.org/abs/1912.11047 CP - 220502 U5 - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.220502 ER - TY - JOUR T1 - Distributional property testing in a quantum world JF - Proceedings of ITCS 2020 Y1 - 2020 A1 - Andras Gilyen A1 - Tongyang Li AB -

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

VL - 25 U4 - 1-25 UR - https://arxiv.org/abs/1902.00814 CP - 19 U5 - http://dx.doi.org/10.4230/LIPIcs.ITCS.2020.25 ER - TY - JOUR T1 - Dynamical Purification Phase Transition Induced by Quantum Measurements JF - Physical Review X Y1 - 2020 A1 - Michael Gullans A1 - Huse, David A. AB -

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

VL - 10 UR - https://arxiv.org/abs/1905.05195 CP - 4 J1 - Phys. Rev. X U5 - 10.1103/PhysRevX.10.041020 ER - TY - JOUR T1 - Entanglement Bounds on the Performance of Quantum Computing Architectures JF - Phys. Rev. Research Y1 - 2020 A1 - Zachary Eldredge A1 - Leo Zhou A1 - Aniruddha Bapat A1 - James R. Garrison A1 - Abhinav Deshpande A1 - Frederic T. Chong A1 - Alexey V. Gorshkov AB -

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

VL - 2 UR - https://arxiv.org/abs/1908.04802 CP - 033316 U5 - https://doi.org/10.1103/PhysRevResearch.2.033316 ER - TY - JOUR T1 - Exotic photonic molecules via Lennard-Jones-like potentials JF - Phys. Rev. Lett. Y1 - 2020 A1 - Przemyslaw Bienias A1 - Michael Gullans A1 - Marcin Kalinowski A1 - Alexander N. Craddock A1 - Dalia P. Ornelas-Huerta A1 - Steven L. Rolston A1 - J. V. Porto A1 - Alexey V. Gorshkov AB -

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

VL - 125 UR - https://arxiv.org/abs/2003.07864 CP - 093601 U5 - https://doi.org/10.1103/PhysRevLett.125.093601 ER - TY - JOUR T1 - Feedback Induced Magnetic Phases in Binary Bose-Einstein Condensates Y1 - 2020 A1 - Hilary M. Hurst A1 - Shangjie Guo A1 - I. B. Spielman AB -

Weak measurement in tandem with real-time feedback control is a new route toward engineering novel non-equilibrium quantum matter. Here we develop a theoretical toolbox for quantum feedback control of multicomponent Bose-Einstein condensates (BECs) using backaction-limited weak measurements in conjunction with spatially resolved feedback. Feedback in the form of a single-particle potential can introduce effective interactions that enter into the stochastic equation governing system dynamics. The effective interactions are tunable and can be made analogous to Feshbach resonances -- spin-independent and spin-dependent -- but without changing atomic scattering parameters. Feedback cooling prevents runaway heating due to measurement backaction and we present an analytical model to explain its effectiveness. We showcase our toolbox by studying a two-component BEC using a stochastic mean-field theory, where feedback induces a phase transition between easy-axis ferromagnet and spin-disordered paramagnet phases. We present the steady-state phase diagram as a function of intrinsic and effective spin-dependent interaction strengths. Our result demonstrates that closed-loop quantum control of Bose-Einstein condensates is a powerful new tool for quantum engineering in cold-atom systems.

UR - https://arxiv.org/abs/2007.07266 ER - TY - JOUR T1 - Fluctuations in Extractable Work Bound the Charging Power of Quantum Batteries JF - Phys. Rev. Lett. Y1 - 2020 A1 - Luis Pedro García-Pintos A1 - Alioscia Hamma A1 - Adolfo del Campo AB -

We study the connection between the charging power of quantum batteries and the fluctuations of the stored work. We prove that in order to have a non-zero rate of change of the extractable work, the state ρW of the battery cannot be an eigenstate of a `\emph{work operator}', defined by F ≡ HW + β−1log(ρW), where HW is the Hamiltonian of the battery and β is the inverse temperature of a reference thermal bath with respect to which the extractable work is calculated. We do so by proving that fluctuations in the stored work upper bound the charging power of a quantum battery. Our findings also suggest that quantum coherence in the battery enhances the charging process, which we illustrate on a toy model of a heat engine. 

VL - 125 UR - https://arxiv.org/abs/1909.03558 CP - 040601 U5 - 10.1103/PhysRevLett.125.040601 ER - TY - JOUR T1 - Gravitational Direct Detection of Dark Matter JF - Phys. Rev. D Y1 - 2020 A1 - Daniel Carney A1 - Sohitri Ghosh A1 - Gordan Krnjaic A1 - J. M. Taylor AB -

The only coupling dark matter is guaranteed to have with the standard model is through gravity. Here we propose a concept for direct dark matter detection using only this gravitational coupling, enabling a new regime of detection. Leveraging dramatic advances in the ability to create, maintain, and probe quantum states of massive objects, we suggest that an array of quantum-limited impulse sensors may be capable of detecting the correlated gravitational force created by a passing dark matter particle. We present two concrete realizations of this scheme, using either mechanical resonators or freely-falling masses. With currently available technology, a meter-scale apparatus of this type could detect any dark matter candidate around the Planck mass or heavier.

VL - 102 UR - https://arxiv.org/abs/1903.00492 CP - 072003 U5 - https://doi.org/10.1103/PhysRevD.102.072003 ER - TY - JOUR T1 - Hierarchy of linear light cones with long-range interactions JF - Physical Review X Y1 - 2020 A1 - Minh C. Tran A1 - Chi-Fang Chen A1 - Adam Ehrenberg A1 - Andrew Y. Guo A1 - Abhinav Deshpande A1 - Yifan Hong A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov A1 - Andrew Lucas AB -

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a "linear light cone," which expands at an emergent velocity analogous to the speed of light. Yet most non-relativistic physical systems realized in nature have long-range interactions: two degrees of freedom separated by a distance r interact with potential energy V(r)∝1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: at the same α, some quantum information processing tasks are constrained by a linear light cone while others are not. In one spatial dimension, commutators of local operators ⟨ψ|[Ox(t),Oy]|ψ⟩ are negligible in every state |ψ⟩ when |x−y|≳vt, where v is finite when α>3 (Lieb-Robinson light cone); in a typical state |ψ⟩ drawn from the infinite temperature ensemble, v is finite when α>52 (Frobenius light cone); in non-interacting systems, v is finite in every state when α>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones, and their tightness, also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that quantum state transfer and many-body quantum chaos are bounded by the Frobenius light cone, and therefore are poorly constrained by all Lieb-Robinson bounds.

VL - 10 UR - https://arxiv.org/abs/2001.11509 CP - 031009 U5 - https://doi.org/10.1103/PhysRevX.10.031009 ER - TY - JOUR T1 - Hilbert-Space Fragmentation from Strict Confinement JF - Phys. Rev. Lett. Y1 - 2020 A1 - Zhi-Cheng Yang A1 - Fangli Liu A1 - Alexey V. Gorshkov A1 - Thomas Iadecola AB -

We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most of the previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of Z2 gauge theory coupled to fermionic matter, leading to a hierarchy of time scales for motion of the fermions. This model can be realized experimentally in two complementary settings.

VL - 124 UR - https://arxiv.org/abs/1912.04300 CP - 207602 U5 - https://doi.org/10.1103/PhysRevLett.124.207602 ER - TY - JOUR T1 - Limits on Classical Simulation of Free Fermions with Dissipation Y1 - 2020 A1 - Oles Shtanko A1 - Abhinav Deshpande A1 - Paul S. Julienne A1 - Alexey V. Gorshkov AB -

Free-fermionic systems are a valuable, but limited, class of many-body problems efficiently simulable on a classical computer. We examine how classical simulability of noninteracting fermions is modified in the presence of Markovian dissipation described by quadratic Lindblad operators, including, for example, incoherent transitions or pair losses. On the one hand, we establish three broad classes of Markovian dynamics that are efficiently simulable classically, by devising efficient algorithms. On the other hand, we demonstrate that, in the worst case, simulating Markovian dynamics with quadratic Lindblad operators is at least as hard as simulating universal quantum circuits. This result is applicable to an experimentally relevant setting in cold atomic systems, where magnetic Feshbach resonances can be used to engineer the desired dissipation. For such systems, our hardness result provides a direct scheme for dissipation-assisted quantum computing with a potential significant advantage in the speed of two-qubit gates and, therefore, in error tolerance.

UR - https://arxiv.org/abs/2005.10840 ER - TY - JOUR T1 - Localization and criticality in antiblockaded 2D Rydberg atom arrays Y1 - 2020 A1 - Fangli Liu A1 - Zhi-Cheng Yang A1 - Przemyslaw Bienias A1 - Thomas Iadecola A1 - Alexey V. Gorshkov AB -

Controllable Rydberg atom arrays have provided new insights into fundamental properties of quantum matter both in and out of equilibrium. In this work, we study the effect of experimentally relevant positional disorder on Rydberg atoms trapped in a 2D square lattice under anti-blockade (facilitation) conditions. We show that the facilitation conditions lead the connectivity graph of a particular subspace of the full Hilbert space to form a 2D Lieb lattice, which features a singular flat band. Remarkably, we find three distinct regimes as the disorder strength is varied: a critical regime, a delocalized but nonergodic regime, and a regime with a disorder-induced flat band. The critical regime's existence depends crucially upon the singular flat band in our model, and is absent in any 1D array or ladder system. We propose to use quench dynamics to probe the three different regimes experimentally. 

UR - https://arxiv.org/abs/2012.03946 ER - TY - JOUR T1 - Many-Body Dephasing in a Trapped-Ion Quantum Simulator JF - Phys. Rev. Lett. Y1 - 2020 A1 - Harvey B. Kaplan A1 - Lingzhen Guo A1 - Wen Lin Tan A1 - Arinjoy De A1 - Florian Marquardt A1 - Guido Pagano A1 - Christopher Monroe AB -

How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this work, we observe and analyse the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles and observe the experimental evidence for the theoretically predicted regime of many-body dephasing. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions even for the long-time non-integrable dynamics. We find that the measured fluctuations are exponentially suppressed with increasing system size, consistent with theoretical predictions. 

VL - 125 UR - https://arxiv.org/abs/2001.02477 CP - 120605 U5 - https://doi.org/10.1103/PhysRevLett.125.120605 ER - TY - JOUR T1 - Mechanical Quantum Sensing in the Search for Dark Matter Y1 - 2020 A1 - D. Carney A1 - G. Krnjaic A1 - D. C. Moore A1 - C. A. Regal A1 - G. Afek A1 - S. Bhave A1 - B. Brubaker A1 - T. Corbitt A1 - J. Cripe A1 - N. Crisosto A1 - A.Geraci A1 - S. Ghosh A1 - J. G. E. Harris A1 - A. Hook A1 - E. W. Kolb A1 - J. Kunjummen A1 - R. F. Lang A1 - T. Li A1 - T. Lin A1 - Z. Liu A1 - J. Lykken A1 - L. Magrini A1 - J. Manley A1 - N. Matsumoto A1 - A. Monte A1 - F. Monteiro A1 - T. Purdy A1 - C. J. Riedel A1 - R. Singh A1 - S. Singh A1 - K. Sinha A1 - J. M. Taylor A1 - J. Qin A1 - D. J. Wilson A1 - Y. Zhao AB -

Numerous astrophysical and cosmological observations are best explained by the existence of dark matter, a mass density which interacts only very weakly with visible, baryonic matter. Searching for the extremely weak signals produced by this dark matter strongly motivate the development of new, ultra-sensitive detector technologies. Paradigmatic advances in the control and readout of massive mechanical systems, in both the classical and quantum regimes, have enabled unprecedented levels of sensitivity. In this white paper, we outline recent ideas in the potential use of a range of solid-state mechanical sensing technologies to aid in the search for dark matter in a number of energy scales and with a variety of coupling mechanisms.

UR - https://arxiv.org/abs/2008.06074 ER - TY - JOUR T1 - Minimal model for fast scrambling JF - Phys. Rev. Lett. Y1 - 2020 A1 - Ron Belyansky A1 - Przemyslaw Bienias A1 - Yaroslav A. Kharkov A1 - Alexey V. Gorshkov A1 - Brian Swingle AB -

We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two exactly solvable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled non-linear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results can be verified with state-of-the-art quantum simulators.

VL - 125 UR - https://arxiv.org/abs/2005.05362 CP - 130601 U5 - https://doi.org/10.1103/PhysRevLett.125.130601 ER - TY - JOUR T1 - Nearly optimal time-independent reversal of a spin chain JF - accepted for publication in Physical Review Research Y1 - 2020 A1 - Aniruddha Bapat A1 - Eddie Schoute A1 - Alexey V. Gorshkov A1 - Andrew M. Childs AB -

We propose a time-independent Hamiltonian protocol for the reversal of qubit ordering in a chain of N spins. Our protocol has an easily implementable nearest-neighbor, transverse-field Ising model Hamiltonian with time-independent, non-uniform couplings. Under appropriate normalization, we implement this state reversal three times faster than a naive approach using SWAP gates, in time comparable to a protocol of Raussendorf [Phys. Rev. A 72, 052301 (2005)] that requires dynamical control. We also prove lower bounds on state reversal by using results on the entanglement capacity of Hamiltonians and show that we are within a factor 1.502(1+1/N) of the shortest time possible. Our lower bound holds for all nearest-neighbor qubit protocols with arbitrary finite ancilla spaces and local operations and classical communication. Finally, we extend our protocol to an infinite family of nearest-neighbor, time-independent Hamiltonian protocols for state reversal. This includes chains with nearly uniform coupling that may be especially feasible for experimental implementation. 

UR - https://arxiv.org/abs/2003.02843 ER - TY - JOUR T1 - Non-equilibrium fixed points of coupled Ising models JF - Phys. Rev. X Y1 - 2020 A1 - Jeremy T. Young A1 - Alexey V. Gorshkov A1 - Michael Foss-Feig A1 - Mohammad F. Maghrebi AB -

Driven-dissipative systems can exhibit non-equilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions present in these systems generically exhibit an effectively classical equilibrium behavior in spite of their quantum non-equilibrium origin. In this paper, we show that multicritical points in driven-dissipative systems can give rise to genuinely non-equilibrium behavior. We investigate a non-equilibrium driven-dissipative model of interacting bosons that exhibits two distinct phase transitions: one from a high- to a low-density phase---reminiscent of a liquid-gas transition---and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) Z2 symmetry. They, however, coalesce at a multicritical point giving rise to a non-equilibrium model of coupled Ising-like order parameters described by a Z2×Z2 symmetry. Using a dynamical renormalization-group approach, we show that a pair of non-equilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents, spiraling phase boundaries, and a complex Liouvillian gap even close to the phase transition. As direct evidence of the non-equilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths. Finally, we argue that this non-equilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.

VL - 10 UR - https://arxiv.org/abs/1903.02569 CP - 011039 U5 - https://doi.org/10.1103/PhysRevX.10.011039 ER - TY - JOUR T1 - Non-interactive classical verification of quantum computation JF - Theory of Cryptography Conference (TCC) Y1 - 2020 A1 - Gorjan Alagic A1 - Andrew M. Childs A1 - Alex B. Grilo A1 - Shih-Han Hung AB -

In a recent breakthrough, Mahadev constructed an interactive protocol that enables a purely classical party to delegate any quantum computation to an untrusted quantum prover. In this work, we show that this same task can in fact be performed non-interactively and in zero-knowledge.
Our protocols result from a sequence of significant improvements to the original four-message protocol of Mahadev. We begin by making the first message instance-independent and moving it to an offline setup phase. We then establish a parallel repetition theorem for the resulting three-message protocol, with an asymptotically optimal rate. This, in turn, enables an application of the Fiat-Shamir heuristic, eliminating the second message and giving a non-interactive protocol. Finally, we employ classical non-interactive zero-knowledge (NIZK) arguments and classical fully homomorphic encryption (FHE) to give a zero-knowledge variant of this construction. This yields the first purely classical NIZK argument system for QMA, a quantum analogue of NP.
We establish the security of our protocols under standard assumptions in quantum-secure cryptography. Specifically, our protocols are secure in the Quantum Random Oracle Model, under the assumption that Learning with Errors is quantumly hard. The NIZK construction also requires circuit-private FHE.

VL - Lecture Notes in Computer Science 12552 U4 - 153-180 UR - https://arxiv.org/abs/1911.08101 ER - TY - JOUR T1 - On-demand indistinguishable single photons from an efficient and pure source based on a Rydberg ensemble Y1 - 2020 A1 - Dalia P. Ornelas-Huerta A1 - Alexander N. Craddock A1 - Elizabeth A. Goldschmidt A1 - Andrew J. Hachtel A1 - Yidan Wang A1 - P. Bienias A1 - Alexey V. Gorshkov A1 - Steve L. Rolston A1 - James V. Porto AB -

Single photons coupled to atomic systems have shown to be a promising platform for developing quantum technologies. Yet a bright on-demand, highly pure and highly indistinguishable single-photon source compatible with atomic platforms is lacking. In this work, we demonstrate such a source based on a strongly interacting Rydberg system. The large optical nonlinearities in a blockaded Rydberg ensemble convert coherent light into a single-collective excitation that can be coherently retrieved as a quantum field. We observe a single-transverse-mode efficiency up to 0.18(2), g(2)=2.0(1.5)×10−4, and indistinguishability of 0.982(7), making this system promising for scalable quantum information applications. Accounting for losses, we infer a generation probability up to 0.40(4). Furthermore, we investigate the effects of contaminant Rydberg excitations on the source efficiency. Finally, we introduce metrics to benchmark the performance of on-demand single-photon sources. 

UR - https://arxiv.org/abs/2003.02202 ER - TY - JOUR T1 - One-shot dynamical resource theory Y1 - 2020 A1 - Xiao Yuan A1 - Pei Zeng A1 - Minbo Gao A1 - Qi Zhao AB -

A fundamental problem in resource theory is to study the manipulation of the resource. Focusing on a general dynamical resource theory of quantum channels, here we consider tasks of one-shot resource distillation and dilution with a single copy of the resource. For any target of unitary channel or pure state preparation channel, we establish a universal strategy to determine upper and lower bounds on rates that convert between any given resource and the target. We show that the rates are related to resource measures based on the channel robustness and the channel hypothesis testing entropy, with regularization factors of the target resource measures. The strategy becomes optimal with converged bounds when the channel robustness is finite and measures of the target resource collapse to the same value. The single-shot result also applies to asymptotic parallel manipulation of channels to obtain asymptotic resource conversion rates. We give several examples of dynamical resources, including the purity, classical capacity, quantum capacity, non-uniformity, coherence, and entanglement of quantum channels. Our results are applicable to general dynamical resource theories with potential applications in quantum communication, fault-tolerant quantum computing, and quantum thermodynamics.

UR - https://arxiv.org/abs/2012.02781 ER - TY - JOUR T1 - The operator Lévy flight: light cones in chaotic long-range interacting systems JF - Phys. Rev. Lett. Y1 - 2020 A1 - Tianci Zhou A1 - Shenglong Xu A1 - Xiao Chen A1 - Andrew Guo A1 - Brian Swingle AB -

We propose a generic light cone phase diagram for chaotic long-range r−α interacting systems, where a linear light cone appears for α≥d+1/2 in d dimension. Utilizing the dephasing nature of quantum chaos, we argue that the universal behavior of the squared commutator is described by a stochastic model, for which the exact phase diagram is known. We provide an interpretation in terms of the Lévy flights and show that this suffices to capture the scaling of the squared commutator. We verify these phenomena in numerical computation of a long-range spin chain with up to 200 sites. 

VL - 124 UR - https://arxiv.org/abs/1909.08646 CP - 180601 U5 - https://doi.org/10.1103/PhysRevLett.124.180601 ER - TY - JOUR T1 - Optical quantum memory with optically inaccessible noble-gas spins Y1 - 2020 A1 - Or Katz A1 - Eran Reches A1 - Roy Shaham A1 - Alexey V. Gorshkov A1 - Ofer Firstenberg AB -

Optical quantum memories, which store and preserve the quantum state of photons, rely on a coherent mapping of the photonic state onto matter states that are optically accessible. Here we outline a new physical mechanism to map the state of photons onto the long-lived but optically inaccessible collective state of noble-gas spins. The mapping employs the coherent spin-exchange interaction arising from random collisions with alkali vapor. We analyze optimal strategies for high-efficiency storage and retrieval of non-classical light at various parameter regimes. Based on these strategies, we identify feasible experimental conditions for realizing efficient quantum memories with noble-gas spins having hours-long coherence times at room temperature and above

UR - https://arxiv.org/abs/2007.08770 ER - TY - JOUR T1 - Optimal Measurement of Field Properties with Quantum Sensor Networks Y1 - 2020 A1 - Timothy Qian A1 - Jacob Bringewatt A1 - Igor Boettcher A1 - Przemyslaw Bienias A1 - Alexey V. Gorshkov AB -

We consider a quantum sensor network of qubit sensors coupled to a field f(x⃗ ;θ⃗ ) analytically parameterized by the vector of parameters θ⃗ . The qubit sensors are fixed at positions x⃗ 1,…,x⃗ d. While the functional form of f(x⃗ ;θ⃗ ) is known, the parameters θ⃗  are not. We derive saturable bounds on the precision of measuring an arbitrary analytic function q(θ⃗ ) of these parameters and construct the optimal protocols that achieve these bounds. Our results are obtained from a combination of techniques from quantum information theory and duality theorems for linear programming. They can be applied to many problems, including optimal placement of quantum sensors, field interpolation, and the measurement of functionals of parametrized fields.

UR - https://arxiv.org/abs/2011.01259 ER - TY - JOUR T1 - Optimal Protocols in Quantum Annealing and QAOA Problems Y1 - 2020 A1 - Lucas T. Brady A1 - Christopher L. Baldwin A1 - Aniruddha Bapat A1 - Yaroslav Kharkov A1 - Alexey V. Gorshkov AB -

Quantum Annealing (QA) and the Quantum Approximate Optimization Algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or "bang-bang") structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. Through simulations of various transverse field Ising models, we demonstrate that bang-anneal-bang protocols are more common. The general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

UR - https://arxiv.org/abs/2003.08952 ER - TY - JOUR T1 - Optimal state transfer and entanglement generation in power-law interacting systems Y1 - 2020 A1 - Minh C. Tran A1 - Abhinav Deshpande A1 - Andrew Y. Guo A1 - Andrew Lucas A1 - Alexey V. Gorshkov AB -

We present an optimal protocol for encoding an unknown qubit state into a multiqubit Greenberger-Horne-Zeilinger-like state and, consequently, transferring quantum information in large systems exhibiting power-law (1/rα) interactions. For all power-law exponents α between d and 2d+1, where d is the dimension of the system, the protocol yields a polynomial speedup for α>2d and a superpolynomial speedup for α≤2d, compared to the state of the art. For all α>d, the protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections), thereby establishing the optimality of the protocol and the tightness of the bounds in this regime. The protocol has a wide range of applications, including in quantum sensing, quantum computing, and preparation of topologically ordered states. 

UR - https://arxiv.org/abs/2010.02930 ER - TY - JOUR T1 - Optimal Two-Qubit Circuits for Universal Fault-Tolerant Quantum Computation Y1 - 2020 A1 - Andrew N. Glaudell A1 - Neil J. Ross A1 - J. M. Taylor AB -

We study two-qubit circuits over the Clifford+CS gate set which consists of Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes with magic state distillation. However, since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is desirable to construct circuits that use few CS gates. In the present paper, we introduce an algorithm to construct optimal circuits for two-qubit Clifford+CS operators. Our algorithm inputs a Clifford+CS operator U and efficiently produces a Clifford+CS circuit for U using the least possible number of CS gates. Because our algorithm is deterministic, the circuit it associates to a Clifford+CS operator can be viewed as a normal form for the operator. We give a formal description of these normal forms as walks over certain graphs and use this description to derive an asymptotic lower bound of 5log(1/epsilon)+O(1) on the number CS gates required to epsilon-approximate any 4x4 unitary matrix. 

UR - https://arxiv.org/abs/2001.05997 ER - TY - JOUR T1 - Quantum coding with low-depth random circuits Y1 - 2020 A1 - Michael Gullans A1 - Stefan Krastanov A1 - David A. Huse A1 - Liang Jiang A1 - Steven T. Flammia AB -

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity in D≥1 spatial dimensions to generate quantum error-correcting codes. For random stabilizer codes and the erasure channel, we find strong evidence that a depth O(logN) random circuit is necessary and sufficient to converge (with high probability) to zero failure probability for any finite amount below the channel capacity for any D. Previous results on random circuits have only shown that O(N1/D) depth suffices or that O(log3N) depth suffices for all-to-all connectivity (D→∞). We then study the critical behavior of the erasure threshold in the so-called moderate deviation limit, where both the failure probability and the distance to the channel capacity converge to zero with N. We find that the requisite depth scales like O(logN) only for dimensions D≥2, and that random circuits require O(N−−√) depth for D=1. Finally, we introduce an "expurgation" algorithm that uses quantum measurements to remove logical operators that cause the code to fail by turning them into either additional stabilizers or into gauge operators in a subsystem code. With such targeted measurements, we can achieve sub-logarithmic depth in D≥2 spatial dimensions below capacity without increasing the maximum weight of the check operators. We find that for any rate beneath the capacity, high-performing codes with thousands of logical qubits are achievable with depth 4-8 expurgated random circuits in D=2 dimensions. These results indicate that finite-rate quantum codes are practically relevant for near-term devices and may significantly reduce the resource requirements to achieve fault tolerance for near-term applications. 

UR - https://arxiv.org/abs/2010.09775 ER - TY - JOUR T1 - Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry JF - Phys. Rev. A Y1 - 2020 A1 - Igor Boettcher A1 - Przemyslaw Bienias A1 - Ron Belyansky A1 - Alicia J. Kollár A1 - Alexey V. Gorshkov AB -

We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Our analysis also reveals in which sense discrete hyperbolic lattices emulate the continuous geometry of negatively curved space and thus can be used to resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

VL - 102 UR - https://arxiv.org/abs/1910.12318 CP - 032208 U5 - https://doi.org/10.1103/PhysRevA.102.032208 ER - TY - JOUR T1 - Random Quantum Batteries JF - Phys. Rev. Research Y1 - 2020 A1 - Francesco Caravelli A1 - Ghislaine Coulter-De Wit A1 - Luis Pedro García-Pintos A1 - Alioscia Hamma AB -

Quantum nano-devices are fundamental systems in quantum thermodynamics that have been the subject of profound interest in recent years. Among these, quantum batteries play a very important role. In this paper we lay down a theory of random quantum batteries and provide a systematic way of computing the average work and work fluctuations in such devices by investigating their typical behavior. We show that the performance of random quantum batteries exhibits typicality and depends only on the spectral properties of the time evolving operator, the initial state and the measuring Hamiltonian. At given revival times a random quantum battery features a quantum advantage over classical random batteries. Our method is particularly apt to be used both for exactly solvable models like the Jaynes-Cummings model or in perturbation theory, e.g., systems subject to harmonic perturbations. We also study the setting of quantum adiabatic random batteries.

VL - 2 UR - https://arxiv.org/abs/1908.08064 CP - 023095 U5 - https://doi.org/10.1103/PhysRevResearch.2.023095 ER - TY - JOUR T1 - Realizing and Probing Baryonic Excitations in Rydberg Atom Arrays Y1 - 2020 A1 - Fangli Liu A1 - Seth Whitsitt A1 - Przemyslaw Bienias A1 - Rex Lundgren A1 - Alexey V. Gorshkov AB -

We propose a realization of mesonic and baryonic quasiparticle excitations in Rydberg atom arrays with programmable interactions. Recent experiments have shown that such systems possess a Z3-ordered crystalline phase whose low-energy quasiparticles are defects in the crystalline order. By engineering a Z3-translational-symmetry breaking field on top of the Rydberg-blockaded Hamiltonian, we show that different types of defects experience confinement, and as a consequence form mesonic or baryonic quasiparticle excitations. We illustrate the formation of these quasiparticles by studying a quantum chiral clock model related to the Rydberg Hamiltonian. We then propose an experimental protocol involving out-of-equilibrium dynamics to directly probe the spectrum of the confined excitations. We show that the confined quasiparticle spectrum can limit quantum information spreading in this system. This proposal is readily applicable to current Rydberg experiments, and the method can be easily generalized to more complex confined excitations (e.g. `tetraquarks', `pentaquarks') in phases with Zq order for q>3. 

UR - https://arxiv.org/abs/2007.07258 ER - TY - JOUR T1 - Resonant enhancement of three-body loss between strongly interacting photons Y1 - 2020 A1 - Marcin Kalinowski A1 - Yidan Wang A1 - Przemyslaw Bienias A1 - Michael Gullans A1 - Dalia P. Ornelas-Huerta A1 - Alexander N. Craddock A1 - Steven L. Rolston A1 - J. V. Porto A1 - Hans Peter Büchler A1 - Alexey V. Gorshkov AB -

Rydberg polaritons provide an example of a rare type of system where three-body interactions can be as strong or even stronger than two-body interactions. The three-body interactions can be either dispersive or dissipative, with both types possibly giving rise to exotic, strongly-interacting, and topological phases of matter. Despite past theoretical and experimental studies of the regime with dispersive interaction, the dissipative regime is still mostly unexplored. Using a renormalization group technique to solve the three-body Schrödinger equation, we show how the shape and strength of dissipative three-body forces can be universally enhanced for Rydberg polaritons. We demonstrate how these interactions relate to the transmission through a single-mode cavity, which can be used as a probe of the three-body physics in current experiment

UR - https://arxiv.org/abs/2010.09772 ER - TY - JOUR T1 - Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning JF - to appear in Proceedings of STOC 2020 Y1 - 2020 A1 - Nai-Hui Chia A1 - Andras Gilyen A1 - Tongyang Li A1 - Han-Hsuan Lin A1 - Ewin Tang A1 - Chunhao Wang AB -

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang's breakthrough quantum-inspired algorithm for recommendation systems [STOC'19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén et al. [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all recent results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: ℓ2-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.

UR - https://arxiv.org/abs/1910.06151 U5 - https://doi.org/10.1145/3357713.3384314 ER - TY - JOUR T1 - Signaling and Scrambling with Strongly Long-Range Interactions JF - Physical Review A Y1 - 2020 A1 - Andrew Y. Guo A1 - Minh C. Tran A1 - Andrew M. Childs A1 - Alexey V. Gorshkov A1 - Zhe-Xuan Gong AB -

Strongly long-range interacting quantum systems---those with interactions decaying as a power-law 1/rα in the distance r on a D-dimensional lattice for α≤D---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. As a first step towards rectifying this problem, we prove two new Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for α≤D/2. Our second bound pertains to generic long-range interacting spin Hamiltonians, and leads to a tight lower bound for the signaling time to extensive subsets of the system for all α<D. This result also lower-bounds the scrambling time, and suggests a path towards achieving a tight scrambling bound that can prove the long-standing fast scrambling conjecture. 

VL - 102 UR - https://arxiv.org/abs/1906.02662 CP - 010401(R) U5 - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.010401 ER - TY - JOUR T1 - Spin-Mediated Mott Excitons Y1 - 2020 A1 - T. -S. Huang A1 - Christopher L. Baldwin A1 - M. Hafezi A1 - V. Galitski AB -

Motivated by recent experiments on Mott insulators, in both iridates and ultracold atoms, we theoretically study the effects of magnetic order on the Mott-Hubbard excitons. In particular, we focus on spin-mediated doublon-holon pairing in Hubbard materials. We use several complementary theoretical techniques: mean-field theory to describe the spin degrees of freedom, the self-consistent Born approximation to characterize individual charge excitations across the Hubbard gap, and the Bethe-Salpeter equation to identify bound states of doublons and holons. The binding energy of the Hubbard exciton is found to increase with increasing the N{é}el order parameter, while the exciton mass decreases. We observe that these trends rely significantly on the retardation of the effective interaction, and require consideration of multiple effects from changing the magnetic order. Our results are consistent with the key qualitative trends observed in recent experiments on iridates. Moreover, the findings could have direct implications on ultracold atom Mott insulators, where the Hubbard model is the exact description of the system and the microscopic degrees of freedom can be directly accessed. 

UR - https://arxiv.org/abs/2004.10825 ER - TY - CONF T1 - Symmetries, graph properties, and quantum speedups T2 - Proceedings of the 61st IEEE Symposium on Foundations of Computer Science (FOCS 2020), pp. 649–660 (2020) Y1 - 2020 A1 - Shalev Ben-David A1 - Andrew M. Childs A1 - Andras Gilyen A1 - William Kretschmer A1 - Supartha Podder A1 - Daochen Wang AB -

Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup?
In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups.
In contrast, in the adjacency list model for bounded-degree graphs (where graph symmetry is manifested differently), we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013).

JA - Proceedings of the 61st IEEE Symposium on Foundations of Computer Science (FOCS 2020), pp. 649–660 (2020) UR - https://arxiv.org/abs/2006.12760 U5 - https://doi.org/10.1109/FOCS46700.2020.00066 ER - TY - JOUR T1 - Symmetry breaking and error correction in open quantum systems JF - Phys. Rev. Lett. Y1 - 2020 A1 - Simon Lieu A1 - Ron Belyansky A1 - Jeremy T. Young A1 - Rex Lundgren A1 - Victor V. Albert A1 - Alexey V. Gorshkov AB -

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system---a Lindbladian---a unitary symmetry can be imposed in a "weak" or a "strong" way. We characterize the possible Zn symmetry breaking transitions for both cases. In the case of Z2, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially-protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correctio

VL - 125 U4 - 240405 UR - https://arxiv.org/abs/2008.02816 U5 - https://doi.org/10.1103/PhysRevLett.125.240405 ER - TY - JOUR T1 - Time evolution of correlation functions in quantum many-body systems JF - Phys. Rev. Lett Y1 - 2020 A1 - Álvaro M. Alhambra A1 - Jonathon Riddell A1 - Luis Pedro García-Pintos AB -

We give rigorous analytical results on the temporal behavior of two-point correlation functions --also known as dynamical response functions or Green's functions-- in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times ⟨A(t)B⟩β→⟨A⟩β⟨B⟩β, thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For auto-correlation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values, and does not increase with system size. We give numerical examples that show that this bound is a good estimate in non-integrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.

VL - 124 UR - https://arxiv.org/abs/1906.11280 CP - 110605 U5 - https://doi.org/10.1103/PhysRevLett.124.110605 ER - TY - JOUR T1 - Time-information uncertainty relations in thermodynamics JF - Nat. Phys. Y1 - 2020 A1 - Schuyler B. Nicholson A1 - Luis Pedro García-Pintos A1 - Adolfo del Campo A1 - Jason R. Green AB -

Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we show that rates of energy and entropy exchange are subject to a speed limit -- a time-information uncertainty relation -- imposed by the rates of change in the information content of the system. This uncertainty relation bounds the time that elapses before the change in a thermodynamic quantity has the same magnitude as its initial standard deviation. From this general bound, we establish a family of speed limits for heat, work, entropy production, and entropy flow depending on the experimental constraints on the system. In all of these inequalities, the time scale of transient dynamical fluctuations is universally bounded by the Fisher information. Moreover, they all have a mathematical form that mirrors the Mandelstam-Tamm version of the time-energy uncertainty relation in quantum mechanics. These bounds on the speed of arbitrary observables apply to transient systems away from thermodynamic equilibrium, independent of the physical assumptions about the stochastic dynamics or their function. 

UR - https://arxiv.org/abs/2001.05418 U5 - https://doi.org/10.1038/s41567-020-0981-y ER - TY - JOUR T1 - Transport and dynamics in the frustrated two-bath spin-boson model Y1 - 2020 A1 - Ron Belyansky A1 - Seth Whitsitt A1 - Rex Lundgren A1 - Yidan Wang A1 - Andrei Vrajitoarea A1 - Andrew A. Houck A1 - Alexey V. Gorshkov AB -

We study the strong coupling dynamics as well as transport properties of photons in the two-bath spin-boson model, in which a spin-1/2 particle is frustratingly coupled to two independent Ohmic bosonic baths. Using a combination of numerical and analytical methods, we show that the frustration in this model gives rise to rich physics in a very wide range of energies. This is in contrast to the one-bath spin-boson model, where the non-trivial physics occurs at an energy scale close to the renormalized spin frequency. The renormalized spin frequency in the two-bath spin-boson model is still important, featuring in different observables, including the non-equiblirum dynamics of both the spin and the baths along with the elastic transport properties of a photon. The latter however reveals a much more complex structure. The elastic scattering displays non-monotonic behavior at high frequencies, and is very different in the two channels: intra- and inter-bath scattering. The photon can also be inelastically scattered, a process in which it is split into several photons of smaller energies. We show that such inelastic processes are highly anisotropic, with the outgoing particles being preferentially emitted into only one of the baths. Moreover, the inelastic scattering rate is parameterically larger than in the one-bath case, and can even exceed the total elastic rate. Our results can be verified with state-of-the-art circuit and cavity quantum electrodynamics experiments. 

UR - https://arxiv.org/abs/2007.03690 ER - TY - JOUR T1 - Beyond Spontaneous Emission: Giant Atom Bounded in Continuum Y1 - 2019 A1 - Shangjie Guo A1 - Yidan Wang A1 - Thomas Purdy A1 - J. M. Taylor AB -

The quantum coupling of individual superconducting qubits to microwave photons leads to remarkable experimental opportunities. Here we consider the phononic case where the qubit is coupled to an electromagnetic surface acoustic wave antenna that enables supersonic propagation of the qubit oscillations. This can be considered as a giant atom that is many phonon wavelengths long. We study an exactly solvable toy model that captures these effects, and find that this non-Markovian giant atom has a suppressed relaxation, as well as an effective vacuum coupling between a qubit excitation and a localized wave packet of sound, even in the absence of a cavity for the sound waves. Finally, we consider practical implementations of these ideas in current surface acoustic wave devices. 

UR - https://arxiv.org/abs/1912.09980 ER - TY - JOUR T1 - Canonical forms for single-qutrit Clifford+T operators JF - Annals of Physics Y1 - 2019 A1 - Andrew N. Glaudell A1 - Neil J. Ross A1 - J. M. Taylor AB -

We introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the single-qutrit Clifford+T circuits implementing a given operator our canonical form uses the least number of T gates. Finally, we provide an algorithm which inputs the description of an operator (as a matrix or a circuit) and constructs the canonical form for this operator. The algorithm runs in time linear in the number of T gates. Our results provide a higher-dimensional generalization of prior work by Matsumoto and Amano who introduced similar canonical forms for single-qubit Clifford+T circuits. 

VL - 406 U4 - 54-70 UR - https://arxiv.org/abs/1803.05047 U5 - https://doi.org/10.1016/j.aop.2019.04.001 ER - TY - JOUR T1 - A characterization of quantum chaos by two-point correlation functions Y1 - 2019 A1 - Hrant Gharibyan A1 - Masanori Hanada A1 - Brian Swingle A1 - Masaki Tezuka AB -

We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

UR - https://arxiv.org/abs/1902.11086 ER - TY - JOUR T1 - Complexity phase diagram for interacting and long-range bosonic Hamiltonians Y1 - 2019 A1 - Nishad Maskara A1 - Abhinav Deshpande A1 - Minh C. Tran A1 - Adam Ehrenberg A1 - Bill Fefferman A1 - Alexey V. Gorshkov AB -

Recent years have witnessed a growing interest in topics at the intersection of many-body physics and complexity theory. Many-body physics aims to understand and classify emergent behavior of systems with a large number of particles, while complexity theory aims to classify computational problems based on how the time required to solve the problem scales as the problem size becomes large. In this work, we use insights from complexity theory to classify phases in interacting many-body systems. Specifically, we demonstrate a "complexity phase diagram" for the Bose-Hubbard model with long-range hopping. This shows how the complexity of simulating time evolution varies according to various parameters appearing in the problem, such as the evolution time, the particle density, and the degree of locality. We find that classification of complexity phases is closely related to upper bounds on the spread of quantum correlations, and protocols to transfer quantum information in a controlled manner. Our work motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena. 

UR - https://arxiv.org/abs/1906.04178 ER - TY - JOUR T1 - Confined Dynamics in Long-Range Interacting Quantum Spin Chains JF - Phys. Rev. Lett. Y1 - 2019 A1 - Fangli Liu A1 - Rex Lundgren A1 - Paraj Titum A1 - Guido Pagano A1 - Jiehang Zhang A1 - Christopher Monroe A1 - Alexey V. Gorshkov AB -

We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law (1/rα) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic bound states in high-energy physics. We show that these bound states have dramatic consequences for the non-equilibrium dynamics following a global quantum quench, such as suppressed spreading of quantum information and oscillations of order parameters. The masses of these bound states can be read out from the Fourier spectrum of these oscillating order parameters. We then use a two-kink model to qualitatively explain the phenomenon of long-range-interaction-induced confinement. The masses of the bound states predicted by this model are in good quantitative agreement with exact diagonalization results. Moreover, we illustrate that these bound states lead to weak thermalization of local observables for initial states with energy near the bottom of the many-body energy spectrum. Our work is readily applicable to current trapped-ion experiments.

VL - 122 UR - https://arxiv.org/abs/1810.02365 CP - 150601 U5 - https://doi.org/10.1103/PhysRevLett.122.150601 ER - TY - JOUR T1 - Development of Quantum InterConnects for Next-Generation Information Technologies Y1 - 2019 A1 - David Awschalom A1 - Karl K. Berggren A1 - Hannes Bernien A1 - Sunil Bhave A1 - Lincoln D. Carr A1 - Paul Davids A1 - Sophia E. Economou A1 - Dirk Englund A1 - Andrei Faraon A1 - Marty Fejer A1 - Saikat Guha A1 - Martin V. Gustafsson A1 - Evelyn Hu A1 - Liang Jiang A1 - Jungsang Kim A1 - Boris Korzh A1 - Prem Kumar A1 - Paul G. Kwiat A1 - Marko Lončar A1 - Mikhail D. Lukin A1 - David A. B. Miller A1 - Christopher Monroe A1 - Sae Woo Nam A1 - Prineha Narang A1 - Jason S. Orcutt AB -

Just as classical information technology rests on a foundation built of interconnected information-processing systems, quantum information technology (QIT) must do the same. A critical component of such systems is the interconnect, a device or process that allows transfer of information between disparate physical media, for example, semiconductor electronics, individual atoms, light pulses in optical fiber, or microwave fields. While interconnects have been well engineered for decades in the realm of classical information technology, quantum interconnects (QuICs) present special challenges, as they must allow the transfer of fragile quantum states between different physical parts or degrees of freedom of the system. The diversity of QIT platforms (superconducting, atomic, solid-state color center, optical, etc.) that will form a quantum internet poses additional challenges. As quantum systems scale to larger size, the quantum interconnect bottleneck is imminent, and is emerging as a grand challenge for QIT. For these reasons, it is the position of the community represented by participants of the NSF workshop on Quantum Interconnects that accelerating QuIC research is crucial for sustained development of a national quantum science and technology program. Given the diversity of QIT platforms, materials used, applications, and infrastructure required, a convergent research program including partnership between academia, industry and national laboratories is required. This document is a summary from a U.S. National Science Foundation supported workshop held on 31 October - 1 November 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum interconnects over the next 2-5 years. 

UR - https://arxiv.org/abs/1912.06642 ER - TY - JOUR T1 - Feshbach resonances in p-wave three-body recombination within Fermi-Fermi mixtures of open-shell 6Li and closed-shell 173Yb atoms Y1 - 2019 A1 - Alaina Green A1 - Hui Li A1 - Jun Hui See Toh A1 - Xinxin Tang A1 - Katherine McCormick A1 - Ming Li A1 - Eite Tiesinga A1 - Svetlana Kotochigova A1 - Subhadeep Gupta AB -

We report on observations and modeling of interspecies magnetic Feshbach resonances in dilute ultracold mixtures of open-shell alkali-metal 6Li and closed-shell 173Yb atoms with temperatures just above quantum degeneracy for both fermionic species. Resonances are located by detecting magnetic-field-dependent atom loss due to three-body recombination. We resolve closely-located resonances that originate from a weak separation-dependent hyperfine coupling between the electronic spin of 6Li and the nuclear spin of 173Yb, and confirm their magnetic field spacing by ab initio electronic-structure calculations. Through quantitative comparisons of theoretical atom-loss profiles and experimental data at various temperatures between 1 μK and 20 μK, we show that three-body recombination in fermionic mixtures has a p-wave Wigner threshold behavior leading to characteristic asymmetric loss profiles. Such resonances can be applied towards the formation of ultracold doublet ground-state molecules and quantum simulation of superfluid p-wave pairing.

UR - https://arxiv.org/abs/1912.04874 ER - TY - JOUR T1 - Floquet engineering of optical lattices with spatial features and periodicity below the diffraction limit Y1 - 2019 A1 - S. Subhankar A1 - P. Bienias A1 - P. Titum A1 - T-C. Tsui A1 - Y. Wang A1 - Alexey V. Gorshkov A1 - S. L. Rolston A1 - J. V. Porto AB -

Floquet engineering or coherent time periodic driving of quantum systems has been successfully used to synthesize Hamiltonians with novel properties. In ultracold atomic systems, this has led to experimental realizations of artificial gauge fields, topological band structures, and observation of dynamical localization, to name just a few. Here we present a Floquet-based framework to stroboscopically engineer Hamiltonians with spatial features and periodicity below the diffraction limit of light used to create them by time-averaging over various configurations of a 1D optical Kronig-Penney (KP) lattice. The KP potential is a lattice of narrow subwavelength barriers spaced by half the optical wavelength (λ/2) and arises from the non-linear optical response of the atomic dark state. Stroboscopic control over the strength and position of this lattice requires time-dependent adiabatic manipulation of the dark state spin composition. We investigate adiabaticity requirements and shape our time-dependent light fields to respect the requirements. We apply this framework to show that a λ/4-spaced lattice can be synthesized using realistic experimental parameters as an example, discuss mechanisms that limit lifetimes in these lattices, explore candidate systems and their limitations, and treat adiabatic loading into the ground band of these lattices.

UR - https://arxiv.org/abs/1906.07646 ER - TY - JOUR T1 - Fluctuation-induced torque on a topological insulator out of thermal equilibrium JF - Phys. Rev. Lett. Y1 - 2019 A1 - M. F. Maghrebi A1 - Alexey V. Gorshkov A1 - J. D. Sau AB -

Topological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well-understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. Utilizing the Keldysh framework, we investigate the universal nonequilibrium response of the TI to the temperature difference with the environment. Finally, we argue that experimental observation of this effect is within reach.

VL - 123 UR - https://arxiv.org/abs/1811.06080 CP - 055901 U5 - https://doi.org/10.1103/PhysRevLett.123.055901 ER - TY - JOUR T1 - Heisenberg-Scaling Measurement Protocol for Analytic Functions with Quantum Sensor Networks JF - Phys. Rev. A Y1 - 2019 A1 - Kevin Qian A1 - Zachary Eldredge A1 - Wenchao Ge A1 - Guido Pagano A1 - Christopher Monroe A1 - James V. Porto A1 - Alexey V. Gorshkov AB -

We generalize past work on quantum sensor networks to show that, for d input parameters, entanglement can yield a factor O(d) improvement in mean squared error when estimating an analytic function of these parameters. We show that the protocol is optimal for qubit sensors, and conjecture an optimal protocol for photons passing through interferometers. Our protocol is also applicable to continuous variable measurements, such as one quadrature of a field operator. We outline a few potential applications, including calibration of laser operations in trapped ion quantum computing.

VL - 100 UR - https://arxiv.org/abs/1901.09042 CP - 042304 U5 - https://doi.org/10.1103/PhysRevA.100.042304 ER - TY - JOUR T1 - Interacting Qubit-Photon Bound States with Superconducting Circuits JF - Phys. Rev. Y1 - 2019 A1 - Neereja M. Sundaresan A1 - Rex Lundgren A1 - Guanyu Zhu A1 - Alexey V. Gorshkov A1 - Andrew A. Houck AB -

Qubits strongly coupled to a photonic crystal give rise to many exotic physical scenarios, beginning with single and multi-excitation qubit-photon dressed bound states comprising induced spatially localized photonic modes, centered around the qubits, and the qubits themselves. The localization of these states changes with qubit detuning from the band-edge, offering an avenue of in situ control of bound state interaction. Here, we present experimental results from a device with two qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and inter-bound state interactions. We observe a fourth-order two photon virtual process between bound states indicating strong coupling between the photonic crystal and qubits. Due to their localization-dependent interaction, these states offer the ability to create one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits' spatial organization, a key criterion for realization of certain quantum many-body models. The widely tunable, strong and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems of bound states.

VL - X 9 UR - http://arxiv.org/abs/1801.10167 CP - 011021 U5 - https://doi.org/10.1103/PhysRevX.9.011021 ER - TY - JOUR T1 - Interaction-induced transition in the quantum chaotic dynamics of a disordered metal JF - Ann. Phys. Y1 - 2019 A1 - S. V. Syzranov A1 - Alexey V. Gorshkov A1 - V. M. Galitski AB -

We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups.

VL - 405 UR - https://arxiv.org/abs/1709.09296 CP - 1 U5 - https://doi.org/10.1016/j.aop.2019.03.008 ER - TY - JOUR T1 - Interference of Temporally Distinguishable Photons Using Frequency-Resolved Detection JF - Phys. Rev. Lett. Y1 - 2019 A1 - Venkata Vikram Orre A1 - Elizabeth A. Goldschmidt A1 - Abhinav Deshpande A1 - Alexey V. Gorshkov A1 - Vincenzo Tamma A1 - Mohammad Hafezi A1 - Sunil Mittal AB -

We demonstrate quantum interference of three photons that are distinguishable in time, by resolving them in the conjugate parameter, frequency. We show that the multiphoton interference pattern in our setup can be manipulated by tuning the relative delays between the photons, without the need for reconfiguring the optical network. Furthermore, we observe that the symmetries of our optical network and the spectral amplitude of the input photons are manifested in the interference pattern. Moreover, we demonstrate time-reversed HOM-like interference in the spectral correlations using time-bin entangled photon pairs. By adding a time-varying dispersion using a phase modulator, our setup can be used to realize dynamically reconfigurable and scalable boson sampling in the time domain as well as frequency-resolved multiboson correlation sampling.

VL - 123 UR - https://arxiv.org/abs/1904.03222 CP - 123603 U5 - https://doi.org/10.1103/PhysRevLett.123.123603 ER - TY - JOUR T1 - Locality and digital quantum simulation of power-law interactions JF - Phys. Rev. X 9, 031006 Y1 - 2019 A1 - Minh C. Tran A1 - Andrew Y. Guo A1 - Yuan Su A1 - James R. Garrison A1 - Zachary Eldredge A1 - Michael Foss-Feig A1 - Andrew M. Childs A1 - Alexey V. Gorshkov AB -

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/rα. The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al. [arXiv:1801.03922]. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when α>3D (where D is the number of dimensions).

VL - 9 UR - https://arxiv.org/abs/1808.05225 CP - 031006 U5 - https://doi.org/10.1103/PhysRevX.9.031006 ER - TY - JOUR T1 - Locality and Heating in Periodically Driven, Power-law Interacting Systems JF - Phys. Rev. A Y1 - 2019 A1 - Minh C. Tran A1 - Adam Ehrenberg A1 - Andrew Y. Guo A1 - Paraj Titum A1 - Dmitry A. Abanin A1 - Alexey V. Gorshkov AB -

We study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power-law 1/rα. Using linear response theory, we show that the heating time is exponentially long as a function of the drive frequency for α>D. For systems that may not obey linear response theory, we use a more general Magnus-like expansion to show the existence of quasi-conserved observables, which imply exponentially long heating time, for α>2D. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound. 

VL - 100 UR - https://arxiv.org/abs/1908.02773 CP - 052103 U5 - https://doi.org/10.1103/PhysRevA.100.052103 ER - TY - JOUR T1 - On the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model Y1 - 2019 A1 - Rex Lundgren A1 - Alexey V. Gorshkov A1 - Mohammad F. Maghrebi AB -

The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this work, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents, including those, such as the dynamical critical exponent, that have not been previously considered. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely non-equilibrium. We derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that capture the system's long-time memory as well as its non-equilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.

UR - https://arxiv.org/abs/1910.04319 ER - TY - JOUR T1 - Nondestructive cooling of an atomic quantum register via state-insensitive Rydberg interactions Y1 - 2019 A1 - Ron Belyansky A1 - Jeremy T. Young A1 - Przemyslaw Bienias A1 - Zachary Eldredge A1 - Adam M. Kaufman A1 - Peter Zoller A1 - Alexey V. Gorshkov AB -

We propose a protocol for sympathetically cooling neutral atoms without destroying the quantum information stored in their internal states. This is achieved by designing state-insensitive Rydberg interactions between the data-carrying atoms and cold auxiliary atoms. The resulting interactions give rise to an effective phonon coupling, which leads to the transfer of heat from the data atoms to the auxiliary atoms, where the latter can be cooled by conventional methods. This can be used to extend the lifetime of quantum storage based on neutral atoms and can have applications for long quantum computations. The protocol can also be modified to realize state-insensitive interactions between the data and the auxiliary atoms but tunable and non-trivial interactions among the data atoms, allowing one to simultaneously cool and simulate a quantum spin-model. 

UR - https://arxiv.org/abs/1907.11156 ER - TY - JOUR T1 - Number-Theoretic Characterizations of Some Restricted Clifford+T Circuits Y1 - 2019 A1 - Matthew Amy A1 - Andrew N. Glaudell A1 - Neil J. Ross AB -

Kliuchnikov, Maslov, and Mosca proved in 2012 that a 2×2 unitary matrix V can be exactly represented by a single-qubit Clifford+T circuit if and only if the entries of V belong to the ring Z[1/2–√,i]. Later that year, Giles and Selinger showed that the same restriction applies to matrices that can be exactly represented by a multi-qubit Clifford+T circuit. These number-theoretic characterizations shed new light upon the structure of Clifford+T circuits and led to remarkable developments in the field of quantum compiling. In the present paper, we provide number-theoretic characterizations for certain restricted Clifford+T circuits by considering unitary matrices over subrings of Z[1/2–√,i]. We focus on the subrings Z[1/2], Z[1/2–√], Z[1/-2−−√], and Z[1/2,i], and we prove that unitary matrices with entries in these rings correspond to circuits over well-known universal gate sets. In each case, the desired gate set is obtained by extending the set of classical reversible gates {X,CX,CCX} with an analogue of the Hadamard gate and an optional phase gate.

UR - https://arxiv.org/abs/1908.06076 ER - TY - JOUR T1 - Observation of Domain Wall Confinement and Dynamics in a Quantum Simulator Y1 - 2019 A1 - W. L. Tan A1 - P. Becker A1 - F. Liu A1 - G. Pagano A1 - K. S. Collins A1 - A. De A1 - L. Feng A1 - H. B. Kaplan A1 - A. Kyprianidis A1 - R. Lundgren A1 - W. Morong A1 - S. Whitsitt A1 - Alexey V. Gorshkov A1 - C. Monroe AB -

Confinement is a ubiquitous mechanism in nature, whereby particles feel an attractive force that increases without bound as they separate. A prominent example is color confinement in particle physics, in which baryons and mesons are produced by quark confinement. Analogously, confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here, we report the first observation of magnetic domain wall confinement in interacting spin chains with a trapped-ion quantum simulator. By measuring how correlations spread, we show that confinement can dramatically suppress information propagation and thermalization in such many-body systems. We are able to quantitatively determine the excitation energy of domain wall bound states from non-equilibrium quench dynamics. Furthermore, we study the number of domain wall excitations created for different quench parameters, in a regime that is difficult to model with classical computers. This work demonstrates the capability of quantum simulators for investigating exotic high-energy physics phenomena, such as quark collision and string breaking

UR - https://arxiv.org/abs/1912.11117 ER - TY - JOUR T1 - Opportunities for Nuclear Physics & Quantum Information Science Y1 - 2019 A1 - I. C. Cloët A1 - Matthew R. Dietrich A1 - John Arrington A1 - Alexei Bazavov A1 - Michael Bishof A1 - Adam Freese A1 - Alexey V. Gorshkov A1 - Anna Grassellino A1 - Kawtar Hafidi A1 - Zubin Jacob A1 - Michael McGuigan A1 - Yannick Meurice A1 - Zein-Eddine Meziani A1 - Peter Mueller A1 - Christine Muschik A1 - James Osborn A1 - Matthew Otten A1 - Peter Petreczky A1 - Tomas Polakovic A1 - Alan Poon A1 - Raphael Pooser A1 - Alessandro Roggero A1 - Mark Saffman A1 - Brent VanDevender A1 - Jiehang Zhang A1 - Erez Zohar AB -

his whitepaper is an outcome of the workshop Intersections between Nuclear Physics and Quantum Information held at Argonne National Laboratory on 28-30 March 2018 [www.phy.anl.gov/npqi2018/]. The workshop brought together 116 national and international experts in nuclear physics and quantum information science to explore opportunities for the two fields to collaborate on topics of interest to the U.S. Department of Energy (DOE) Office of Science, Office of Nuclear Physics, and more broadly to U.S. society and industry. The workshop consisted of 22 invited and 10 contributed talks, as well as three panel discussion sessions. Topics discussed included quantum computation, quantum simulation, quantum sensing, nuclear physics detectors, nuclear many-body problem, entanglement at collider energies, and lattice gauge theories.

UR - https://arxiv.org/abs/1903.05453 ER - TY - JOUR T1 - Probing ground-state phase transitions through quench dynamics JF - Phys. Rev. Lett. Y1 - 2019 A1 - Paraj Titum A1 - Joseph T. Iosue A1 - James R. Garrison A1 - Alexey V. Gorshkov A1 - Zhe-Xuan Gong AB -

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.

VL - 123 UR - https://arxiv.org/abs/1809.06377 CP - 115701 U5 - https://doi.org/10.1103/PhysRevLett.123.115701 ER - TY - JOUR T1 - Programmable Quantum Simulations of Spin Systems with Trapped Ions Y1 - 2019 A1 - C. Monroe A1 - W. C. Campbell A1 - L. -M. Duan A1 - Z. -X. Gong A1 - Alexey V. Gorshkov A1 - P. Hess A1 - R. Islam A1 - K. Kim A1 - G. Pagano A1 - P. Richerme A1 - C. Senko A1 - N. Y. Yao AB -

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. 

UR - https://arxiv.org/abs/1912.07845 ER - TY - JOUR T1 - Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator Y1 - 2019 A1 - G. Pagano A1 - A. Bapat A1 - P. Becker A1 - K. S. Collins A1 - A. De A1 - P. W. Hess A1 - H. B. Kaplan A1 - A. Kyprianidis A1 - W. L. Tan A1 - Christopher L. Baldwin A1 - L. T. Brady A1 - A. Deshpande A1 - F. Liu A1 - S. Jordan A1 - Alexey V. Gorshkov A1 - C. Monroe AB -

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly solving exponentially hard problems, such as optimization and satisfiability. Here we report the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator to estimate the ground state energy of the transverse field Ising model with tunable long-range interactions. First, we exhaustively search the variational control parameters to approximate the ground state energy with up to 40 trapped-ion qubits. We then interface the quantum simulator with a classical algorithm to more efficiently find the optimal set of parameters that minimizes the resulting energy of the system. We finally sample from the full probability distribution of the QAOA output with single-shot and efficient measurements of every qubit. 

UR - https://arxiv.org/abs/1906.02700 ER - TY - JOUR T1 - Quantum Computer Systems for Scientific Discovery Y1 - 2019 A1 - Yuri Alexeev A1 - Dave Bacon A1 - Kenneth R. Brown A1 - Robert Calderbank A1 - Lincoln D. Carr A1 - Frederic T. Chong A1 - Brian DeMarco A1 - Dirk Englund A1 - Edward Farhi A1 - Bill Fefferman A1 - Alexey V. Gorshkov A1 - Andrew Houck A1 - Jungsang Kim A1 - Shelby Kimmel A1 - Michael Lange A1 - Seth Lloyd A1 - Mikhail D. Lukin A1 - Dmitri Maslov A1 - Peter Maunz A1 - Christopher Monroe A1 - John Preskill A1 - Martin Roetteler A1 - Martin Savage A1 - Jeff Thompson A1 - Umesh Vazirani AB -

The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, and significant challenges for the development of quantum computers for science over the next 2-10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21-22, 2019 in Alexandria, VA.

UR - https://arxiv.org/abs/1912.07577 ER - TY - JOUR T1 - Quantum Computing at the Frontiers of Biological Sciences Y1 - 2019 A1 - Prashant S. Emani A1 - Jonathan Warrell A1 - Alan Anticevic A1 - Stefan Bekiranov A1 - Michael Gandal A1 - Michael J. McConnell A1 - Guillermo Sapiro A1 - Alán Aspuru-Guzik A1 - Justin Baker A1 - Matteo Bastiani A1 - Patrick McClure A1 - John Murray A1 - Stamatios N Sotiropoulos A1 - J. M. Taylor A1 - Geetha Senthil A1 - Thomas Lehner A1 - Mark B. Gerstein A1 - Aram W. Harrow AB -

The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems. Innovation in massively parallel, classical computing hardware and algorithms continues to address many of these challenges, but there is a need to simultaneously consider new paradigms to circumvent current barriers to processing speed. Accordingly, we articulate a view towards quantum computation and quantum information science, where algorithms have demonstrated potential polynomial and exponential computational speedups in certain applications, such as machine learning. The maturation of the field of quantum computing, in hardware and algorithm development, also coincides with the growth of several collaborative efforts to address questions across length and time scales, and scientific disciplines. We use this coincidence to explore the potential for quantum computing to aid in one such endeavor: the merging of insights from genetics, genomics, neuroimaging and behavioral phenotyping. By examining joint opportunities for computational innovation across fields, we highlight the need for a common language between biological data analysis and quantum computing. Ultimately, we consider current and future prospects for the employment of quantum computing algorithms in the biological sciences. 

UR - https://arxiv.org/abs/1911.07127 ER - TY - JOUR T1 - Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes Y1 - 2019 A1 - Adam R. Brown A1 - Hrant Gharibyan A1 - Stefan Leichenauer A1 - Henry W. Lin A1 - Sepehr Nezami A1 - Grant Salton A1 - Leonard Susskind A1 - Brian Swingle A1 - Michael Walter AB -

With the long-term goal of studying quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in recent traversable wormhole constructions: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of "teleportation by size" to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semi-classical holographic wormhole corresponds to a rather special property of the operator-size distribution we call "size winding". For more general setups (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable wormhole phenomenon. For example, a form of signalling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole, but rather to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations feasible with current technology in two experimental platforms: Rydberg atom arrays and trapped ions. 

UR - https://arxiv.org/abs/1911.06314 ER - TY - JOUR T1 - Quantum hardness of learning shallow classical circuits Y1 - 2019 A1 - Srinivasan Arunachalam A1 - Alex B. Grilo A1 - Aarthi Sundaram AB -

In this paper we study the quantum learnability of constant-depth classical circuits under the uniform distribution and in the distribution-independent framework of PAC learning. In order to attain our results, we establish connections between quantum learning and quantum-secure cryptosystems. We then achieve the following results. 1) Hardness of learning AC0 and TC0 under the uniform distribution. Our first result concerns the concept class TC0 (resp. AC0), the class of constant-depth and polynomial-sized circuits with unbounded fan-in majority gates (resp. AND, OR, NOT gates). We show that if there exists no quantum polynomial-time (resp. sub-exponential time) algorithm to solve the Learning with Errors (LWE) problem, then there exists no polynomial-time quantum learning algorithm for TC0 (resp. AC0) under the uniform distribution (even with access to quantum membership queries). The main technique in this result uses explicit pseudo-random generators that are believed to be quantum-secure to construct concept classes that are hard to learn quantumly under the uniform distribution. 2) Hardness of learning TC02 in the PAC setting. Our second result shows that if there exists no quantum polynomial time algorithm for the LWE problem, then there exists no polynomial time quantum PAC learning algorithm for the class TC02, i.e., depth-2 TC0 circuits. The main technique in this result is to establish a connection between the quantum security of public-key cryptosystems and the learnability of a concept class that consists of decryption functions of the cryptosystem. This gives a strong conditional negative answer to one of the "Ten Semi-Grand Challenges for Quantum Computing Theory" raised by Aaronson [Aar05], who asked if AC0 and TC0 can be PAC-learned in quantum polynomial time.

UR - https://arxiv.org/abs/1903.02840 ER - TY - JOUR T1 - Quantum Lyapunov Spectrum JF - JHEP04 Y1 - 2019 A1 - Hrant Gharibyan A1 - Masanori Hanada A1 - Brian Swingle A1 - Masaki Tezuka AB -

We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is not just the fastest scrambler, but also the fastest entropy generator. We also study the statistical features of the quantum Lyapunov spectrum and find universal random matrix behavior, which resembles the recently-found universality in classical chaos. The random matrix behavior is lost when the system is deformed away from chaos, towards integrability or a many-body localized phase. We propose that quantum systems holographically dual to gravity satisfy this universality in a strong form. We further argue that the quantum Lyapunov spectrum contains important additional information beyond the largest Lyapunov exponent and hence provides us with a better characterization of chaos in quantum systems. 

VL - 082 UR - https://arxiv.org/abs/1809.01671 U5 - https://doi.org/10.1007/JHEP04(2019)082 ER - TY - JOUR T1 - Quantum Simulators: Architectures and Opportunities Y1 - 2019 A1 - Ehud Altman A1 - Kenneth R. Brown A1 - Giuseppe Carleo A1 - Lincoln D. Carr A1 - Eugene Demler A1 - Cheng Chin A1 - Brian DeMarco A1 - Sophia E. Economou A1 - Mark A. Eriksson A1 - Kai-Mei C. Fu A1 - Markus Greiner A1 - Kaden R. A. Hazzard A1 - Randall G. Hulet A1 - Alicia J. Kollár A1 - Benjamin L. Lev A1 - Mikhail D. Lukin A1 - Ruichao Ma A1 - Xiao Mi A1 - Shashank Misra A1 - Christopher Monroe A1 - Kater Murch A1 - Zaira Nazario A1 - Kang-Kuen Ni A1 - Andrew C. Potter A1 - Pedram Roushan AB -

Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behaviors to explore and solve hard scientific, engineering, and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special purpose simulators to flexible programmable devices. These developments have enabled a convergence of ideas drawn from fundamental physics, computer science, and device engineering. They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes, to enabling the design of new materials with enhanced performance, to solving complex computational problems. It is the position of the community, as represented by participants of the NSF workshop on "Programmable Quantum Simulators," that investment in a national quantum simulator program is a high priority in order to accelerate the progress in this field and to result in the first practical applications of quantum machines. Such a program should address two areas of emphasis: (1) support for creating quantum simulator prototypes usable by the broader scientific community, complementary to the present universal quantum computer effort in industry; and (2) support for fundamental research carried out by a blend of multi-investigator, multi-disciplinary collaborations with resources for quantum simulator software, hardware, and education. 

UR - https://arxiv.org/abs/1912.06938 ER - TY - JOUR T1 - Real-time dynamics of string breaking in quantum spin chains Y1 - 2019 A1 - Roberto Verdel A1 - Fangli Liu A1 - Seth Whitsitt A1 - Alexey V. Gorshkov A1 - Markus Heyl AB -

String breaking is a central dynamical process in theories featuring confinement, where a string connecting two charges decays at the expense of the creation of new particle-antiparticle pairs. Here, we show that this process can also be observed in quantum Ising chains where domain walls get confined either by a symmetry-breaking field or by long-range interactions. We find that string breaking occurs, in general, as a two-stage process: First, the initial charges remain essentially static and stable. The connecting string, however, can become a dynamical object. We develop an effective description of this motion, which we find is strongly constrained. In the second stage, which can be severely delayed due to these dynamical constraints, the string finally breaks. We observe that the associated time scale can depend crucially on the initial separation between domain walls and can grow by orders of magnitude by changing the distance by just a few lattice sites. We discuss how our results generalize to one-dimensional confining gauge theories and how they can be made accessible in quantum simulator experiments such as Rydberg atoms or trapped ions.

UR - https://arxiv.org/abs/1911.11382 ER - TY - JOUR T1 - Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator JF - Phys. Rev. Lett Y1 - 2019 A1 - Su-Kuan Chu A1 - Guanyu Zhu A1 - James R. Garrison A1 - Zachary Eldredge A1 - Ana Valdés Curiel A1 - Przemyslaw Bienias A1 - I. B. Spielman A1 - Alexey V. Gorshkov AB -

The multi-scale entanglement renormalization ansatz (MERA) postulates the existence of quantum circuits that renormalize entanglement in real space at different length scales. Chern insulators, however, cannot have scale-invariant discrete MERA circuits with finite bond dimension. In this Letter, we show that the continuous MERA (cMERA), a modified version of MERA adapted for field theories, possesses a fixed point wavefunction with nonzero Chern number. Additionally, it is well known that reversed MERA circuits can be used to prepare quantum states efficiently in time that scales logarithmically with the size of the system. However, state preparation via MERA typically requires the advent of a full-fledged universal quantum computer. In this Letter, we demonstrate that our cMERA circuit can potentially be realized in existing analog quantum computers, i.e., an ultracold atomic Fermi gas in an optical lattice with light-induced spin-orbit coupling. 

VL - 122 UR - https://arxiv.org/abs/1807.11486 CP - 120502 U5 - https://doi.org/10.1103/PhysRevLett.122.120502 ER - TY - JOUR T1 - Site-by-site quantum state preparation algorithm for preparing vacua of fermionic lattice field theories Y1 - 2019 A1 - Ali Hamed Moosavian A1 - James R. Garrison A1 - Stephen P. Jordan AB -

Answering whether quantum computers can efficiently simulate quantum field theories has both theoretical and practical motivation. From the theoretical point of view, it answers the question of whether a hypothetical computer that utilizes quantum field theory would be more powerful than other quantum computers. From the practical point of view, when reliable quantum computers are eventually built, these algorithms can help us better understand the underlying physics that govern our world. In the best known quantum algorithms for simulating quantum field theories, the time scaling is dominated by initial state preparation. In this paper, we exclusively focus on state preparation and present a heuristic algorithm that can prepare the vacuum of fermionic systems in more general cases and more efficiently than previous methods. With our method, state preparation is no longer the bottleneck, as its runtime has the same asymptotic scaling with the desired precision as the remainder of the simulation algorithm. We numerically demonstrate the effectiveness of our proposed method for the 1+1 dimensional Gross-Neveu model.

UR - https://arxiv.org/abs/1911.03505 ER - TY - JOUR T1 - Statistical Privacy in Distributed Average Consensus on Bounded Real Inputs Y1 - 2019 A1 - Nirupam Gupta A1 - Jonathan Katz A1 - Nikhil Chopra AB -

This paper proposes a privacy protocol for distributed average consensus algorithms on bounded real-valued inputs that guarantees statistical privacy of honest agents' inputs against colluding (passive adversarial) agents, if the set of colluding agents is not a vertex cut in the underlying communication network. This implies that privacy of agents' inputs is preserved against t number of arbitrary colluding agents if the connectivity of the communication network is at least (t+1). A similar privacy protocol has been proposed for the case of bounded integral inputs in our previous paper~\cite{gupta2018information}. However, many applications of distributed consensus concerning distributed control or state estimation deal with real-valued inputs. Thus, in this paper we propose an extension of the privacy protocol in~\cite{gupta2018information}, for bounded real-valued agents' inputs, where bounds are known apriori to all the agents. 

UR - https://arxiv.org/abs/1903.09315 ER - TY - JOUR T1 - Asymmetric Particle Transport and Light-Cone Dynamics Induced by Anyonic Statistics JF - Phys. Rev. Lett Y1 - 2018 A1 - Fangli Liu A1 - James R. Garrison A1 - Dong-Ling Deng A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov AB -

We study the non-equilibrium dynamics of Abelian anyons in a one-dimensional system. We find that the interplay of anyonic statistics and interactions gives rise to spatially asymmetric particle transport together with a novel dynamical symmetry that depends on the anyonic statistical angle and the sign of interactions. Moreover, we show that anyonic statistics induces asymmetric spreading of quantum information, characterized by asymmetric light cones of out-of-time-ordered correlators. Such asymmetric dynamics is in sharp contrast with the dynamics of conventional fermions or bosons, where both the transport and information dynamics are spatially symmetric. We further discuss experiments with cold atoms where the predicted phenomena can be observed using state-of-the-art technologies. Our results pave the way toward experimentally probing anyonic statistics through non-equilibrium dynamics.

VL - 121 UR - https://arxiv.org/abs/1809.02614 CP - 250404 U5 - https://doi.org/10.1103/PhysRevLett.121.250404 ER - TY - JOUR T1 - Bose Condensation of Photons Thermalized via Laser Cooling of Atoms Y1 - 2018 A1 - Chiao-Hsuan Wang A1 - Michael Gullans A1 - J. V. Porto A1 - William D. Phillips A1 - J. M. Taylor AB -

A Bose-Einstein condensate (BEC) is a quantum phase of matter achieved at low temperatures. Photons, one of the most prominent species of bosons, do not typically condense due to the lack of a particle number-conservation. We recently described a photon thermalization mechanism which gives rise to a grand canonical ensemble of light with effective photon number conservation between a subsystem and a particle reservoir. This mechanism occurs during Doppler laser cooling of atoms where the atoms serve as a temperature reservoir while the cooling laser photons serve as a particle reservoir. Here we address the question of the possibility of a BEC of photons in this laser cooling photon thermalization scenario and theoretically demonstrate that a Bose condensation of photons can be realized by cooling an ensemble of two-level atoms (realizable with alkaline earth atoms) inside a Fabry-Perot cavity.

UR - https://arxiv.org/abs/1809.07777 ER - TY - JOUR T1 - Classical lower bounds from quantum upper bounds Y1 - 2018 A1 - Shalev Ben-David A1 - Adam Bouland A1 - Ankit Garg A1 - Robin Kothari AB -

We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the combinatorial group testing problem. 
We show that for any function f, the approximate degree of computing the OR of n copies of f is Omega(sqrt{n}) times the approximate degree of f, which is optimal. No such general result was known prior to our work, and even the lower bound for the OR of ANDs function was only resolved in 2013. 
We then prove an analogous result in communication complexity, showing that the logarithm of the approximate rank (or more precisely, the approximate gamma_2 norm) of F: X x Y -> {0,1} grows by a factor of Omega~(sqrt{n}) when we take the OR of n copies of F, which is also essentially optimal. As a corollary, we give a new proof of Razborov's celebrated Omega(sqrt{n}) lower bound on the quantum communication complexity of the disjointness problem. 
Finally, we generalize both these results from composition with the OR function to composition with arbitrary symmetric functions, yielding nearly optimal lower bounds in this setting as well.

UR - https://arxiv.org/abs/1807.06256 ER - TY - JOUR T1 - Coherent optical nano-tweezers for ultra-cold atoms Y1 - 2018 A1 - P. Bienias A1 - S. Subhankar A1 - Y. Wang A1 - T-C Tsui A1 - F. Jendrzejewski A1 - T. Tiecke A1 - G. Juzeliūnas A1 - L. Jiang A1 - S. L. Rolston A1 - J. V. Porto A1 - Alexey V. Gorshkov AB -

There has been a recent surge of interest and progress in creating subwavelength free-space optical potentials for ultra-cold atoms. A key open question is whether geometric potentials, which are repulsive and ubiquitous in the creation of subwavelength free-space potentials, forbid the creation of narrow traps with long lifetimes. Here, we show that it is possible to create such traps. We propose two schemes for realizing subwavelength traps and demonstrate their superiority over existing proposals. We analyze the lifetime of atoms in such traps and show that long-lived bound states are possible. This work opens a new frontier for the subwavelength control and manipulation of ultracold matter, with applications in quantum chemistry and quantum simulation.

UR - https://arxiv.org/abs/1808.02487 ER - TY - JOUR T1 - Dark state optical lattice with sub-wavelength spatial structure JF - Phys. Rev. Lett. Y1 - 2018 A1 - Yang Wang A1 - Sarthak Subhankar A1 - Przemyslaw Bienias A1 - Mateusz Lacki A1 - Tsz-Chun Tsui A1 - Mikhail A. Baranov A1 - Alexey V. Gorshkov A1 - Peter Zoller A1 - James V. Porto A1 - Steven L. Rolston AB -

We report on the experimental realization of a conservative optical lattice for cold atoms with a subwavelength spatial structure. The potential is based on the nonlinear optical response of three-level atoms in laser-dressed dark states, which is not constrained by the diffraction limit of the light generating the potential. The lattice consists of a one-dimensional array of ultranarrow barriers with widths less than 10 nm, well below the wavelength of the lattice light, physically realizing a Kronig-Penney potential. We study the band structure and dissipation of this lattice and find good agreement with theoretical predictions. Even on resonance, the observed lifetimes of atoms trapped in the lattice are as long as 44 ms, nearly 105times the excited state lifetime, and could be further improved with more laser intensity. The potential is readily generalizable to higher dimensions and different geometries, allowing, for example, nearly perfect box traps, narrow tunnel junctions for atomtronics applications, and dynamically generated lattices with subwavelength spacings.

VL - 120 U4 - 083601 UR - https://link.aps.org/doi/10.1103/PhysRevLett.120.083601 U5 - 10.1103/PhysRevLett.120.083601 ER - TY - JOUR T1 - Dissipation induced dipole blockade and anti-blockade in driven Rydberg systems JF - Phys. Rev. A Y1 - 2018 A1 - Jeremy T. Young A1 - Thomas Boulier A1 - Eric Magnan A1 - Elizabeth A. Goldschmidt A1 - Ryan M. Wilson A1 - Steven L. Rolston A1 - James V. Porto A1 - Alexey V. Gorshkov AB -

We study theoretically and experimentally the competing blockade and antiblockade effects induced by spontaneously generated contaminant Rydberg atoms in driven Rydberg systems. These contaminant atoms provide a source of strong dipole-dipole interactions and play a crucial role in the system's behavior. We study this problem theoretically using two different approaches. The first is a cumulant expansion approximation, in which we ignore third-order and higher connected correlations. Using this approach for the case of resonant drive, a many-body blockade radius picture arises, and we find qualitative agreement with previous experimental results. We further predict that as the atomic density is increased, the Rydberg population's dependence on Rabi frequency will transition from quadratic to linear dependence at lower Rabi frequencies. We study this behavior experimentally by observing this crossover at two different atomic densities. We confirm that the larger density system has a smaller crossover Rabi frequency than the smaller density system. The second theoretical approach is a set of phenomenological inhomogeneous rate equations. We compare the results of our rate-equation model to the experimental observations [E. A. Goldschmidt et al.Phys. Rev. Lett. 116, 113001 (2016)] and find that these rate equations provide quantitatively good scaling behavior of the steady-state Rydberg population for both resonant and off-resonant drives.

VL - 97 U4 - 023424 UR - https://link.aps.org/doi/10.1103/PhysRevA.97.023424 U5 - 10.1103/PhysRevA.97.023424 ER - TY - JOUR T1 - Distributed Quantum Metrology and the Entangling Power of Linear Networks JF - Phys. Rev. Lett. 121, 043604 Y1 - 2018 A1 - Wenchao Ge A1 - Kurt Jacobs A1 - Zachary Eldredge A1 - Alexey V. Gorshkov A1 - Michael Foss-Feig AB -

We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality. 

UR - https://arxiv.org/abs/1707.06655 U5 - https://doi.org/10.1103/PhysRevLett.121.043604 ER - TY - JOUR T1 - Distributed Quantum Metrology and the Entangling Power of Linear Networks Y1 - 2018 A1 - Wenchao Ge A1 - Kurt Jacobs A1 - Zachary Eldredge A1 - Alexey V. Gorshkov A1 - Michael Foss-Feig AB -

We derive a bound on the ability of a linear optical network to estimate a linear combination of independent phase shifts by using an arbitrary non-classical but unentangled input state, thereby elucidating the quantum resources required to obtain the Heisenberg limit with a multi-port interferometer. Our bound reveals that while linear networks can generate highly entangled states, they cannot effectively combine quantum resources that are well distributed across multiple modes for the purposes of metrology: in this sense linear networks endowed with well-distributed quantum resources behave classically. Conversely, our bound shows that linear networks can achieve the Heisenberg limit for distributed metrology when the input photons are hoarded in a small number of input modes, and we present an explicit scheme for doing so. Our results also have implications for measures of non-classicality.

UR - https://arxiv.org/abs/1707.06655 U5 - https://doi.org/10.1103/PhysRevLett.121.043604 ER - TY - JOUR T1 - Dynamical phase transitions in sampling complexity JF - Phys. Rev. Lett. Y1 - 2018 A1 - Abhinav Deshpande A1 - Bill Fefferman A1 - Minh C. Tran A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB -

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time t due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of t with the number of bosons n for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of t with n for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proc. 43rd Annu. ACM Symp. Theory Comput. STOC '11]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular and optical systems.

VL - 121 U4 - 12 pages, 4 figures. v3: published version UR - https://arxiv.org/abs/1703.05332 CP - 030501 U5 - https://doi.org/10.1103/PhysRevLett.121.030501 ER - TY - JOUR T1 - Experimentally Generated Randomness Certified by the Impossibility of Superluminal Signals JF - Nature Y1 - 2018 A1 - Peter Bierhorst A1 - Emanuel Knill A1 - Scott Glancy A1 - Yanbao Zhang A1 - Alan Mink A1 - Stephen Jordan A1 - Andrea Rommal A1 - Yi-Kai Liu A1 - Bradley Christensen A1 - Sae Woo Nam A1 - Martin J. Stevens A1 - Lynden K. Shalm AB -

From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge with random number generators is that it is hard to ensure that their outputs are unpredictable. For a random number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model describing the underlying physics is required to assert unpredictability. Such a model must make a number of assumptions that may not be valid, thereby compromising the integrity of the device. However, it is possible to exploit the phenomenon of quantum nonlocality with a loophole-free Bell test to build a random number generator that can produce output that is unpredictable to any adversary limited only by general physical principles. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1024 random bits uniform to within 10−12. These random bits could not have been predicted within any physical theory that prohibits superluminal signaling and allows one to make independent measurement choices. To certify and quantify the randomness, we describe a new protocol that is optimized for apparatuses characterized by a low per-trial violation of Bell inequalities. We thus enlisted an experimental result that fundamentally challenges the notion of determinism to build a system that can increase trust in random sources. In the future, random number generators based on loophole-free Bell tests may play a role in increasing the security and trust of our cryptographic systems and infrastructure.

VL - 556 U4 - 223-226 UR - https://arxiv.org/abs/1803.06219 U5 - https://doi.org/10.1038/s41586-018-0019-0 ER - TY - JOUR T1 - Fractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal Y1 - 2018 A1 - Tobias Graß A1 - Przemyslaw Bienias A1 - Michael Gullans A1 - Rex Lundgren A1 - Joseph Maciejko A1 - Alexey V. Gorshkov AB -

Highly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems, and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half-filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal phase, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum 4ℏ. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.

UR - https://arxiv.org/abs/1809.04493 ER - TY - JOUR T1 - Geometry of the quantum set of correlations JF - Physical Review A Y1 - 2018 A1 - Koon Tong Goh A1 - Jedrzej Kaniewski A1 - Elie Wolfe A1 - Tamás Vértesi A1 - Xingyao Wu A1 - Yu Cai A1 - Yeong-Cherng Liang A1 - Valerio Scarani AB -

It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.

VL - 97 U4 - 022104 UR - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022104 CP - 2 U5 - 10.1103/PhysRevA.97.022104 ER - TY - JOUR T1 - Information-Theoretic Privacy For Distributed Average Consensus: Bounded Integral Inputs Y1 - 2018 A1 - Nirupam Gupta A1 - Jonathan Katz A1 - Nikhil Chopra AB -

We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents' inputs against colluding passive adversarial agents, as long as the set of colluding passive adversarial agents is not a vertex cut in the underlying communication network. This implies that a network with (t+1)-connectivity guarantees information-theoretic privacy of honest agents' inputs against any t colluding agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm. The agent' inputs are bounded integers, where the bounds are apriori known to all the agents.

UR - https://arxiv.org/abs/1809.01794 ER - TY - JOUR T1 - Information-Theoretic Privacy in Distributed Average Consensus Y1 - 2018 A1 - Nirupam Gupta A1 - Jonathan Katz A1 - Nikhil Chopra AB -

We propose an asynchronous distributed average consensus algorithm that guarantees information-theoretic privacy of honest agents' inputs against colluding semi-honest (passively adversarial) agents, as long as the set of colluding semi-honest agents is not a vertex cut in the underlying communication network. This implies that a network with (t+1)-connectivity guarantees information-theoretic privacy of honest agents' inputs against any t colluding semi-honest agents. The proposed protocol is formed by composing a distributed privacy mechanism we provide with any (non-private) distributed average consensus algorithm. 

UR - https://arxiv.org/abs/1809.01794 ER - TY - JOUR T1 - Observation of three-photon bound states in a quantum nonlinear medium JF - Science Y1 - 2018 A1 - Qi-Yu Liang A1 - Aditya V. Venkatramani A1 - Sergio H. Cantu A1 - Travis L. Nicholson A1 - Michael Gullans A1 - Alexey V. Gorshkov A1 - Jeff D. Thompson A1 - Cheng Chin A1 - Mikhail D. Lukin A1 - Vladan Vuletic AB -

Bound states of massive particles, such as nuclei, atoms or molecules, are ubiquitous in nature and constitute the bulk of the visible world around us. In contrast, photons typically only weakly influence each other due to their very weak interactions and vanishing mass. We report the observation of traveling three-photon bound states in a quantum nonlinear medium where the interactions between photons are mediated by atomic Rydberg states. In particular, photon correlation and conditional phase measurements reveal the distinct features associated with three-photon and two-photon bound states. Such photonic trimers and dimers can be viewed as quantum solitons with shape-preserving wavefunctions that depend on the constituent photon number. The observed bunching and strongly nonlinear optical phase are quantitatively described by an effective field theory (EFT) of Rydberg-induced photon-photon interactions, which demonstrates the presence of a substantial effective three-body force between the photons. These observations pave the way towards the realization, studies, and control of strongly interacting quantum many-body states of light.

VL - 359 U4 - 783-786 UR - http://science.sciencemag.org/content/359/6377/783 CP - 6377 U5 - 10.1126/science.aao7293 ER - TY - JOUR T1 - Optimal and Secure Measurement Protocols for Quantum Sensor Networks Y1 - 2018 A1 - Zachary Eldredge A1 - Michael Foss-Feig A1 - Steven L. Rolston A1 - Alexey V. Gorshkov AB -

Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting where the quantity to be measured is a linear function of parameters coupled to each qubit individually. We first generalize the Heisenberg limit to the measurement of non-local observables in a quantum network, deriving a bound based on the multi-parameter quantum Fisher information. We then propose a protocol that can make use of GHZ states or spin-squeezed states, and show that in the case of GHZ states the procedure is optimal, i.e., it saturates our bound.

UR - http://arxiv.org/abs/1607.04646 U5 - https://doi.org/10.1103/PhysRevA.97.042337 ER - TY - JOUR T1 - Optimization of photon storage fidelity in ordered atomic arrays JF - New Journal of Physics Y1 - 2018 A1 - M. T. Manzoni A1 - M. Moreno-Cardoner A1 - A. Asenjo-Garcia A1 - J. V. Porto A1 - Alexey V. Gorshkov A1 - D. E. Chang AB -

A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell-Bloch equations. The validity of this model can break down, however, in systems such as dense, ordered atomic arrays, where strong interference in emission can give rise to phenomena such as subradiance and "selective" radiance. Here, we develop a general formalism that finds the maximum storage efficiency for a collection of atoms with discrete, known positions, and a given spatial mode in which an optical field is sent. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number Na like ∼(logNa)2/N2a, and that, remarkably, an array of just 4×4 atoms in principle allows for an efficiency comparable to a disordered ensemble with optical depth of around 600.

VL - 20 UR - https://arxiv.org/abs/1710.06312 CP - 083048 U5 - https://doi.org/10.1088/1367-2630/aadb74 ER - TY - JOUR T1 - Photon propagation through dissipative Rydberg media at large input rates Y1 - 2018 A1 - Przemyslaw Bienias A1 - James Douglas A1 - Asaf Paris-Mandoki A1 - Paraj Titum A1 - Ivan Mirgorodskiy A1 - Christoph Tresp A1 - Emil Zeuthen A1 - Michael Gullans A1 - Marco Manzoni A1 - Sebastian Hofferberth A1 - Darrick Chang A1 - Alexey V. Gorshkov AB -

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. 

UR - https://arxiv.org/abs/1807.07586 ER - TY - JOUR T1 - Photon Subtraction by Many-Body Decoherence Y1 - 2018 A1 - Callum R. Murray A1 - Ivan Mirgorodskiy A1 - Christoph Tresp A1 - Christoph Braun A1 - Asaf Paris-Mandoki A1 - Alexey V. Gorshkov A1 - Sebastian Hofferberth A1 - Thomas Pohl AB -

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.

UR - https://arxiv.org/abs/1710.10047 U5 - https://doi.org/10.1103/PhysRevLett.120.113601 ER - TY - JOUR T1 - Photon thermalization via laser cooling of atoms JF - Phys. Rev. A 98, 013834 Y1 - 2018 A1 - Chiao-Hsuan Wang A1 - Michael Gullans A1 - J. V. Porto A1 - William D. Phillips A1 - J. M. Taylor AB -

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.

UR - https://arxiv.org/abs/1712.08643 U5 - https://doi.org/10.1103/PhysRevA.98.013834 ER - TY - JOUR T1 - Probing electron-phonon interactions in the charge-photon dynamics of cavity-coupled double quantum dots JF - Physical Review B Y1 - 2018 A1 - Michael Gullans A1 - J. M. Taylor A1 - J. R. Petta AB -

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.

VL - 97 U4 - 035305 UR - https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.035305 CP - 3 U5 - 10.1103/PhysRevB.97.035305 ER - TY - JOUR T1 - Quantum generalizations of the polynomial hierarchy with applications to QMA(2) JF - Proceedings of 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018) Y1 - 2018 A1 - Sevag Gharibian A1 - Miklos Santha A1 - Jamie Sikora A1 - Aarthi Sundaram A1 - Justin Yirka AB -

The polynomial-time hierarchy (PH) has proven to be a powerful tool for providing separations in computational complexity theory (modulo standard conjectures such as PH does not collapse). Here, we study whether two quantum generalizations of PH can similarly prove separations in the quantum setting. The first generalization, QCPH, uses classical proofs, and the second, QPH, uses quantum proofs. For the former, we show quantum variants of the Karp-Lipton theorem and Toda's theorem. For the latter, we place its third level, QΣ3, into NEXP {using the Ellipsoid Method for efficiently solving semidefinite programs}. These results yield two implications for QMA(2), the variant of Quantum Merlin-Arthur (QMA) with two unentangled proofs, a complexity class whose characterization has proven difficult. First, if QCPH=QPH (i.e., alternating quantifiers are sufficiently powerful so as to make classical and quantum proofs "equivalent"), then QMA(2) is in the Counting Hierarchy (specifically, in PPPPP). Second, unless QMA(2)=QΣ3 (i.e., alternating quantifiers do not help in the presence of "unentanglement"), QMA(2) is strictly contained in NEXP.

UR - https://arxiv.org/abs/1805.11139 U5 - https://doi.org/10.4230/LIPIcs.MFCS.2018.58 ER - TY - JOUR T1 - Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics JF - Proceedings of the 51st ACM Symposium on Theory of Computing Y1 - 2018 A1 - Andras Gilyen A1 - Yuan Su A1 - Guang Hao Low A1 - Nathan Wiebe AB -

Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation" algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang. The proposed quantum circuits have a very simple structure, often give rise to optimal algorithms and have appealing constant factors, while usually only use a constant number of ancilla qubits. We show that singular value transformation leads to novel algorithms. We give an efficient solution to a certain "non-commutative" measurement problem and propose a new method for singular value estimation. We also show how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum. Finally, as a quantum machine learning application we show how to efficiently implement principal component regression. "Singular value transformation" is conceptually simple and efficient, and leads to a unified framework of quantum algorithms incorporating a variety of quantum speed-ups. We illustrate this by showing how it generalizes a number of prominent quantum algorithms, including: optimal Hamiltonian simulation, implementing the Moore-Penrose pseudoinverse with exponential precision, fixed-point amplitude amplification, robust oblivious amplitude amplification, fast QMA amplification, fast quantum OR lemma, certain quantum walk results and several quantum machine learning algorithms. In order to exploit the strengths of the presented method it is useful to know its limitations too, therefore we also prove a lower bound on the efficiency of singular value transformation, which often gives optimal bounds.

U4 - 193-204 UR - https://arxiv.org/abs/1806.01838 U5 - https://doi.org/10.1145/3313276.3316366 ER - TY - JOUR T1 - Recovering quantum gates from few average gate fidelities JF - Phys. Rev. Lett. Y1 - 2018 A1 - Ingo Roth A1 - Richard Kueng A1 - Shelby Kimmel A1 - Yi-Kai Liu A1 - David Gross A1 - Jens Eisert A1 - Martin Kliesch AB -

Characterising quantum processes is a key task in and constitutes a challenge for the development of quantum technologies, especially at the noisy intermediate scale of today's devices. One method for characterising processes is randomised benchmarking, which is robust against state preparation and measurement (SPAM) errors, and can be used to benchmark Clifford gates. A complementing approach asks for full tomographic knowledge. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency. So far, guarantees for compressed sensing protocols rely on unstructured random measurements and can not be applied to the data acquired from randomised benchmarking experiments. It has been an open question whether or not the favourable features of both worlds can be combined. In this work, we give a positive answer to this question. For the important case of characterising multi-qubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured respect to random Clifford unitaries. Moreover, for general unital quantum channels we provide an explicit expansion into a unitary 2-design, allowing for a practical and guaranteed reconstruction also in that case. As a side result, we obtain a new statistical interpretation of the unitarity -- a figure of merit that characterises the coherence of a process. In our proofs we exploit recent representation theoretic insights on the Clifford group, develop a version of Collins' calculus with Weingarten functions for integration over the Clifford group, and combine this with proof techniques from compressed sensing.

VL - 121 U4 - 170502 UR - https://arxiv.org/abs/1803.00572 U5 - https://doi.org/10.1103/PhysRevLett.121.170502 ER - TY - JOUR T1 - Single-photon bound states in atomic ensembles Y1 - 2018 A1 - Yidan Wang A1 - Michael Gullans A1 - Antoine Browaeys A1 - J. V. Porto A1 - Darrick E. Chang A1 - Alexey V. Gorshkov AB -

We illustrate the existence of single-excitation bound states for propagating photons interacting with N two-level atoms. These bound states can be calculated from an effective spin model, and their existence relies on dissipation in the system. The appearance of these bound states is in a one-to-one correspondence with zeros in the single-photon transmission and with divergent bunching in the second-order photon-photon correlation function. We also formulate a dissipative version of Levinson's theorem for this system by looking at the relation between the number of bound states and the winding number of the transmission phases. This theorem allows a direct experimental measurement of the number of bound states using the measured transmission phases.

UR - https://arxiv.org/abs/1809.01147 ER - TY - JOUR T1 - Spectrum estimation of density operators with alkaline-earth atoms Y1 - 2018 A1 - Michael E. Beverland A1 - Jeongwan Haah A1 - Gorjan Alagic A1 - Gretchen K. Campbell A1 - Ana Maria Rey A1 - Alexey V. Gorshkov AB -

We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing, quantum simulation, and time-keeping with alkalineearth atoms are discussed.

VL - 120 UR - http://arxiv.org/abs/1608.02045 CP - 025301 U5 - https://doi.org/10.1103/PhysRevLett.120.025301 ER - TY - JOUR T1 - A spinor Bose-Einstein condensate phase-sensitive amplifier for SU(1,1) interferometry JF - Phys. Rev Y1 - 2018 A1 - J. P. Wrubel A1 - A. Schwettmann A1 - D. P. Fahey A1 - Z. Glassman A1 - H. K. Pechkis A1 - P. F. Griffin A1 - R. Barnett A1 - E. Tiesinga A1 - P. D. Lett AB -

The SU(1,1) interferometer was originally conceived as a Mach-Zehnder interferometer with the beam-splitters replaced by parametric amplifiers. The parametric amplifiers produce states with correlations that result in enhanced phase sensitivity. F=1 spinor Bose-Einstein condensates (BECs) can serve as the parametric amplifiers for an atomic version of such an interferometer by collisionally producing entangled pairs of ⟨F=1,m=±1| atoms. We simulate the effect of single and double-sided seeding of the inputs to the amplifier using the truncated-Wigner approximation. We find that single-sided seeding degrades the performance of the interferometer exactly at the phase the unseeded interferometer should operate the best. Double-sided seeding results in a phase-sensitive amplifier, where the maximal sensitivity is a function of the phase relationship between the input states of the amplifier. In both single and double-sided seeding we find there exists an optimal phase shift that achieves sensitivity beyond the standard quantum limit. Experimentally, we demonstrate a spinor phase-sensitive amplifier using a BEC of 23Na in an optical dipole trap. This configuration could be used as an input to such an interferometer. We are able to control the initial phase of the double-seeded amplifier, and demonstrate sensitivity to initial population fractions as small as 0.1\%. 

VL - A 98 UR - https://arxiv.org/abs/1807.06676 CP - 023620 ER - TY - JOUR T1 - Studying community development: a network analytical approach Y1 - 2018 A1 - C. A. Hass A1 - Florian Genz A1 - Mary Bridget Kustusch A1 - Pierre-P. A. Ouime A1 - Katarzyna Pomian A1 - Eleanor C. Sayre A1 - Justyna P. Zwolak AB -

Research shows that community plays a central role in learning, and strong community engages students and aids in student persistence. Thus, understanding the function and structure of communities in learning environments is essential to education. We use social network analysis to explore the community dynamics of students in a pre-matriculation, two-week summer program. Unlike previous network analysis studies in PER, we build our networks from classroom video that has been coded for student interactions using labeled, directed ties. We define 3 types of interaction: on task interactions (regarding the assigned task), on topic interactions (having to do with science, technology, engineering, and mathematics (STEM)), and off topic interactions (unrelated to the assignment or STEM). To study the development of community in this program, we analyze the shift in conversation topicality over the course of the program. Conversations are more on-task toward the end of the program and we propose that this conversational shift represents a change in student membership within their forming community. 

UR - https://arxiv.org/abs/1808.08193 ER - TY - JOUR T1 - Unforgeable Quantum Encryption JF - In: Nielsen J., Rijmen V. (eds) Advances in Cryptology – EUROCRYPT 2018. Lecture Notes in Computer Science, Springer, Cham Y1 - 2018 A1 - Gorjan Alagic A1 - Tommaso Gagliardoni A1 - Christian Majenz AB -

We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i) ciphertext unforgeability, (ii) indistinguishability under adaptive chosen-ciphertext attack, and (iii) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies   INT-CTXT , (ii) implies   IND-CCA2 , and (iii) implies   AE . All of our new notions also imply   QIND-CPA  privacy. Combining one-time authentication and classical pseudorandomness, we construct symmetric-key quantum encryption schemes for each of these new security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.

VL - 10822 U5 - https://doi.org/10.1007/978-3-319-78372-7_16 ER - TY - JOUR T1 - Unitary Entanglement Construction in Hierarchical Networks Y1 - 2018 A1 - Aniruddha Bapat A1 - Zachary Eldredge A1 - James R. Garrison A1 - Abhinav Desphande A1 - Frederic T. Chong A1 - Alexey V. Gorshkov AB -

The construction of large-scale quantum computers will require modular architectures that allow physical resources to be localized in easy-to-manage packages. In this work, we examine the impact of different graph structures on the preparation of entangled states. We begin by explaining a formal framework, the hierarchical product, in which modular graphs can be easily constructed. This framework naturally leads us to suggest a class of graphs, which we dub hierarchies. We argue that such graphs have favorable properties for quantum information processing, such as a small diameter and small total edge weight, and use the concept of Pareto efficiency to identify promising quantum graph architectures. We present numerical and analytical results on the speed at which large entangled states can be created on nearest-neighbor grids and hierarchy graphs. We also present a scheme for performing circuit placement--the translation from circuit diagrams to machine qubits--on quantum systems whose connectivity is described by hierarchies.

UR - https://arxiv.org/abs/1808.07876 ER - TY - JOUR T1 - Complexity of sampling as an order parameter Y1 - 2017 A1 - Abhinav Deshpande A1 - Bill Fefferman A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB -

We consider the classical complexity of approximately simulating time evolution under spatially local quadratic bosonic Hamiltonians for time t. We obtain upper and lower bounds on the scaling of twith the number of bosons, n, for which simulation, cast as a sampling problem, is classically efficient and provably hard, respectively. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian and conjecture a link to dynamical phase transitions. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter systems.

UR - https://arxiv.org/abs/1703.05332 ER - TY - JOUR T1 - Correlated Photon Dynamics in Dissipative Rydberg Media JF - Physical Review Letters Y1 - 2017 A1 - Emil Zeuthen A1 - Michael Gullans A1 - Mohammad F. Maghrebi A1 - Alexey V. Gorshkov AB -

Rydberg blockade physics in optically dense atomic media under the conditions of electromagnetically induced transparency (EIT) leads to strong dissipative interactions between single photons. We introduce a new approach to analyzing this challenging many-body problem in the limit of large optical depth per blockade radius. In our approach, we separate the single-polariton EIT physics from Rydberg-Rydberg interactions in a serialized manner while using a hard-sphere model for the latter, thus capturing the dualistic particle-wave nature of light as it manifests itself in dissipative Rydberg-EIT media. Using this approach, we analyze the saturation behavior of the transmission through one-dimensional Rydberg-EIT media in the regime of non-perturbative dissipative interactions relevant to current experiments. Our model is in good agreement with experimental data. We also analyze a scheme for generating regular trains of single photons from continuous-wave input and derive its scaling behavior in the presence of imperfect single-photon EIT.

VL - 119 U4 - 043602 UR - https://arxiv.org/abs/1608.06068 CP - 4 U5 - 10.1103/PhysRevLett.119.043602 ER - TY - JOUR T1 - Entanglement area laws for long-range interacting systems JF - Physical Review Letters Y1 - 2017 A1 - Zhe-Xuan Gong A1 - Michael Foss-Feig A1 - Fernando G. S. L. Brandão A1 - Alexey V. Gorshkov AB -

We prove that the entanglement entropy of any state evolved under an arbitrary 1/rα long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any α > D + 1. We also prove that for any α > 2D + 2, the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.

VL - 119 U4 - 050501 UR - https://arxiv.org/abs/1702.05368 CP - 5 U5 - 10.1103/PhysRevLett.119.050501 ER - TY - JOUR T1 - Efimov States of Strongly Interacting Photons JF - Physical Review Letters Y1 - 2017 A1 - Michael Gullans A1 - S. Diehl A1 - S. T. Rittenhouse A1 - B. P. Ruzic A1 - J. P. D'Incao A1 - P. Julienne A1 - Alexey V. Gorshkov A1 - J. M. Taylor AB -

We demonstrate the emergence of universal Efimov physics for interacting photons in cold gases of Rydberg atoms. We consider the behavior of three photons injected into the gas in their propagating frame, where a paraxial approximation allows us to consider them as massive particles. In contrast to atoms and nuclei, the photons have a large anisotropy between their longitudinal mass, arising from dispersion, and their transverse mass, arising from diffraction. Nevertheless, we show that in suitably rescaled coordinates the effective interactions become dominated by s-wave scattering near threshold and, as a result, give rise to an Efimov effect near unitarity, but with spatially anisotropic wavefunctions in the original coordinates. We show that the three-body loss of these Efimov trimers can be strongly suppressed and determine conditions under which these states are observable in current experiments. These effects can be naturally extended to probe few-body universality beyond three bodies, as well as the role of Efimov physics in the non-equilbrium, many-body regime.

VL - 119 U4 - 233601 UR - https://arxiv.org/abs/1709.01955 CP - 23 U5 - 10.1103/PhysRevLett.119.233601 ER - TY - JOUR T1 - Emergent equilibrium in many-body optical bistability JF - Physical Review A Y1 - 2017 A1 - Michael Foss-Feig A1 - Pradeep Niroula A1 - Jeremy T. Young A1 - Mohammad Hafezi A1 - Alexey V. Gorshkov A1 - Ryan M. Wilson A1 - Mohammad F. Maghrebi AB -

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.

VL - 95 U4 - 043826 UR - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.043826 U5 - doi.org/10.1103/PhysRevA.95.043826 ER - TY - JOUR T1 - Exact sampling hardness of Ising spin models JF - Physical Review A Y1 - 2017 A1 - Bill Fefferman A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB -

We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example of an Ising Hamiltonian that, after time evolution starting from a trivial initial state, produces a particular output configuration with probability very nearly proportional to the square of the permanent of a matrix with arbitrary integer entries. In a similar spirit to boson sampling, the ability to sample classically from the probability distribution induced by time evolution under this Hamiltonian would imply unlikely complexity theoretic consequences, suggesting that the dynamics of such a spin model cannot be efficiently simulated with a classical computer. Physical Ising spin systems capable of achieving problem-size instances (i.e., qubit numbers) large enough so that classical sampling of the output distribution is classically difficult in practice may be achievable in the near future. Unlike boson sampling, our current results only imply hardness of exact classical sampling, leaving open the important question of whether a much stronger approximate-sampling hardness result holds in this context. The latter is most likely necessary to enable a convincing experimental demonstration of quantum supremacy. As referenced in a recent paper [A. Bouland, L. Mancinska, and X. Zhang, in Proceedings of the 31st Conference on Computational Complexity (CCC 2016), Leibniz International Proceedings in Informatics (Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl, 2016)], our result completes the sampling hardness classification of two-qubit commuting Hamiltonians.

VL - 96 U4 - 032324 UR - https://arxiv.org/abs/1701.03167 CP - 3 U5 - 10.1103/PhysRevA.96.032324 ER - TY - JOUR T1 - Exactly soluble model of boundary degeneracy JF - Physical Review B Y1 - 2017 A1 - Sriram Ganeshan A1 - Alexey V. Gorshkov A1 - Victor Gurarie A1 - Victor M. Galitski AB -

We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as "boundary degeneracy") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic model manifesting this topological degeneracy and solve it using the recently developed technique [S. Ganeshan and M. Levin, Phys. Rev. B 93, 075118 (2016)]. The corresponding string operators spanning this degeneracy are explicitly calculated. It is argued that the proposed scheme is experimentally reasonable.

VL - 95 UR - http://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.045309 U5 - 10.1103/PhysRevB.95.045309 ER - TY - JOUR T1 - Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling Y1 - 2017 A1 - Peter Bierhorst A1 - Emanuel Knill A1 - Scott Glancy A1 - Alan Mink A1 - Stephen P. Jordan A1 - Andrea Rommal A1 - Yi-Kai Liu A1 - Bradley Christensen A1 - Sae Woo Nam A1 - Lynden K. Shalm AB -

Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimental regime characterized by low violation of Bell inequalities. Applying an extractor function to our data, we obtained 256 new random bits, uniform to within 0.001.

UR - https://arxiv.org/abs/1702.05178# ER - TY - JOUR T1 - Extracting entanglement geometry from quantum states JF - Physical Review Letters Y1 - 2017 A1 - Katharine Hyatt A1 - James R. Garrison A1 - Bela Bauer AB -

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks as tractable models for holographic dualities. Conventionally, the structure of the network - and hence the geometry - is largely fixed a priori by the choice of tensor network ansatz. Here, we evade this restriction and describe an unbiased approach that allows us to extract the appropriate geometry from a given quantum state. We develop an algorithm that iteratively finds a unitary circuit that transforms a given quantum state into an unentangled product state. We then analyze the structure of the resulting unitary circuits. In the case of non-interacting, critical systems in one dimension, we recover signatures of scale invariance in the unitary network, and we show that appropriately defined geodesic paths between physical degrees of freedom exhibit known properties of a hyperbolic geometry.

VL - 119 UR - https://arxiv.org/abs/1704.01974 CP - 14 U5 - 10.1103/PhysRevLett.119.140502 ER - TY - JOUR T1 - Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions JF - Physical Review Letters Y1 - 2017 A1 - Zachary Eldredge A1 - Zhe-Xuan Gong A1 - Ali Hamed Moosavian A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB -

In short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speed-up possible is an open question. In this paper, we present a protocol capable of transferring a quantum state across a distance L in d dimensions using long-range interactions with strength bounded by 1/rα. If α<d, the state transfer time is asymptotically independent of L; if α=d, the time is logarithmic in distance L; if d<α<d+1, transfer occurs in time proportional to Lαd; and if αd+1, it occurs in time proportional to L. We then use this protocol to upper bound the time required to create a state specified by a MERA (multiscale entanglement renormalization ansatz) tensor network, and show that, if the linear size of the MERA state is L, then it can be created in time that scales with L identically to state transfer up to multiplicative logarithmic corrections.

VL - 119 U4 - 170503 UR - https://arxiv.org/abs/1612.02442 CP - 17 U5 - 10.1103/PhysRevLett.119.170503 ER - TY - JOUR T1 - High-Order Multipole Radiation from Quantum Hall States in Dirac Materials JF - Physical Review B Y1 - 2017 A1 - Michael Gullans A1 - J. M. Taylor A1 - Atac Imamoglu A1 - Pouyan Ghaemi A1 - Mohammad Hafezi AB -

Topological states can exhibit electronic coherence on macroscopic length scales. When the coherence length exceeds the wavelength of light, one can expect new phenomena to occur in the optical response of these states. We theoretically characterize this limit for integer quantum Hall states in two-dimensional Dirac materials. We find that the radiation from the bulk is dominated by dipole emission, whose spectral properties vary with the local disorder potential. On the other hand, the radiation from the edge is characterized by large multipole moments in the far-field associated with the efficient transfer of angular momentum from the electrons into the scattered light. These results demonstrate that high-order multipole transitions are a necessary component for the optical spectroscopy and control of quantum Hall and related topological states in electronic systems.

VL - 95 U4 - 235439 UR - https://arxiv.org/abs/1701.03464 CP - 23 U5 - 10.1103/PhysRevB.95.235439 ER - TY - JOUR T1 - Lieb-Robinson bounds on n-partite connected correlation functions JF - Phys. Rev. A 96, 052334 Y1 - 2017 A1 - Minh C. Tran A1 - James R. Garrison A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov AB -

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

UR - https://arxiv.org/abs/1705.04355 U5 - https://doi.org/10.1103/PhysRevA.96.052334 ER - TY - JOUR T1 - Lieb-Robinson bounds on n-partite connected correlations JF - Physical Review A Y1 - 2017 A1 - Minh C. Tran A1 - James R. Garrison A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov AB -

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

VL - 96 UR - https://arxiv.org/abs/1705.04355 CP - 5 U5 - 10.1103/PhysRevA.96.052334 ER - TY - JOUR T1 - Light-induced fractional quantum Hall phases in graphene JF - Physical Review Letters Y1 - 2017 A1 - Areg Ghazaryan A1 - Tobias Graß A1 - Michael Gullans A1 - Pouyan Ghaemi A1 - Mohammad Hafezi AB -

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at non-zero relative angular momentum can become dominant, resembling a hollow-core pseudo-potential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν = 1/2 and ν = 2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

VL - 119 U4 - 247403 UR - https://arxiv.org/abs/1612.08748 CP - 24 U5 - 10.1103/PhysRevLett.119.247403 ER - TY - JOUR T1 - Multicritical behavior in dissipative Ising models JF - Physical Review A Y1 - 2017 A1 - Vincent R. Overbeck A1 - Mohammad F. Maghrebi A1 - Alexey V. Gorshkov A1 - Hendrik Weimer AB -

We analyze theoretically the many-body dynamics of a dissipative Ising model in a transverse field using a variational approach. We find that the steady state phase diagram is substantially modified compared to its equilibrium counterpart, including the appearance of a multicritical point belonging to a different universality class. Building on our variational analysis, we establish a field-theoretical treatment corresponding to a dissipative variant of a Ginzburg-Landau theory, which allows us to compute the upper critical dimension of the system. Finally, we present a possible experimental realization of the dissipative Ising model using ultracold Rydberg gases.

VL - 95 U4 - 042133 UR - https://journals.aps.org/pra/abstract/10.1103/PhysRevA.95.042133 U5 - doi.org/10.1103/PhysRevA.95.042133 ER - TY - JOUR T1 - Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator JF - Nature Y1 - 2017 A1 - J. Zhang A1 - G. Pagano A1 - P. W. Hess A1 - A. Kyprianidis A1 - P. Becker A1 - H. Kaplan A1 - Alexey V. Gorshkov A1 - Z. -X. Gong A1 - C. Monroe AB -

A quantum simulator is a restricted class of quantum computer that controls the interactions between quantum bits in a way that can be mapped to certain difficult quantum many-body problems. As more control is exerted over larger numbers of qubits, the simulator can tackle a wider range of problems, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems. We use a quantum simulator composed of up to 53 qubits to study a non-equilibrium phase transition in the transverse field Ising model of magnetism, in a regime where conventional statistical mechanics does not apply. The qubits are represented by trapped ion spins that can be prepared in a variety of initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with near 99% efficiency. This allows the single-shot measurement of arbitrary many-body correlations for the direct probing of the dynamical phase transition and the uncovering of computationally intractable features that rely on the long-range interactions and high connectivity between the qubits.

VL - 551 U4 - 601-604 UR - https://www.nature.com/articles/nature24654 U5 - 10.1038/nature24654 ER - TY - JOUR T1 - Out-of-time-order correlators in finite open systems Y1 - 2017 A1 - S. V. Syzranov A1 - Alexey V. Gorshkov A1 - V. Galitski AB -

We study out-of-time order correlators (OTOCs) of the form hAˆ(t)Bˆ(0)Cˆ(t)Dˆ(0)i for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially ∝ Paie −t/τi + const to a constant value at t → ∞, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focussing on the case of a two-level system, we calculate microscopically the decay times τi and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.

UR - https://arxiv.org/abs/1704.08442 U5 - https://doi.org/10.1103/PhysRevB.97.161114 ER - TY - JOUR T1 - Partial breakdown of quantum thermalization in a Hubbard-like model JF - Physical Review B Y1 - 2017 A1 - James R. Garrison A1 - Ryan V. Mishmash A1 - Matthew P. A. Fisher AB -

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.

VL - 95 U4 - 054204 UR - http://link.aps.org/doi/10.1103/PhysRevB.95.054204 U5 - 10.1103/PhysRevB.95.054204 ER - TY - JOUR T1 - Simultaneous, Full Characterization of a Single-Photon State JF - Physical Review X Y1 - 2017 A1 - Thomay, Tim A1 - Polyakov, Sergey V. A1 - Gazzano, Olivier A1 - Goldschmidt, Elizabeth A1 - Eldredge, Zachary D. A1 - Huber, Tobias A1 - Loo, Vivien A1 - Solomon, Glenn S. AB -

As single-photon sources become more mature and are used more often in quantum information, communications, and measurement applications, their characterization becomes more important. Singlephoton-like light is often characterized by its brightness, as well as two quantum properties: the suppression of multiphoton content and the photon indistinguishability. While it is desirable to obtain these quantities from a single measurement, currently two or more measurements are required. Here, we show that using two-photon (n ¼ 2) number-resolving detectors, one can completely characterize single-photon-like states in a single measurement, where previously two or more measurements were necessary. We simultaneously determine the brightness, the suppression of multiphoton states, the indistinguishability, and the statistical distribution of Fock states to third order for a quantum light source. We find n ≥ 3 number-resolving detectors provide no additional advantage in the single-photon characterization. The new method extracts more information per experimental trial than a conventional measurement for all input states and is particularly more efficient for statistical mixtures of photon states. Thus, using this n ¼ 2, number-resolving detector scheme will provide advantages in a variety of quantum optics measurements and systems.

VL - 7 U4 - 041036 UR - https://link.aps.org/doi/10.1103/PhysRevX.7.041036 CP - 4 U5 - 10.1103/PhysRevX.7.041036 ER - TY - JOUR T1 - A solvable family of driven-dissipative many-body systems JF - Physical Review Letters Y1 - 2017 A1 - Michael Foss-Feig A1 - Jeremy T. Young A1 - Victor V. Albert A1 - Alexey V. Gorshkov A1 - Mohammad F. Maghrebi AB -

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. And conversely, the relative scarcity of solutions for non-equilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently in any number of spatial dimensions. We leverage these solutions to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions, and to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture.

VL - 119 UR - https://arxiv.org/abs/1703.04626 CP - 19 U5 - 10.1103/PhysRevLett.119.190402 ER - TY - JOUR T1 - Threshold Dynamics of a Semiconductor Single Atom Maser JF - Physical Review Letters Y1 - 2017 A1 - Liu, Y.-Y. A1 - Stehlik, J. A1 - Eichler, C. A1 - Mi, X. A1 - Hartke, T. R. A1 - Michael Gullans A1 - J. M. Taylor A1 - Petta, J. R. AB -

We demonstrate a single atom maser consisting of a semiconductor double quantum dot (DQD) that is embedded in a high-quality-factor microwave cavity. A finite bias drives the DQD out of equilibrium, resulting in sequential single electron tunneling and masing. We develop a dynamic tuning protocol that allows us to controllably increase the time-averaged repumping rate of the DQD at a fixed level detuning, and quantitatively study the transition through the masing threshold. We further examine the crossover from incoherent to coherent emission by measuring the photon statistics across the masing transition. The observed threshold behavior is in agreement with an existing single atom maser theory when small corrections from lead emission are taken into account.

VL - 119 U4 - 097702 UR - https://link.aps.org/doi/10.1103/PhysRevLett.119.097702 CP - 9 U5 - 10.1103/PhysRevLett.119.097702 ER - TY - JOUR T1 - Unforgeable Quantum Encryption Y1 - 2017 A1 - Gorjan Alagic A1 - Tommaso Gagliardoni A1 - Christian Majenz AB -

We study the problem of encrypting and authenticating quantum data in the presence of adversaries making adaptive chosen plaintext and chosen ciphertext queries. Classically, security games use string copying and comparison to detect adversarial cheating in such scenarios. Quantumly, this approach would violate no-cloning. We develop new techniques to overcome this problem: we use entanglement to detect cheating, and rely on recent results for characterizing quantum encryption schemes. We give definitions for (i.) ciphertext unforgeability , (ii.) indistinguishability under adaptive chosen-ciphertext attack, and (iii.) authenticated encryption. The restriction of each definition to the classical setting is at least as strong as the corresponding classical notion: (i) implies INT-CTXT, (ii) implies IND-CCA2, and (iii) implies AE. All of our new notions also imply QIND-CPA privacy. Combining one-time authentication and classical pseudorandomness, we construct schemes for each of these new quantum security notions, and provide several separation examples. Along the way, we also give a new definition of one-time quantum authentication which, unlike all previous approaches, authenticates ciphertexts rather than plaintexts.

UR - https://arxiv.org/abs/1709.06539 ER - TY - JOUR T1 - Valley Blockade in a Silicon Double Quantum Dot JF - Physical Review B Y1 - 2017 A1 - Justin K. Perron A1 - Michael Gullans A1 - J. M. Taylor A1 - M. D. Stewart, Jr. A1 - Neil M. Zimmerman AB -

Electrical transport in double quantum dots (DQDs) illuminates many interesting features of the dots' carrier states. Recent advances in silicon quantum information technologies have renewed interest in the valley states of electrons confined in silicon. Here we show measurements of DC transport through a mesa-etched silicon double quantum dot. Comparing bias triangles (i.e., regions of allowed current in DQDs) at positive and negative bias voltages we find a systematic asymmetry in the size of the bias triangles at the two bias polarities. Asymmetries of this nature are associated with blocking of tunneling events due to the occupation of a metastable state. Several features of our data lead us to conclude that the states involved are not simple spin states. Rather, we develop a model based on selective filling of valley states in the DQD that is consistent with all of the qualitative features of our data.

VL - 96 U4 - 205302 UR - https://arxiv.org/abs/1607.06107 CP - 20 U5 - 10.1103/PhysRevB.96.205302 ER - TY - JOUR T1 - Anomalous broadening in driven dissipative Rydberg systems JF - Physical Review Letters Y1 - 2016 A1 - E. A. Goldschmidt A1 - T. Boulier A1 - R. C. Brown A1 - S. B. Koller A1 - J. T. Young A1 - Alexey V. Gorshkov A1 - S. L. Rolston A1 - J. V. Porto AB - We observe interaction-induced broadening of the two-photon 5s-18s transition in 87Rb atoms trapped in a 3D optical lattice. The measured linewidth increases by nearly two orders of magnitude with increasing atomic density and excitation strength, with corresponding suppression of resonant scattering and enhancement of off-resonant scattering. We attribute the increased linewidth to resonant dipole-dipole interactions of 18s atoms with spontaneously created populations of nearby np states. Over a range of initial atomic densities and excitation strengths, the transition width is described by a single function of the steady-state density of Rydberg atoms, and the observed resonant excitation rate corresponds to that of a two-level system with the measured, rather than natural, linewidth. The broadening mechanism observed here is likely to have negative implications for many proposals with coherently interacting Rydberg atoms. VL - 116 U4 - 113001 UR - http://arxiv.org/abs/1510.08710 CP - 11 U5 - 10.1103/PhysRevLett.116.113001 ER - TY - JOUR T1 - Causality and quantum criticality in long-range lattice models JF - Physical Review B Y1 - 2016 A1 - Mohammad F. Maghrebi A1 - Zhe-Xuan Gong A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov VL - 93 U4 - 125128 UR - http://link.aps.org/doi/10.1103/PhysRevB.93.125128 U5 - 10.1103/PhysRevB.93.125128 ER - TY - JOUR T1 - Causality and quantum criticality with long-range interactions JF - Physical Review B Y1 - 2016 A1 - Mohammad F. Maghrebi A1 - Zhe-Xuan Gong A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB - Quantum lattice systems with long-range interactions often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model and a fermionic model with long-range interactions, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of long-range interactions, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent. VL - 92 U4 - 125128 UR - http://arxiv.org/abs/1508.00906 CP - 12 U5 - 10.1103/PhysRevB.93.125128 ER - TY - JOUR T1 - Collective phases of strongly interacting cavity photons JF - Physical Review A Y1 - 2016 A1 - Ryan M. Wilson A1 - Khan W. Mahmud A1 - Anzi Hu A1 - Alexey V. Gorshkov A1 - Mohammad Hafezi A1 - Michael Foss-Feig AB -

We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin-12 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectories simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics, and establish a simple relationship between the switching times and properties of the quantum Liouvillian.

VL - 94 U4 - 033801 UR - http://arxiv.org/abs/1601.06857 CP - 3 U5 - http://dx.doi.org/10.1103/PhysRevA.94.033801 ER - TY - JOUR T1 - Complexity of the XY antiferromagnet at fixed magnetization JF - Quantum Information and Computation Y1 - 2016 A1 - Andrew M. Childs A1 - David Gosset A1 - Zak Webb AB - We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model. VL - 16 U4 - 1-18 UR - http://arxiv.org/abs/1503.07083v1 CP - 1-2 ER - TY - CONF T1 - Computational Security of Quantum Encryption T2 - Computational Security of Quantum Encryption. In: Nascimento A., Barreto P. (eds) Information Theoretic Security. Y1 - 2016 A1 - Gorjan Alagic A1 - Anne Broadbent A1 - Bill Fefferman A1 - Tommaso Gagliardoni A1 - Christian Schaffner A1 - Michael St. Jules AB -

Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notions of semantic security and indistinguishability, and, in analogy with the classical work of Goldwasser and Micali, show that these notions are equivalent. Finally, we construct secure quantum encryption schemes from basic primitives. In particular, we show that quantum-secure one-way functions imply IND-CCA1-secure symmetric-key quantum encryption, and that quantum-secure trapdoor one-way permutations imply semantically-secure public-key quantum encryption.

JA - Computational Security of Quantum Encryption. In: Nascimento A., Barreto P. (eds) Information Theoretic Security. UR - https://link.springer.com/chapter/10.1007%2F978-3-319-49175-2_3 ER - TY - JOUR T1 - Double Quantum Dot Floquet Gain Medium JF - Physical Review X Y1 - 2016 A1 - J. Stehlik A1 - Y.-Y. Liu A1 - C. Eichler A1 - T. R. Hartke A1 - X. Mi A1 - Michael Gullans A1 - J. M. Taylor A1 - J. R. Petta AB -

Strongly driving a two-level quantum system with light leads to a ladder of Floquet states separated by the photon energy. Nanoscale quantum devices allow the interplay of confined electrons, phonons, and photons to be studied under strong driving conditions. Here we show that a single electron in a periodically driven DQD functions as a "Floquet gain medium," where population imbalances in the DQD Floquet quasi-energy levels lead to an intricate pattern of gain and loss features in the cavity response. We further measure a large intra-cavity photon number n_c in the absence of a cavity drive field, due to equilibration in the Floquet picture. Our device operates in the absence of a dc current -- one and the same electron is repeatedly driven to the excited state to generate population inversion. These results pave the way to future studies of non-classical light and thermalization of driven quantum systems.

VL - 6 U4 - 041027 UR - http://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.041027 U5 - 10.1103/PhysRevX.6.041027 ER - TY - JOUR T1 - Effective Field Theory for Rydberg Polaritons JF - Physical Review Letters Y1 - 2016 A1 - Michael Gullans A1 - J. D. Thompson A1 - Y. Wang A1 - Q. -Y. Liang A1 - V. Vuletic A1 - M. D. Lukin A1 - Alexey V. Gorshkov AB -

We study non-perturbative effects in N-body scattering of Rydberg polaritons using effective field theory (EFT). We develop an EFT in one dimension and show how a suitably long medium can be used to prepare shallow N-body bound states. We then derive the effective N-body interaction potential for Rydberg polaritons and the associated N-body contact force that arises in the EFT. We use the contact force to find the leading order corrections to the binding energy of the N-body bound states and determine the photon number at which the EFT description breaks down. We find good agreement throughout between the predictions of EFT and numerical simulations of the exact two and three photon wavefunction transmission.

VL - 117 U4 - 113601 UR - http://arxiv.org/abs/1605.05651 CP - 11 U5 - http://dx.doi.org/10.1103/PhysRevLett.117.113601 ER - TY - JOUR T1 - Entanglement and spin-squeezing without infinite-range interactions Y1 - 2016 A1 - Michael Foss-Feig A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov A1 - Charles W. Clark AB -

Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the achievable benefits in this context are much less clear. Combining recent exact solutions with a controlled expansion in the system size, we analyze quench dynamics in Ising models with power-law (1/r α ) interactions in D dimensions, thereby expanding the understanding of spin squeezing into a broad and experimentally relevant context. In spatially homogeneous systems, we show that for small α the scaling of squeezing with system size is identical to the infinite-range (α = 0) case. This indifference to the interaction range persists up to a critical value α = 2D/3, above which squeezing degrades continuously. Boundaryinduced inhomogeneities present in most experimental systems modify this picture, but it nevertheless remains qualitatively correct for finite-sized systems.

UR - https://arxiv.org/abs/1612.07805 ER - TY - JOUR T1 - Experimental demonstration of quantum fault tolerance Y1 - 2016 A1 - N. M. Linke A1 - M. Gutierrez A1 - K. A. Landsman A1 - C. Figgatt A1 - S. Debnath A1 - K. R. Brown A1 - C. Monroe AB -

Quantum computers will eventually reach a size at which quantum error correction (QEC) becomes imperative. In order to make quantum information robust to errors introduced by qubit imperfections and flawed control operations, QEC protocols encode a logical qubit in multiple physical qubits. This redundancy allows the extraction of error syndromes and the subsequent correction or detection of errors without destroying the logical state itself through direct measurement. While several experiments have shown a reduction of high intrinsic or artificially introduced errors in logical qubits, fault-tolerant encoding of a logical qubit has never been demonstrated. Here we show the encoding and syndrome measurement of a fault-tolerant logical qubit via an error detection protocol on four physical qubits, represented by trapped atomic ions. This demonstrates for the first time the robustness of a fault-tolerant qubit to imperfections in the very operations used to encode it. This advantage persists in the face of large added error rates and experimental calibration errors.

UR - https://arxiv.org/abs/1611.06946 ER - TY - JOUR T1 - Joint product numerical range and geometry of reduced density matrices Y1 - 2016 A1 - Jianxin Chen A1 - Cheng Guo A1 - Zhengfeng Ji A1 - Yiu-Tung Poon A1 - Nengkun Yu A1 - Bei Zeng A1 - Jie Zhou AB - The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti's theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that ruled surface emerge naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines. UR - http://arxiv.org/abs/1606.07422 ER - TY - JOUR T1 - Kaleidoscope of quantum phases in a long-range interacting spin-1 chain JF - Physical Review B Y1 - 2016 A1 - Zhe-Xuan Gong A1 - Mohammad F. Maghrebi A1 - Anzi Hu A1 - Michael Foss-Feig A1 - Philip Richerme A1 - Christopher Monroe A1 - Alexey V. Gorshkov AB - Motivated by recent trapped-ion quantum simulation experiments, we carry out a comprehensive study of the phase diagram of a spin-1 chain with XXZ-type interactions that decay as 1/rα, using a combination of finite and infinite-size DMRG calculations, spin-wave analysis, and field theory. In the absence of long-range interactions, varying the spin-coupling anisotropy leads to four distinct phases: a ferromagnetic Ising phase, a disordered XY phase, a topological Haldane phase, and an antiferromagnetic Ising phase. If long-range interactions are antiferromagnetic and thus frustrated, we find primarily a quantitative change of the phase boundaries. On the other hand, ferromagnetic (non-frustrated) long-range interactions qualitatively impact the entire phase diagram. Importantly, for α≲3, long-range interactions destroy the Haldane phase, break the conformal symmetry of the XY phase, give rise to a new phase that spontaneously breaks a U(1) continuous symmetry, and introduce an exotic tricritical point with no direct parallel in short-range interacting spin chains. We show that the main signatures of all five phases found could be observed experimentally in the near future. VL - 93 U4 - 205115 UR - http://arxiv.org/abs/1510.02108 CP - 20 U5 - http://dx.doi.org/10.1103/PhysRevB.93.205115 ER - TY - JOUR T1 - Many-body decoherence dynamics and optimised operation of a single-photon switch JF - New Journal of Physics Y1 - 2016 A1 - Callum R. Murray A1 - Alexey V. Gorshkov A1 - Thomas Pohl AB -

We develop a theoretical framework to characterize the decoherence dynamics due to multi-photon scattering in an all-optical switch based on Rydberg atom induced nonlinearities. By incorporating the knowledge of this decoherence process into optimal photon storage and retrieval strategies, we establish optimised switching protocols for experimentally relevant conditions, and evaluate the corresponding limits in the achievable fidelities. Based on these results we work out a simplified description that reproduces recent experiments [arXiv:1511.09445] and provides a new interpretation in terms of many-body decoherence involving multiple incident photons and multiple gate excitations forming the switch. Aside from offering insights into the operational capacity of realistic photon switching capabilities, our work provides a complete description of spin wave decoherence in a Rydberg quantum optics setting, and has immediate relevance to a number of further applications employing photon storage in Rydberg media. 

VL - 18 U4 - 092001 UR - http://iopscience.iop.org/article/10.1088/1367-2630/18/9/092001 U5 - 10.1088/1367-2630/18/9/092001 ER - TY - JOUR T1 - Nonequilibrium many-body steady states via Keldysh formalism JF - Physical Review B Y1 - 2016 A1 - Mohammad F. Maghrebi A1 - Alexey V. Gorshkov AB - Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. While these states and their phase transitions have been studied extensively with mean field theory, the validity of the mean field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class. VL - 93 U4 - 014307 UR - http://arxiv.org/abs/1507.01939 CP - 1 U5 - 10.1103/PhysRevB.93.014307 ER - TY - JOUR T1 - Observation of Prethermalization in Long-Range Interacting Spin Chains Y1 - 2016 A1 - B. Neyenhuis A1 - J. Smith A1 - A. C. Lee A1 - J. Zhang A1 - P. Richerme A1 - P. W. Hess A1 - Z. -X. Gong A1 - Alexey V. Gorshkov A1 - C. Monroe AB -

Statistical mechanics can predict thermal equilibrium states for most classical systems, but for an isolated quantum system there is no general understanding on how equilibrium states dynamically emerge from the microscopic Hamiltonian. For instance, quantum systems that are near-integrable usually fail to thermalize in an experimentally realistic time scale and, instead, relax to quasi-stationary prethermal states that can be described by statistical mechanics when approximately conserved quantities are appropriately included in a generalized Gibbs ensemble (GGE). Here we experimentally study the relaxation dynamics of a chain of up to 22 spins evolving under a long-range transverse field Ising Hamiltonian following a sudden quench. For sufficiently long-ranged interactions the system relaxes to a new type of prethermal state that retains a strong memory of the initial conditions. In this case, the prethermal state cannot be described by a GGE, but rather arises from an emergent double-well potential felt by the spin excitations. This result shows that prethermalization occurs in a significantly broader context than previously thought, and reveals new challenges for a generic understanding of the thermalization of quantum systems, particularly in the presence of long-range interactions.

UR - https://arxiv.org/abs/1608.00681 ER - TY - JOUR T1 - Observation of Optomechanical Quantum Correlations at Room Temperature Y1 - 2016 A1 - T. P. Purdy A1 - K. E. Grutter A1 - K. Srinivasan A1 - J. M. Taylor AB -

By shining laser light through a nanomechanical beam, we measure the beam's thermally driven vibrations and perturb its motion with optical forces at a level dictated by the Heisenberg measurement-disturbance uncertainty relation. Such quantum backaction is typically difficult to observe at room temperature where the motion driven by optical quantum intensity fluctuations is many orders of magnitude smaller than the thermal motion. We demonstrate a cross-correlation technique to distinguish optically driven motion from thermally driven motion, observing this quantum backaction signature up to room temperature. While it is often difficult to absolutely calibrate optical detection, we use the scale of the quantum correlations, which is determined by fundamental constants, to gauge the size of thermal motion, demonstrating a path towards absolute thermometry with quantum mechanically calibrated ticks.

UR - http://arxiv.org/abs/1605.05664 ER - TY - JOUR T1 - Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms JF - Physical Review A Y1 - 2016 A1 - Michael E. Beverland A1 - Gorjan Alagic A1 - Michael J. Martin A1 - Andrew P. Koller A1 - Ana M. Rey A1 - Alexey V. Gorshkov AB -

We show that n thermal fermionic alkaline-earth-metal atoms in a flat-bottom trap allow one to robustly implement a spin model displaying two symmetries: the Sn symmetry that permutes atoms occupying different vibrational levels of the trap and the SU(N) symmetry associated with N nuclear spin states. The symmetries make the model exactly solvable, which, in turn, enables the analytic study of dynamical processes such as spin diffusion in this SU(N) system. We also show how to use this system to generate entangled states that allow for Heisenberg-limited metrology. This highly symmetric spin model should be experimentally realizable even when the vibrational levels are occupied according to a high-temperature thermal or an arbitrary nonthermal distribution.

VL - 93 UR - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.051601 CP - 5 U5 - 10.1103/PhysRevA.93.051601 ER - TY - JOUR T1 - Self-organization of atoms coupled to a chiral reservoir JF - Physical Review A Y1 - 2016 A1 - Zachary Eldredge A1 - Pablo Solano A1 - Darrick Chang A1 - Alexey V. Gorshkov AB -

Tightly confined modes of light, as in optical nanofibers or photonic crystal waveguides, can lead to large optical coupling in atomic systems, which mediates long-range interactions between atoms. These one-dimensional systems can naturally possess couplings that are asymmetric between modes propagating in different directions. Strong long-range interaction among atoms via these modes can drive them to a self-organized periodic distribution. In this paper, we examine the self-organizing behavior of atoms in one dimension coupled to a chiral reservoir. We determine the solution to the equations of motion in different parameter regimes, relative to both the detuning of the pump laser that initializes the atomic dipole-dipole interactions and the degree of reservoir chirality. In addition, we calculate possible experimental signatures such as reflectivity from self-organized atoms and motional sidebands.

VL - 94 U4 - 053855 UR - http://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.053855 CP - 5 U5 - 10.1103/PhysRevA.94.053855 ER - TY - JOUR T1 - Serialized Quantum Error Correction Protocol for High-Bandwidth Quantum Repeaters JF - New Journal of Physics Y1 - 2016 A1 - Andrew N. Glaudell A1 - Edo Waks A1 - J. M. Taylor AB -

Advances in single photon creation, transmission, and detection suggest that sending quantum information over optical fibers may have losses low enough to be correctable using a quantum error correcting code. Such error-corrected communication is equivalent to a novel quantum repeater scheme, but crucial questions regarding implementation and system requirements remain open. Here we show that long range entangled bit generation with rates approaching $10^8$ ebits/s may be possible using a completely serialized protocol, in which photons are generated, entangled, and error corrected via sequential, one-way interactions with a minimal number of matter qubits. Provided loss and error rates of the required elements are below the threshold for quantum error correction, this scheme demonstrates improved performance over transmission of single photons. We find improvement in ebit rates at large distances using this serial protocol and various quantum error correcting codes.

VL - 18 U4 - 093008 UR - http://iopscience.iop.org/article/10.1088/1367-2630/18/9/093008/meta CP - 9 U5 - 10.1088/1367-2630/18/9/093008 ER - TY - JOUR T1 - Sisyphus Thermalization of Photons in a Cavity-Coupled Double Quantum Dot JF - Physical Review Letters Y1 - 2016 A1 - Michael Gullans A1 - J. Stehlik A1 - Y. -Y. Liu A1 - J. R. Petta A1 - J. M. Taylor AB -

A strongly driven quantum system, coupled to a thermalizing bath, generically evolves into a highly non-thermal state as the external drive competes with the equilibrating force of the bath. We demonstrate a notable exception to this picture for a microwave resonator interacting with a periodically driven double quantum dot (DQD). In the limit of strong driving and long times, we show that the resonator field can be driven into a thermal state with a chemical potential given by a harmonic of the drive frequency. Such tunable chemical potentials are achievable with current devices and would have broad utility for quantum simulation in circuit quantum electrodynamics. As an example, we show how several DQDs embedded in an array of microwave resonators can induce a phase transition to a Bose-Einstein condensate of light.

VL - 117 U4 - 056801 UR - http://arxiv.org/abs/1512.01248 CP - 5 U5 - http://dx.doi.org/10.1103/PhysRevLett.117.056801 ER - TY - JOUR T1 - Steady-state superradiance with Rydberg polaritons JF - arXiv:1611.00797 Y1 - 2016 A1 - Zhe-Xuan Gong A1 - Minghui Xu A1 - Michael Foss-Feig A1 - James K. Thompson A1 - Ana Maria Rey A1 - Murray Holland A1 - Alexey V. Gorshkov AB -

A steady-state superradiant laser can be used to generate ultranarrow-linewidth light, and thus has important applications in the fields of quantum information and precision metrology. However, the light produced by such a laser is still essentially classical. Here, we show that the introduction of a Rydberg medium into a cavity containing atoms with a narrow optical transition can lead to the steady-state superradiant emission of ultranarrow-linewidth nonclassical light. The cavity nonlinearity induced by the Rydberg medium strongly modifies the superradiance threshold, and leads to a Mollow triplet in the cavity output spectrumthis behavior can be understood as an unusual analogue of resonance fluorescence. The cavity output spectrum has an extremely sharp central peak, with a linewidth that can be far narrower than that of a classical superradiant laser. This unprecedented spectral sharpness, together with the nonclassical nature of the light, could lead to new applications in which spectrally pure quantum light is desired.

UR - https://arxiv.org/abs/1611.00797 ER - TY - JOUR T1 - Subwavelength-width optical tunnel junctions for ultracold atoms JF - Physical Review A Y1 - 2016 A1 - Jendrzejewski, F. A1 - Eckel, S. A1 - Tiecke, T. G. A1 - G. Juzeliūnas A1 - Campbell, G. K. A1 - Jiang, Liang A1 - Alexey V. Gorshkov AB -

We propose a method for creating far-field optical barrier potentials for ultracold atoms with widths that are narrower than the diffraction limit and can approach tens of nanometers. The reduced widths stem from the nonlinear atomic response to control fields that create spatially varying dark resonances. The subwavelength barrier is the result of the geometric scalar potential experienced by an atom prepared in such a spatially varying dark state. The performance of this technique, as well as its applications to the study of many-body physics and to the implementation of quantum-information protocols with ultracold atoms, are discussed, with a focus on the implementation of tunnel junctions.

VL - 94 U4 - 063422 UR - http://link.aps.org/doi/10.1103/PhysRevA.94.063422 CP - 6 U5 - 10.1103/PhysRevA.94.063422 ER - TY - JOUR T1 - Topological phases with long-range interactions JF - Physical Review B Y1 - 2016 A1 - Zhe-Xuan Gong A1 - Mohammad F. Maghrebi A1 - Anzi Hu A1 - Michael L. Wall A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB - Topological phases of matter are primarily studied in quantum many-body systems with short-range interactions. Whether various topological phases can survive in the presence of long-range interactions, however, is largely unknown. Here we show that a paradigmatic example of a symmetry-protected topological phase, the Haldane phase of an antiferromagnetic spin-1 chain, surprisingly remains intact in the presence of arbitrarily slowly decaying power-law interactions. The influence of long-range interactions on the topological order is largely quantitative, and we expect similar results for more general systems. Our conclusions are based on large-scale matrix-product-state simulations and two complementary effective-field-theory calculations. The striking agreement between the numerical and analytical results rules out finite-size effects. The topological phase considered here should be experimentally observable in a recently developed trapped-ion quantum simulator. VL - 93 U4 - 041102 UR - http://arxiv.org/abs/1505.03146 CP - 4 U5 - 10.1103/PhysRevB.93.041102 ER - TY - JOUR T1 - 2D Superexchange mediated magnetization dynamics in an optical lattice JF - Science Y1 - 2015 A1 - R. C. Brown A1 - R. Wyllie A1 - S. B. Koller A1 - E. A. Goldschmidt A1 - Michael Foss-Feig A1 - J. V. Porto AB - The competition of magnetic exchange interactions and tunneling underlies many complex quantum phenomena observed in real materials. We study non-equilibrium magnetization dynamics in an extended 2D system by loading effective spin-1/2 bosons into a spin-dependent optical lattice, and we use the lattice to separately control the resonance conditions for tunneling and superexchange. After preparing a non-equilibrium anti-ferromagnetically ordered state, we observe relaxation dynamics governed by two well-separated rates, which scale with the underlying Hamiltonian parameters associated with superexchange and tunneling. Remarkably, with tunneling off-resonantly suppressed, we are able to observe superexchange dominated dynamics over two orders of magnitude in magnetic coupling strength, despite the presence of vacancies. In this regime, the measured timescales are in agreement with simple theoretical estimates, but the detailed dynamics of this 2D, strongly correlated, and far-from-equilibrium quantum system remain out of reach of current computational techniques. VL - 348 U4 - 540 - 544 UR - http://arxiv.org/abs/1411.7036v1 CP - 6234 J1 - Science U5 - 10.1126/science.aaa1385 ER - TY - JOUR T1 - Atom induced cavities and tunable long-range interactions between atoms trapped near photonic crystals JF - Nature Photon. 9, 326 (2015) Y1 - 2015 A1 - J S Douglas A1 - H Habibian A1 - Alexey V. Gorshkov A1 - H J Kimble A1 - D E Chang AB -

Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, achieving tunable, coherent long-range interactions between atoms is an outstanding challenge, which currently leaves a large class of models inaccessible to quantum simulation. Here, we propose a solution exploiting the powerful new platform of cold atoms trapped near nano-photonic systems. We show that the dielectric contrast of an atom trapped near a photonic crystal can seed a localized cavity mode around the atomic position. In a dynamic form of “all-atomic” cavity QED, the length of these cavity modes can be tuned, and atoms separated by the order of the e↵ective cavity length can interact coherently with each other. Considering realistic conditions such as fabrication disorder and photon losses, coherent long-range potentials or spin interactions can be dominant in the system over length scales up to hundreds of wavelengths.

UR - http://www.nature.com/nphoton/journal/v9/n5/full/nphoton.2015.57.html U5 - doi:10.1038/nphoton.2015.57 ER - TY - JOUR T1 - Bilayer fractional quantum Hall states with ultracold dysprosium JF - Physical Review A Y1 - 2015 A1 - Norman Y. Yao A1 - Steven D. Bennett A1 - Chris R. Laumann A1 - Benjamin L. Lev A1 - Alexey V. Gorshkov AB - We show how dipolar interactions between dysprosium atoms in an optical lattice can be used to obtain fractional quantum Hall states. In our approach, dysprosium atoms are trapped one atom per site in a deep optical lattice with negligible tunneling. Microwave and spatially dependent optical dressing fields are used to define an effective spin-1/2 or spin-1 degree of freedom in each atom. Thinking of spin-1/2 particles as hardcore bosons, dipole-dipole interactions give rise to boson hopping, topological flat bands with Chern number 1, and the \nu = 1/2 Laughlin state. Thinking of spin-1 particles as two-component hardcore bosons, dipole-dipole interactions again give rise to boson hopping, topological flat bands with Chern number 2, and the bilayer Halperin (2,2,1) state. By adjusting the optical fields, we find a phase diagram, in which the (2,2,1) state competes with superfluidity. Generalizations to solid-state magnetic dipoles are discussed. VL - 92 U4 - 033609 UR - http://arxiv.org/abs/1505.03099v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.92.033609 ER - TY - JOUR T1 - Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems Y1 - 2015 A1 - Mohammad F. Maghrebi A1 - Zhe-Xuan Gong A1 - Alexey V. Gorshkov AB - Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)∼1/rα, directly relevant to ion-trap experiments. Using bosonization and renormalization group theory, we find CSB for α smaller than a critical exponent αc(≤3) depending on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal symmetry due to long-range interactions, and is described by a new universality class akin to the Berezinskii-Kosterlitz-Thouless transition. Our analytical findings are in good agreement with a numerical calculation. Signatures of the CSB phase should be accessible in existing trapped-ion experiments. UR - http://arxiv.org/abs/1510.01325 ER - TY - JOUR T1 - Coulomb bound states of strongly interacting photons JF - Physical Review Letters Y1 - 2015 A1 - Mohammad F. Maghrebi A1 - Michael Gullans A1 - P. Bienias A1 - S. Choi A1 - I. Martin A1 - O. Firstenberg A1 - M. D. Lukin A1 - H. P. Büchler A1 - Alexey V. Gorshkov AB - We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. VL - 115 U4 - 123601 UR - http://arxiv.org/abs/1505.03859v1 CP - 12 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.115.123601 ER - TY - JOUR T1 - Fractional Quantum Hall States of Rydberg Polaritons JF - Physical Review A Y1 - 2015 A1 - Mohammad F. Maghrebi A1 - Norman Y. Yao A1 - Mohammad Hafezi A1 - Thomas Pohl A1 - Ofer Firstenberg A1 - Alexey V. Gorshkov AB - We propose a scheme for realizing fractional quantum Hall states of light. In our scheme, photons of two polarizations are coupled to different atomic Rydberg states to form two flavors of Rydberg polaritons that behave as an effective spin. An array of optical cavity modes overlapping with the atomic cloud enables the realization of an effective spin-1/2 lattice. We show that the dipolar interaction between such polaritons, inherited from the Rydberg states, can be exploited to create a flat, topological band for a single spin-flip excitation. At half filling, this gives rise to a photonic (or polaritonic) fractional Chern insulator -- a lattice-based, fractional quantum Hall state of light. VL - 91 U4 - 033838 UR - http://arxiv.org/abs/1411.6624v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.91.033838 ER - TY - JOUR T1 - Injection Locking of a Semiconductor Double Quantum Dot Micromaser JF - Physical Review A Y1 - 2015 A1 - Y. -Y. Liu A1 - J. Stehlik A1 - Michael Gullans A1 - J. M. Taylor A1 - J. R. Petta AB - Emission linewidth is an important figure of merit for masers and lasers. We recently demonstrated a semiconductor double quantum dot (DQD) micromaser where photons are generated through single electron tunneling events. Charge noise directly couples to the DQD energy levels, resulting in a maser linewidth that is more than 100 times larger than the Schawlow-Townes prediction. Here we demonstrate a linewidth narrowing of more than a factor 10 by locking the DQD emission to a coherent tone that is injected to the input port of the cavity. We measure the injection locking range as a function of cavity input power and show that it is in agreement with the Adler equation. The position and amplitude of distortion sidebands that appear outside of the injection locking range are quantitatively examined. Our results show that this unconventional maser, which is impacted by strong charge noise and electron-phonon coupling, is well described by standard laser models. VL - 92 U4 - 053802 UR - http://arxiv.org/abs/1508.04147 CP - 5 U5 - 10.1103/PhysRevA.92.053802 ER - TY - JOUR T1 - Momentum switches JF - Quantum Information and Computation Y1 - 2015 A1 - Andrew M. Childs A1 - David Gosset A1 - Daniel Nagaj A1 - Mouktik Raha A1 - Zak Webb AB - Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct momentum switches, graphs that route particles depending on their momenta. We also give an example where there is no exact momentum switch, although we construct an arbitrarily good approximation. VL - 15 U4 - 601-621 UR - http://arxiv.org/abs/1406.4510v1 CP - 7-8 J1 - Quantum Information and Computation 15 ER - TY - JOUR T1 - Nearly-linear light cones in long-range interacting quantum systems JF - Physical Review Letters Y1 - 2015 A1 - Michael Foss-Feig A1 - Zhe-Xuan Gong A1 - Charles W. Clark A1 - Alexey V. Gorshkov AB - In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems. VL - 114 U4 - 157201 UR - http://arxiv.org/abs/1410.3466v1 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.114.157201 ER - TY - JOUR T1 - Optical Control of Donor Spin Qubits in Silicon JF - Physical Review B Y1 - 2015 A1 - Michael Gullans A1 - J. M. Taylor AB - We show how to achieve optical, spin-selective transitions from the ground state to excited orbital states of group-V donors (P, As, Sb, Bi) in silicon. We consider two approaches based on either resonant, far-infrared (IR) transitions of the neutral donor or resonant, near-IR excitonic transitions. For far-IR light, we calculate the dipole matrix elements between the valley-orbit and spin-orbit split states for all the goup-V donors using effective mass theory. We then calculate the maximum rate and amount of electron-nuclear spin-polarization achievable through optical pumping with circularly polarized light. We find this approach is most promising for Bi donors due to their large spin-orbit and valley-orbit interactions. Using near-IR light, spin-selective excitation is possible for all the donors by driving a two-photon $\Lambda$-transition from the ground state to higher orbitals with even parity. We show that externally applied electric fields or strain allow similar, spin-selective $\Lambda$-transition to odd-parity excited states. We anticipate these results will be useful for future spectroscopic investigations of donors, quantum control and state preparation of donor spin qubits, and for developing a coherent interface between donor spin qubits and single photons. VL - 92 U4 - 195411 UR - http://arxiv.org/abs/1507.07929 CP - 19 U5 - 10.1103/PhysRevB.92.195411 ER - TY - JOUR T1 - Optomechanical reference accelerometer JF - Metrologia Y1 - 2015 A1 - Oliver Gerberding A1 - Felipe Guzman Cervantes A1 - John Melcher A1 - Jon R. Pratt A1 - J. M. Taylor AB -

We present an optomechanical accelerometer with high dynamic range, high bandwidth and read-out noise levels below 8 ${\mu}$g/$\sqrt{\mathrm{Hz}}$. The straightforward assembly and low cost of our device make it a prime candidate for on-site reference calibrations and autonomous navigation. We present experimental data taken with a vacuum sealed, portable prototype and deduce the achieved bias stability and scale factor accuracy. Additionally, we present a comprehensive model of the device physics that we use to analyze the fundamental noise sources and accuracy limitations of such devices.

VL - 52 U4 - 654 UR - http://iopscience.iop.org/article/10.1088/0026-1394/52/5/654/meta;jsessionid=C2B417A5CD50B9B57EE14C78E1783802.ip-10-40-1-105 CP - 5 U5 - 10.1088/0026-1394/52/5/654 ER - TY - JOUR T1 - Parafermionic zero modes in ultracold bosonic systems JF - Physical Review Letters Y1 - 2015 A1 - Mohammad F. Maghrebi A1 - Sriram Ganeshan A1 - David J. Clarke A1 - Alexey V. Gorshkov A1 - Jay D. Sau AB - 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. VL - 115 U4 - 065301 UR - http://arxiv.org/abs/1504.04012v2 CP - 6 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.115.065301 ER - TY - JOUR T1 - Phonon-Assisted Gain in a Semiconductor Double Quantum Dot Maser JF - Physical Review Letters Y1 - 2015 A1 - Michael Gullans A1 - Y. -Y. Liu A1 - J. Stehlik A1 - J. R. Petta A1 - J. M. Taylor AB - 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. VL - 114 U4 - 196802 UR - http://arxiv.org/abs/1501.03499v3 CP - 19 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.114.196802 ER - TY - JOUR T1 - Quantum many-body models with cold atoms coupled to photonic crystals JF - Nature Photonics Y1 - 2015 A1 - Douglas, J. S. A1 - Habibian, H. A1 - Hung, C.-L. A1 - Alexey V. Gorshkov A1 - Kimble, H. J. A1 - Chang, D. E. VL - 9 U4 - 326 - 331 UR - http://www.nature.com/doifinder/10.1038/nphoton.2015.57 CP - 5 J1 - Nature Photon U5 - 10.1038/nphoton.2015.57 ER - TY - JOUR T1 - Quantum Nonlinear Optics Near Optomechanical Instabilities JF - Physical Review A Y1 - 2015 A1 - Xunnong Xu A1 - Michael Gullans A1 - J. M. Taylor AB - Optomechanical systems provide a unique platform for observing quantum behavior of macroscopic objects. However, efforts towards realizing nonlinear behavior at the single photon level have been inhibited by the small size of the radiation pressure interaction. Here we show that it is not necessary to reach the single-photon strong-coupling regime in order to realize significant optomechanical nonlinearities. Instead, nonlinearities at the few quanta level can be achieved, even with weak-coupling, in a two-mode optomechanical system driven near instability. In this limit, we establish a new figure of merit for realizing strong nonlinearity which scales with the single-photon optomechanical coupling and the sideband resolution of the mechanical mode with respect to the cavity linewidth. We find that current devices based on optomechanical crystals, thought to be in the weak-coupling regime, can still achieve strong quantum nonlinearity; enabling deterministic interactions between single photons. VL - 91 U4 - 013818 UR - http://arxiv.org/abs/1404.3726v2 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.91.013818 ER - TY - JOUR T1 - Semiconductor double quantum dot micromaser JF - Science Y1 - 2015 A1 - Y. -Y. Liu A1 - J. Stehlik A1 - C. Eichler A1 - Michael Gullans A1 - J. M. Taylor A1 - J. R. Petta AB - The coherent generation of light, from masers to lasers, relies upon the specific structure of the individual emitters that lead to gain. Devices operating as lasers in the few-emitter limit provide opportunities for understanding quantum coherent phenomena, from THz sources to quantum communication. Here we demonstrate a maser that is driven by single electron tunneling events. Semiconductor double quantum dots (DQDs) serve as a gain medium and are placed inside of a high quality factor microwave cavity. We verify maser action by comparing the statistics of the emitted microwave field above and below the maser threshold. VL - 347 U4 - 285 - 287 UR - http://arxiv.org/abs/1507.06359v1 CP - 6219 J1 - Science U5 - 10.1126/science.aaa2501 ER - TY - JOUR T1 - Tensor network non-zero testing JF - Quantum Information & Computation Y1 - 2015 A1 - Sevag Gharibian A1 - Zeph Landau A1 - Seung Woo Shin A1 - Guoming Wang AB - Tensor networks are a central tool in condensed matter physics. In this paper, we initiate the study of tensor network non-zero testing (TNZ): Given a tensor network T, does T represent a non-zero vector? We show that TNZ is not in the Polynomial-Time Hierarchy unless the hierarchy collapses. We next show (among other results) that the special cases of TNZ on non-negative and injective tensor networks are in NP. Using this, we make a simple observation: The commuting variant of the MA-complete stoquastic k-SAT problem on D-dimensional qudits is in NP for logarithmic k and constant D. This reveals the first class of quantum Hamiltonians whose commuting variant is known to be in NP for all (1) logarithmic k, (2) constant D, and (3) for arbitrary interaction graphs. VL - 15 U4 - 885-899 UR - http://arxiv.org/abs/1406.5279 CP - 9-10 ER - TY - JOUR T1 - Beyond the spin model approximation for Ramsey spectroscopy JF - Phys. Rev. Lett. Y1 - 2014 A1 - A P Koller A1 - M Beverland A1 - Alexey V. Gorshkov A1 - A M Rey VL - 112 U4 - 123001 UR - http://link.aps.org/doi/10.1103/PhysRevLett.112.123001 ER - TY - JOUR T1 - The Bose-Hubbard model is QMA-complete JF - Proceedings of the 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014) Y1 - 2014 A1 - Andrew M. Childs A1 - David Gosset A1 - Zak Webb AB - The Bose-Hubbard model is a system of interacting bosons that live on the vertices of a graph. The particles can move between adjacent vertices and experience a repulsive on-site interaction. The Hamiltonian is determined by a choice of graph that specifies the geometry in which the particles move and interact. We prove that approximating the ground energy of the Bose-Hubbard model on a graph at fixed particle number is QMA-complete. In our QMA-hardness proof, we encode the history of an n-qubit computation in the subspace with at most one particle per site (i.e., hard-core bosons). This feature, along with the well-known mapping between hard-core bosons and spin systems, lets us prove a related result for a class of 2-local Hamiltonians defined by graphs that generalizes the XY model. By avoiding the use of perturbation theory in our analysis, we circumvent the need to multiply terms in the Hamiltonian by large coefficients. VL - 8572 U4 - 308-319 UR - http://arxiv.org/abs/1311.3297v1 J1 - Proceedings of the 41st International Colloquium on Automata U5 - 10.1007/978-3-662-43948-7_26 ER - TY - JOUR T1 - Kitaev chains with long-range pairing JF - Physical Review Letters Y1 - 2014 A1 - Davide Vodola A1 - Luca Lepori A1 - Elisa Ercolessi A1 - Alexey V. Gorshkov A1 - Guido Pupillo AB - We propose and analyze a generalization of the Kitaev chain for fermions with long-range $p$-wave pairing, which decays with distance as a power-law with exponent $\alpha$. Using the integrability of the model, we demonstrate the existence of two types of gapped regimes, where correlation functions decay exponentially at short range and algebraically at long range ($\alpha > 1$) or purely algebraically ($\alpha < 1$). Most interestingly, along the critical lines, long-range pairing is found to break conformal symmetry for sufficiently small $\alpha$. This is accompanied by a violation of the area law for the entanglement entropy in large parts of the phase diagram in the presence of a gap, and can be detected via the dynamics of entanglement following a quench. Some of these features may be relevant for current experiments with cold atomic ions. VL - 113 UR - http://arxiv.org/abs/1405.5440v2 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.113.156402 ER - TY - JOUR T1 - Many-body dynamics of dipolar molecules in an optical lattice JF - Physical Review Letters Y1 - 2014 A1 - Kaden R. A. Hazzard A1 - Bryce Gadway A1 - Michael Foss-Feig A1 - Bo Yan A1 - Steven A. Moses A1 - Jacob P. Covey A1 - Norman Y. Yao A1 - Mikhail D. Lukin A1 - Jun Ye A1 - Deborah S. Jin A1 - Ana Maria Rey AB - Understanding the many-body dynamics of isolated quantum systems is one of the central challenges in modern physics. To this end, the direct experimental realization of strongly correlated quantum systems allows one to gain insights into the emergence of complex phenomena. Such insights enable the development of theoretical tools that broaden our understanding. Here, we theoretically model and experimentally probe with Ramsey spectroscopy the quantum dynamics of disordered, dipolar-interacting, ultracold molecules in a partially filled optical lattice. We report the capability to control the dipolar interaction strength, and we demonstrate that the many-body dynamics extends well beyond a nearest-neighbor or mean-field picture, and cannot be quantitatively described using previously available theoretical tools. We develop a novel cluster expansion technique and demonstrate that our theoretical method accurately captures the measured dependence of the spin dynamics on molecule number and on the dipolar interaction strength. In the spirit of quantum simulation, this agreement simultaneously benchmarks the new theoretical method and verifies our microscopic understanding of the experiment. Our findings pave the way for numerous applications in quantum information science, metrology, and condensed matter physics. VL - 113 UR - http://arxiv.org/abs/1402.2354v1 CP - 19 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.113.195302 ER - TY - JOUR T1 - Non-local propagation of correlations in long-range interacting quantum systems JF - Nature Y1 - 2014 A1 - Philip Richerme A1 - Zhe-Xuan Gong A1 - Aaron Lee A1 - Crystal Senko A1 - Jacob Smith A1 - Michael Foss-Feig A1 - Spyridon Michalakis A1 - Alexey V. Gorshkov A1 - Christopher Monroe AB - The maximum speed with which information can propagate in a quantum many-body system directly affects how quickly disparate parts of the system can become correlated and how difficult the system will be to describe numerically. For systems with only short-range interactions, Lieb and Robinson derived a constant-velocity bound that limits correlations to within a linear effective light cone. However, little is known about the propagation speed in systems with long-range interactions, since the best long-range bound is too loose to give the correct light-cone shape for any known spin model and since analytic solutions rarely exist. In this work, we experimentally determine the spatial and time-dependent correlations of a far-from-equilibrium quantum many-body system evolving under a long-range Ising- or XY-model Hamiltonian. For several different interaction ranges, we extract the shape of the light cone and measure the velocity with which correlations propagate through the system. In many cases we find increasing propagation velocities, which violate the Lieb-Robinson prediction, and in one instance cannot be explained by any existing theory. Our results demonstrate that even modestly-sized quantum simulators are well-poised for studying complicated many-body systems that are intractable to classical computation. VL - 511 U4 - 198 - 201 UR - http://arxiv.org/abs/1401.5088v1 CP - 7508 J1 - Nature U5 - 10.1038/nature13450 ER - TY - JOUR T1 - Persistence of locality in systems with power-law interactions JF - Physical Review Letters Y1 - 2014 A1 - Zhe-Xuan Gong A1 - Michael Foss-Feig A1 - Spyridon Michalakis A1 - Alexey V. Gorshkov AB - 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. VL - 113 UR - http://arxiv.org/abs/1401.6174v2 CP - 3 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.113.030602 ER - TY - JOUR T1 - Probing many-body interactions in an optical lattice clock JF - Ann. Phys. Y1 - 2014 A1 - Rey, A M A1 - Alexey V. Gorshkov A1 - Kraus, C V A1 - Martin, M J A1 - Bishof, M A1 - Swallows, M D A1 - Zhang, X A1 - Benko, C A1 - Ye, J A1 - Lemke, N D A1 - Ludlow, A D VL - 340 U4 - 311 UR - http://www.sciencedirect.com/science/article/pii/S0003491613002546 ER - TY - JOUR T1 - A Quantum Network of Silicon Qubits using Mid-Infrared Graphene Plasmons Y1 - 2014 A1 - Michael Gullans A1 - J. M. Taylor AB - We consider a quantum network of mid-infrared, graphene plasmons coupled to the hydrogen-like excited states of group-V donors in silicon. First, we show how to use plasmon-enhanced light-matter interactions to achieve single-shot spin readout of the donor qubits via optical excitation and electrical detection of the emitted plasmons. We then show how plasmons in high mobility graphene nanoribbons can be used to achieve high-fidelity, two-qubit gates and entanglement of distant Si donor qubits. The proposed device is readily compatible with existing technology and fabrication methods. UR - http://arxiv.org/abs/1407.7035v1 ER - TY - JOUR T1 - Scattering resonances and bound states for strongly interacting Rydberg polaritons JF - Physical Review A Y1 - 2014 A1 - P. Bienias A1 - S. Choi A1 - O. Firstenberg A1 - Mohammad F. Maghrebi A1 - Michael Gullans A1 - M. D. Lukin A1 - Alexey V. Gorshkov A1 - H. P. Büchler AB - We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments. VL - 90 UR - http://arxiv.org/abs/1402.7333v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.90.053804 ER - TY - JOUR T1 - Spatial search by continuous-time quantum walks on crystal lattices JF - Physical Review A Y1 - 2014 A1 - Andrew M. Childs A1 - Yimin Ge AB - We consider the problem of searching a general $d$-dimensional lattice of $N$ vertices for a single marked item using a continuous-time quantum walk. We demand locality, but allow the walk to vary periodically on a small scale. By constructing lattice Hamiltonians exhibiting Dirac points in their dispersion relations and exploiting the linear behaviour near a Dirac point, we develop algorithms that solve the problem in a time of $O(\sqrt N)$ for $d>2$ and $O(\sqrt N \log N)$ in $d=2$. In particular, we show that such algorithms exist even for hypercubic lattices in any dimension. Unlike previous continuous-time quantum walk algorithms on hypercubic lattices in low dimensions, our approach does not use external memory. VL - 89 UR - http://arxiv.org/abs/1403.2676v2 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.89.052337 ER - TY - JOUR T1 - Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect JF - Physical Review Letters Y1 - 2014 A1 - Bihui Zhu A1 - Bryce Gadway A1 - Michael Foss-Feig A1 - Johannes Schachenmayer A1 - Michael Wall A1 - Kaden R. A. Hazzard A1 - Bo Yan A1 - Steven A. Moses A1 - Jacob P. Covey A1 - Deborah S. Jin A1 - Jun Ye A1 - Murray Holland A1 - Ana Maria Rey AB - We investigate theoretically the suppression of two-body losses when the on-site loss rate is larger than all other energy scales in a lattice. This work quantitatively explains the recently observed suppression of chemical reactions between two rotational states of fermionic KRb molecules confined in one-dimensional tubes with a weak lattice along the tubes [Yan et al., Nature 501, 521-525 (2013)]. New loss rate measurements performed for different lattice parameters but under controlled initial conditions allow us to show that the loss suppression is a consequence of the combined effects of lattice confinement and the continuous quantum Zeno effect. A key finding, relevant for generic strongly reactive systems, is that while a single-band theory can qualitatively describe the data, a quantitative analysis must include multiband effects. Accounting for these effects reduces the inferred molecule filling fraction by a factor of five. A rate equation can describe much of the data, but to properly reproduce the loss dynamics with a fixed filling fraction for all lattice parameters we develop a mean-field model and benchmark it with numerically exact time-dependent density matrix renormalization group calculations. VL - 112 UR - http://arxiv.org/abs/1310.2221v2 CP - 7 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.112.070404 ER - TY - JOUR T1 - All-Optical Switch and Transistor Gated by One Stored Photon JF - Science Y1 - 2013 A1 - Wenlan Chen A1 - Kristin M. Beck A1 - Robert Bücker A1 - Michael Gullans A1 - Mikhail D. Lukin A1 - Haruka Tanji-Suzuki A1 - Vladan Vuletic AB - The realization of an all-optical transistor where one 'gate' photon controls a 'source' light beam, is a long-standing goal in optics. By stopping a light pulse in an atomic ensemble contained inside an optical resonator, we realize a device in which one stored gate photon controls the resonator transmission of subsequently applied source photons. A weak gate pulse induces bimodal transmission distribution, corresponding to zero and one gate photons. One stored gate photon produces fivefold source attenuation, and can be retrieved from the atomic ensemble after switching more than one source photon. Without retrieval, one stored gate photon can switch several hundred source photons. With improved storage and retrieval efficiency, our work may enable various new applications, including photonic quantum gates, and deterministic multiphoton entanglement. VL - 341 U4 - 768 - 770 UR - http://arxiv.org/abs/1401.3194v1 CP - 6147 J1 - Science U5 - 10.1126/science.1238169 ER - TY - JOUR T1 - Attractive Photons in a Quantum Nonlinear Medium JF - Nature (London) Y1 - 2013 A1 - Ofer Firstenberg A1 - Thibault Peyronel A1 - Qi-Yu Liang A1 - Alexey V. Gorshkov A1 - Mikhail D. Lukin A1 - Vladan Vuletic VL - 502 U4 - 71 UR - http://dx.doi.org/10.1038/nature12512 ER - TY - JOUR T1 - Controllable quantum spin glasses with magnetic impurities embedded in quantum solids JF - Physical Review B Y1 - 2013 A1 - Mikhail Lemeshko A1 - Norman Y. Yao A1 - Alexey V. Gorshkov A1 - Hendrik Weimer A1 - Steven D. Bennett A1 - Takamasa Momose A1 - Sarang Gopalakrishnan AB - Magnetic impurities embedded in inert solids can exhibit long coherence times and interact with one another via their intrinsic anisotropic dipolar interaction. We argue that, as a consequence of these properties, disordered ensembles of magnetic impurities provide an effective platform for realizing a controllable, tunable version of the dipolar quantum spin glass seen in LiHo$_x$Y$_{1-x}$F$_4$. Specifically, we propose and analyze a system composed of dysprosium atoms embedded in solid helium. We describe the phase diagram of the system and discuss the realizability and detectability of the quantum spin glass and antiglass phases. VL - 88 UR - http://arxiv.org/abs/1307.1130v1 CP - 1 J1 - Phys. Rev. B U5 - 10.1103/PhysRevB.88.014426 ER - TY - JOUR T1 - Dissipative Many-body Quantum Optics in Rydberg Media JF - Physical Review Letters Y1 - 2013 A1 - Alexey V. Gorshkov A1 - Rejish Nath A1 - Thomas Pohl AB - We develop a theoretical framework for the dissipative propagation of quantized light in interacting optical media under conditions of electromagnetically induced transparency (EIT). The theory allows us to determine the peculiar spatiotemporal structure of the output of two complementary Rydberg-EIT-based light-processing modules: the recently demonstrated single-photon filter and the recently proposed single-photon subtractor, which, respectively, let through and absorb a single photon. In addition to being crucial for applications of these and other optical quantum devices, the theory opens the door to the study of exotic dissipative many-body dynamics of strongly interacting photons in nonlinear nonlocal media. VL - 110 UR - http://arxiv.org/abs/1211.7060v1 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.110.153601 ER - TY - JOUR T1 - Individual Addressing in Quantum Computation through Spatial Refocusing JF - Physical Review A Y1 - 2013 A1 - Chao Shen A1 - Zhe-Xuan Gong A1 - Luming Duan AB - Separate addressing of individual qubits is a challenging requirement for scalable quantum computation, and crosstalk between operations on neighboring qubits remains as a significant source of noise for current experimental implementation of multi-qubit platforms. We propose a scheme based on spatial refocusing from interference of several coherent laser beams to significantly reduce the crosstalk noise for any type of quantum gates. A general framework is developed for the spatial refocusing technique, in particular with practical Gaussian beams, and we show under typical experimental conditions, the crosstalk-induced infidelity of quantum gates can be reduced by several orders of magnitude with a moderate cost of a few correction laser beams. VL - 88 UR - http://arxiv.org/abs/1305.2798v3 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.88.052325 ER - TY - JOUR T1 - An Introduction to Quantum Programming in Quipper JF - Lecture Notes in Computer Science Y1 - 2013 A1 - Alexander S. Green A1 - Peter LeFanu Lumsdaine A1 - Neil J. Ross A1 - Peter Selinger A1 - Benoît Valiron AB - Quipper is a recently developed programming language for expressing quantum computations. This paper gives a brief tutorial introduction to the language, through a demonstration of how to make use of some of its key features. We illustrate many of Quipper's language features by developing a few well known examples of Quantum computation, including quantum teleportation, the quantum Fourier transform, and a quantum circuit for addition. VL - 7948 U4 - 110-124 SN - 978-3-642-38986-3 UR - http://arxiv.org/abs/1304.5485v1 J1 - Lecture Notes in Computer Science 7948:110-124 U5 - 10.1007/978-3-642-38986-3_10 ER - TY - JOUR T1 - Kitaev honeycomb and other exotic spin models with polar molecules JF - Molecular Physics Y1 - 2013 A1 - Alexey V. Gorshkov A1 - Kaden R. A. Hazzard A1 - Ana Maria Rey AB - We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole-dipole interactions give rise to interactions between the spins. In particular, we show that, with sufficient microwave control, the interaction between two spins can be written as a sum of five independently controllable Hamiltonian terms proportional to the five rank-2 spherical harmonics Y_{2,q}(theta,phi), where (theta,phi) are the spherical coordinates of the vector connecting the two molecules. To demonstrate the potential of this approach beyond the simplest examples studied in [S. R. Manmana et al., arXiv:1210.5518v2], we focus on the realization of the Kitaev honeycomb model, which can support exotic non-Abelian anyonic excitations. We also discuss the possibility of generating spin Hamiltonians with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry. VL - 111 U4 - 1908 - 1916 UR - http://arxiv.org/abs/1301.5636v1 CP - 12-13 J1 - Molecular Physics U5 - 10.1080/00268976.2013.800604 ER - TY - JOUR T1 - Preparation of Non-equilibrium Nuclear Spin States in Double Quantum Dots JF - Physical Review B Y1 - 2013 A1 - Michael Gullans A1 - J. J. Krich A1 - J. M. Taylor A1 - B. I. Halperin A1 - M. D. Lukin AB - 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. VL - 88 UR - http://arxiv.org/abs/1212.6953v3 CP - 3 J1 - Phys. Rev. B U5 - 10.1103/PhysRevB.88.035309 ER - TY - JOUR T1 - Prethermalization and dynamical transition in an isolated trapped ion spin chain JF - New Journal of Physics Y1 - 2013 A1 - Zhe-Xuan Gong A1 - L. -M. Duan AB - 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. VL - 15 U4 - 113051 UR - http://arxiv.org/abs/1305.0985v1 CP - 11 J1 - New J. Phys. U5 - 10.1088/1367-2630/15/11/113051 ER - TY - JOUR T1 - Quantum Cherenkov Radiation and Non-contact Friction JF - Physical Review A Y1 - 2013 A1 - Mohammad F. Maghrebi A1 - Ramin Golestanian A1 - Mehran Kardar AB - We present a number of arguments to demonstrate that a quantum analog of Cherenkov effect occurs when two dispersive objects are in relative motion. Specifically we show that two semi-infinite plates experience friction beyond a threshold velocity which, in their center-of-mass frame, is the phase speed of light within their medium. The loss in mechanical energy is radiated away through the plates before getting fully absorbed in the form of heat. By deriving various correlation functions inside and outside the two plates, we explicitly compute the radiation, and discuss its dependence on the reference frame. VL - 88 UR - http://arxiv.org/abs/1304.4909v2 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.88.042509 ER - TY - JOUR T1 - Quantum Logic between Remote Quantum Registers JF - Physical Review A Y1 - 2013 A1 - Norman Y. Yao A1 - Zhe-Xuan Gong A1 - Chris R. Laumann A1 - Steven D. Bennett A1 - L. -M. Duan A1 - Mikhail D. Lukin A1 - Liang Jiang A1 - Alexey V. Gorshkov AB - We analyze two approaches to quantum state transfer in solid-state spin systems. First, we consider unpolarized spin-chains and extend previous analysis to various experimentally relevant imperfections, including quenched disorder, dynamical decoherence, and uncompensated long range coupling. In finite-length chains, the interplay between disorder-induced localization and decoherence yields a natural optimal channel fidelity, which we calculate. Long-range dipolar couplings induce a finite intrinsic lifetime for the mediating eigenmode; extensive numerical simulations of dipolar chains of lengths up to L=12 show remarkably high fidelity despite these decay processes. We further consider the extension of the protocol to bosonic systems of coupled oscillators. Second, we introduce a quantum mirror based architecture for universal quantum computing which exploits all of the spins in the system as potential qubits. While this dramatically increases the number of qubits available, the composite operations required to manipulate "dark" spin qubits significantly raise the error threshold for robust operation. Finally, as an example, we demonstrate that eigenmode-mediated state transfer can enable robust long-range logic between spatially separated Nitrogen-Vacancy registers in diamond; numerical simulations confirm that high fidelity gates are achievable even in the presence of moderate disorder. VL - 87 UR - http://arxiv.org/abs/1206.0014v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.87.022306 ER - TY - JOUR T1 - A quantum many-body spin system in an optical lattice clock JF - Science Y1 - 2013 A1 - M J Martin A1 - Bishof, M A1 - Swallows, M D A1 - X Zhang A1 - C Benko A1 - J von-Stecher A1 - Alexey V. Gorshkov A1 - Rey, A M A1 - Jun Ye VL - 341 U4 - 632 UR - http://www.sciencemag.org/content/341/6146/632.abstract ER - TY - JOUR T1 - Quantum Nonlinear Optics: Strongly Interacting Photons JF - Opt. Photonics News Y1 - 2013 A1 - Firstenberg, O A1 - Lukin, M D A1 - Peyronel, T A1 - Liang, Q -Y A1 - Vuletic, V A1 - Alexey V. Gorshkov A1 - Hofferberth, S A1 - Pohl, T VL - 24 U4 - 48 UR - http://www.osa-opn.org/abstract.cfm?URI=opn-24-12-48 ER - TY - JOUR T1 - Quipper: A Scalable Quantum Programming Language JF - ACM SIGPLAN Notices Y1 - 2013 A1 - Alexander S. Green A1 - Peter LeFanu Lumsdaine A1 - Neil J. Ross A1 - Peter Selinger A1 - Benoît Valiron AB -

The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higher-order quantum programming language. Quipper has been used to program a diverse set of non-trivial quantum algorithms, and can generate quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze quantum algorithms.

VL - 48 U4 - 333-342 UR - http://arxiv.org/abs/1304.3390v1 CP - 6 J1 - SIGPLAN Not. U5 - 10.1145/2499370.2462177 ER - TY - JOUR T1 - Realizing Fractional Chern Insulators with Dipolar Spins JF - Physical Review Letters Y1 - 2013 A1 - Norman Y. Yao A1 - Alexey V. Gorshkov A1 - Chris R. Laumann A1 - Andreas M. Läuchli A1 - Jun Ye A1 - Mikhail D. Lukin AB - Strongly correlated quantum systems can exhibit exotic behavior controlled by topology. We predict that the \nu=1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins. As a specific implementation, we analyze how to prepare and detect synthetic gauge potentials for the rotational excitations of ultra-cold polar molecules trapped in a deep optical lattice. While the orbital motion of the molecules is pinned, at finite densities, the rotational excitations form a fractional Chern insulator. We present a detailed experimental blueprint for KRb, and demonstrate that the energetics are consistent with near-term capabilities. Prospects for the realization of such phases in solid-state dipolar systems are discussed as are their possible applications. VL - 110 UR - http://arxiv.org/abs/1212.4839v1 CP - 18 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.110.185302 ER - TY - JOUR T1 - The Resonant Exchange Qubit JF - Physical Review Letters Y1 - 2013 A1 - J. Medford A1 - J. Beil A1 - J. M. Taylor A1 - E. I. Rashba A1 - H. Lu A1 - A. C. Gossard A1 - C. M. Marcus AB - We introduce a solid-state qubit in which exchange interactions among confined electrons provide both the static longitudinal field and the oscillatory transverse field, allowing rapid and full qubit control via rf gate-voltage pulses. We demonstrate two-axis control at a detuning sweet-spot, where leakage due to hyperfine coupling is suppressed by the large exchange gap. A {\pi}/2-gate time of 2.5 ns and a coherence time of 19 {\mu}s, using multi-pulse echo, are also demonstrated. Model calculations that include effects of hyperfine noise are in excellent quantitative agreement with experiment. VL - 111 UR - http://arxiv.org/abs/1304.3413v2 CP - 5 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.111.050501 ER - TY - JOUR T1 - A Scattering Approach to the Dynamical Casimir Effect JF - Physical Review D Y1 - 2013 A1 - Mohammad F. Maghrebi A1 - Ramin Golestanian A1 - Mehran Kardar AB - We develop a unified scattering approach to dynamical Casimir problems which can be applied to both accelerating boundaries, as well as dispersive objects in relative motion. A general (trace) formula is derived for the radiation from accelerating boundaries. Applications are provided for objects with different shapes in various dimensions, and undergoing rotational or linear motion. Within this framework, photon generation is discussed in the context of a modulated optical mirror. For dispersive objects, we find general results solely in terms of the scattering matrix. Specifically, we discuss the vacuum friction on a rotating object, and the friction on an atom moving parallel to a surface. VL - 87 UR - http://arxiv.org/abs/1210.1842v2 CP - 2 J1 - Phys. Rev. D U5 - 10.1103/PhysRevD.87.025016 ER - TY - JOUR T1 - Self-Consistent Measurement and State Tomography of an Exchange-Only Spin Qubit JF - Nature Nanotechnology Y1 - 2013 A1 - J. Medford A1 - J. Beil A1 - J. M. Taylor A1 - S. D. Bartlett A1 - A. C. Doherty A1 - E. I. Rashba A1 - D. P. DiVincenzo A1 - H. Lu A1 - A. C. Gossard A1 - C. M. Marcus AB - We report initialization, complete electrical control, and single-shot readout of an exchange-only spin qubit. Full control via the exchange interaction is fast, yielding a demonstrated 75 qubit rotations in under 2 ns. Measurement and state tomography are performed using a maximum-likelihood estimator method, allowing decoherence, leakage out of the qubit state space, and measurement fidelity to be quantified. The methods developed here are generally applicable to systems with state leakage, noisy measurements, and non-orthogonal control axes. VL - 8 U4 - 654 - 659 UR - http://arxiv.org/abs/1302.1933v1 CP - 9 J1 - Nature Nanotech U5 - 10.1038/nnano.2013.168 ER - TY - JOUR T1 - Single-photon nonlinear optics with graphene plasmons JF - Physical Review Letters Y1 - 2013 A1 - Michael Gullans A1 - D. E. Chang A1 - F. H. L. Koppens A1 - F. J. García de Abajo A1 - M. D. Lukin AB - We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch. VL - 111 UR - http://arxiv.org/abs/1309.2651v3 CP - 24 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.111.247401 ER - TY - JOUR T1 - Spinor dynamics in an antiferromagnetic spin-1 thermal Bose gas JF - Physical Review Letters Y1 - 2013 A1 - Hyewon K. Pechkis A1 - Jonathan P. Wrubel A1 - Arne Schwettmann A1 - Paul F. Griffin A1 - Ryan Barnett A1 - Eite Tiesinga A1 - Paul D. Lett AB - We present experimental observations of coherent spin-population oscillations in a cold thermal, Bose gas of spin-1 sodium-23 atoms. The population oscillations in a multi-spatial-mode thermal gas have the same behavior as those observed in a single-spatial-mode antiferromagnetic spinor Bose Einstein condensate. We demonstrate this by showing that the two situations are described by the same dynamical equations, with a factor of two change in the spin-dependent interaction coefficient, which results from the change to particles with distinguishable momentum states in the thermal gas. We compare this theory to the measured spin population evolution after times up to a few hundreds of ms, finding quantitative agreement with the amplitude and period. We also measure the damping time of the oscillations as a function of magnetic field. VL - 111 UR - http://arxiv.org/abs/1306.4255v1 CP - 2 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.111.025301 ER - TY - JOUR T1 - Symmetries of Codeword Stabilized Quantum Codes JF - 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) Y1 - 2013 A1 - Salman Beigi A1 - Jianxin Chen A1 - Markus Grassl A1 - Zhengfeng Ji A1 - Qiang Wang A1 - Bei Zeng AB - Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be represented by a self-dual additive code S and a classical code C, i.,e., Q=(S,C), however this representation is in general not unique. We show that for any CWS code Q with certain permutation symmetry, one can always find a self-dual additive code S with the same permutation symmetry as Q such that Q=(S,C). As many good CWS codes have been found by starting from a chosen S, this ensures that when trying to find CWS codes with certain permutation symmetry, the choice of S with the same symmetry will suffice. A key step for this result is a new canonical representation for CWS codes, which is given in terms of a unique decomposition as union stabilizer codes. For CWS codes, so far mainly the standard form (G,C) has been considered, where G is a graph state. We analyze the symmetry of the corresponding graph of G, which in general cannot possess the same permutation symmetry as Q. We show that it is indeed the case for the toric code on a square lattice with translational symmetry, even if its encoding graph can be chosen to be translational invariant. VL - 22 U4 - 192-206 UR - http://arxiv.org/abs/1303.7020v2 U5 - 10.4230/LIPIcs.TQC.2013.192 ER - TY - JOUR T1 - Topological phases in ultracold polar-molecule quantum magnets JF - Physical Review B Y1 - 2013 A1 - Salvatore R. Manmana A1 - E. M. Stoudenmire A1 - Kaden R. A. Hazzard A1 - Ana Maria Rey A1 - Alexey V. Gorshkov AB - We show how to use polar molecules in an optical lattice to engineer quantum spin models with arbitrary spin S >= 1/2 and with interactions featuring a direction-dependent spin anisotropy. This is achieved by encoding the effective spin degrees of freedom in microwave-dressed rotational states of the molecules and by coupling the spins through dipolar interactions. We demonstrate how one of the experimentally most accessible anisotropies stabilizes symmetry protected topological phases in spin ladders. Using the numerically exact density matrix renormalization group method, we find that these interacting phases -- previously studied only in the nearest-neighbor case -- survive in the presence of long-range dipolar interactions. We also show how to use our approach to realize the bilinear-biquadratic spin-1 and the Kitaev honeycomb models. Experimental detection schemes and imperfections are discussed. VL - 87 UR - http://arxiv.org/abs/1210.5518v2 CP - 8 J1 - Phys. Rev. B U5 - 10.1103/PhysRevB.87.081106 ER - TY - JOUR T1 - Topologically Protected Quantum State Transfer in a Chiral Spin Liquid JF - Nature Communications Y1 - 2013 A1 - Norman Y. Yao A1 - Chris R. Laumann A1 - Alexey V. Gorshkov A1 - Hendrik Weimer A1 - Liang Jiang A1 - J. Ignacio Cirac A1 - Peter Zoller A1 - Mikhail D. Lukin AB - Topology plays a central role in ensuring the robustness of a wide variety of physical phenomena. Notable examples range from the robust current carrying edge states associated with the quantum Hall and the quantum spin Hall effects to proposals involving topologically protected quantum memory and quantum logic operations. Here, we propose and analyze a topologically protected channel for the transfer of quantum states between remote quantum nodes. In our approach, state transfer is mediated by the edge mode of a chiral spin liquid. We demonstrate that the proposed method is intrinsically robust to realistic imperfections associated with disorder and decoherence. Possible experimental implementations and applications to the detection and characterization of spin liquid phases are discussed. VL - 4 U4 - 1585 UR - http://arxiv.org/abs/1110.3788v1 J1 - Nat Comms U5 - 10.1038/ncomms2531 ER - TY - JOUR T1 - Universal computation by multi-particle quantum walk JF - Science Y1 - 2013 A1 - Andrew M. Childs A1 - David Gosset A1 - Zak Webb AB - A quantum walk is a time-homogeneous quantum-mechanical process on a graph defined by analogy to classical random walk. The quantum walker is a particle that moves from a given vertex to adjacent vertices in quantum superposition. Here we consider a generalization of quantum walk to systems with more than one walker. A continuous-time multi-particle quantum walk is generated by a time-independent Hamiltonian with a term corresponding to a single-particle quantum walk for each particle, along with an interaction term. Multi-particle quantum walk includes a broad class of interacting many-body systems such as the Bose-Hubbard model and systems of fermions or distinguishable particles with nearest-neighbor interactions. We show that multi-particle quantum walk is capable of universal quantum computation. Since it is also possible to efficiently simulate a multi-particle quantum walk of the type we consider using a universal quantum computer, this model exactly captures the power of quantum computation. In principle our construction could be used as an architecture for building a scalable quantum computer with no need for time-dependent control. VL - 339 U4 - 791 - 794 UR - http://arxiv.org/abs/1205.3782v2 CP - 6121 J1 - Science U5 - 10.1126/science.1229957 ER - TY - JOUR T1 - Cavity QED with atomic mirrors JF - New J. Phys. Y1 - 2012 A1 - D E Chang A1 - Jiang, L A1 - Alexey V. Gorshkov A1 - H J Kimble VL - 14 U4 - 063003 UR - http://iopscience.iop.org/1367-2630/14/6/063003/ ER - TY - JOUR T1 - Levinson's theorem for graphs II JF - Journal of Mathematical Physics Y1 - 2012 A1 - Andrew M. Childs A1 - David Gosset AB - We prove Levinson's theorem for scattering on an (m+n)-vertex graph with n semi-infinite paths each attached to a different vertex, generalizing a previous result for the case n=1. This theorem counts the number of bound states in terms of the winding of the determinant of the S-matrix. We also provide a proof that the bound states and incoming scattering states of the Hamiltonian together form a complete basis for the Hilbert space, generalizing another result for the case n=1. VL - 53 U4 - 102207 UR - http://arxiv.org/abs/1203.6557v2 CP - 10 J1 - J. Math. Phys. U5 - 10.1063/1.4757665 ER - TY - JOUR T1 - Nanoplasmonic Lattices for Ultracold atoms JF - Physical Review Letters Y1 - 2012 A1 - Michael Gullans A1 - T. Tiecke A1 - D. E. Chang A1 - J. Feist A1 - J. D. Thompson A1 - J. I. Cirac A1 - P. Zoller A1 - M. D. Lukin AB - We propose to use sub-wavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the sub-wavelength manipulation and strong light-matter interaction associated with nano-plasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed. VL - 109 UR - http://arxiv.org/abs/1208.6293v3 CP - 23 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.109.235309 ER - TY - JOUR T1 - Non-Recursively Constructible Recursive Families of Graphs JF - The Electronic Journal of Combinatorics Y1 - 2012 A1 - Colleen Bouey A1 - Christina Graves A1 - Aaron Ostrander A1 - Gregory Palma AB - In a publication by Noy and Ribó, it was shown that recursively constructible families of graphs are recursive. The authors also conjecture that the converse holds; that is, recursive families are also recursively constructible. In this paper, we provide two specific counterexamples to this conjecture, which we then extend to an infinite family of counterexamples. VL - 19 UR - http://www.combinatorics.org/ojs/index.php/eljc/article/view/2211 CP - 2 ER - TY - JOUR T1 - Photonic quantum simulation of ground state configurations of Heisenberg square and checkerboard lattice spin systems Y1 - 2012 A1 - Xiao-song Ma A1 - Borivoje Dakic A1 - Sebastian Kropatsche A1 - William Naylor A1 - Yang-hao Chan A1 - Zhe-Xuan Gong A1 - Lu-ming Duan A1 - Anton Zeilinger A1 - Philip Walther AB - 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. UR - http://arxiv.org/abs/1205.2801v1 ER - TY - JOUR T1 - Quantum nonlinear optics with single photons enabled by strongly interacting atoms JF - Nature (London) Y1 - 2012 A1 - Peyronel, Thibault A1 - Firstenberg, Ofer A1 - Liang, Qi-Yu A1 - Hofferberth, Sebastian A1 - Alexey V. Gorshkov A1 - Pohl, Thomas A1 - Lukin, Mikhail D. A1 - Vuletic, Vladan VL - 488 U4 - 57 UR - http://www.nature.com/nature/journal/v488/n7409/full/nature11361.html ER - TY - JOUR T1 - Quantum Simulation of Spin Models on an Arbitrary Lattice with Trapped Ions JF - New Journal of Physics Y1 - 2012 A1 - Simcha Korenblit A1 - Dvir Kafri A1 - Wess C. Campbell A1 - Rajibul Islam A1 - Emily E. Edwards A1 - Zhe-Xuan Gong A1 - Guin-Dar Lin A1 - Luming Duan A1 - Jungsang Kim A1 - Kihwan Kim A1 - Christopher Monroe AB - A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create long-range effective spin-spin interactions and allow the simulation of spin Hamiltonians that possess nontrivial phases and dynamics. Here we show how appropriate design of laser fields can provide for arbitrary multidimensional spin-spin interaction graphs even for the case of a linear spatial array of ions. This scheme uses currently existing trap technology and is scalable to levels where classical methods of simulation are intractable. VL - 14 U4 - 095024 UR - http://arxiv.org/abs/1201.0776v1 CP - 9 J1 - New J. Phys. U5 - 10.1088/1367-2630/14/9/095024 ER - TY - JOUR T1 - Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators JF - New Journal of Physics Y1 - 2012 A1 - Steven T. Flammia A1 - David Gross A1 - Yi-Kai Liu A1 - Jens Eisert AB - Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition. First, we show that a low-rank density matrix can be estimated using fewer copies of the state, i.e., the sample complexity of tomography decreases with the rank. Second, we show that unknown low-rank states can be reconstructed from an incomplete set of measurements, using techniques from compressed sensing and matrix completion. These techniques use simple Pauli measurements, and their output can be certified without making any assumptions about the unknown state. We give a new theoretical analysis of compressed tomography, based on the restricted isometry property (RIP) for low-rank matrices. Using these tools, we obtain near-optimal error bounds, for the realistic situation where the data contains noise due to finite statistics, and the density matrix is full-rank with decaying eigenvalues. We also obtain upper-bounds on the sample complexity of compressed tomography, and almost-matching lower bounds on the sample complexity of any procedure using adaptive sequences of Pauli measurements. Using numerical simulations, we compare the performance of two compressed sensing estimators with standard maximum-likelihood estimation (MLE). We find that, given comparable experimental resources, the compressed sensing estimators consistently produce higher-fidelity state reconstructions than MLE. In addition, the use of an incomplete set of measurements leads to faster classical processing with no loss of accuracy. Finally, we show how to certify the accuracy of a low rank estimate using direct fidelity estimation and we describe a method for compressed quantum process tomography that works for processes with small Kraus rank. VL - 14 U4 - 095022 UR - http://arxiv.org/abs/1205.2300v2 CP - 9 J1 - New J. Phys. U5 - 10.1088/1367-2630/14/9/095022 ER - TY - JOUR T1 - Reply to Comment on "Space-Time Crystals of Trapped Ions Y1 - 2012 A1 - Tongcang Li A1 - Zhe-Xuan Gong A1 - Zhang-qi Yin A1 - H. T. Quan A1 - Xiaobo Yin A1 - Peng Zhang A1 - L. -M. Duan A1 - Xiang Zhang AB - This is a reply to the comment from Patrick Bruno (arXiv:1211.4792) on our paper (Phys. Rev. Lett. 109, 163001 (2012)). UR - http://arxiv.org/abs/1212.6959v2 U5 - http://dx.doi.org/10.1103/PhysRevLett.109.163001 ER - TY - JOUR T1 - Scalable Architecture for a Room Temperature Solid-State Quantum Information Processor JF - Nature Communications Y1 - 2012 A1 - Norman Y. Yao A1 - Liang Jiang A1 - Alexey V. Gorshkov A1 - Peter C. Maurer A1 - Geza Giedke A1 - J. Ignacio Cirac A1 - Mikhail D. Lukin AB - The realization of a scalable quantum information processor has emerged over the past decade as one of the central challenges at the interface of fundamental science and engineering. Much progress has been made towards this goal. Indeed, quantum operations have been demonstrated on several trapped ion qubits, and other solid-state systems are approaching similar levels of control. Extending these techniques to achieve fault-tolerant operations in larger systems with more qubits remains an extremely challenging goal, in part, due to the substantial technical complexity of current implementations. Here, we propose and analyze an architecture for a scalable, solid-state quantum information processor capable of operating at or near room temperature. The architecture is applicable to realistic conditions, which include disorder and relevant decoherence mechanisms, and includes a hierarchy of control at successive length scales. Our approach is based upon recent experimental advances involving Nitrogen-Vacancy color centers in diamond and will provide fundamental insights into the physics of non-equilibrium many-body quantum systems. Additionally, the proposed architecture may greatly alleviate the stringent constraints, currently limiting the realization of scalable quantum processors. VL - 3 U4 - 800 UR - http://arxiv.org/abs/1012.2864v1 J1 - Nat Comms U5 - 10.1038/ncomms1788 ER - TY - JOUR T1 - Space-Time Crystals of Trapped Ions JF - Physical Review Letters Y1 - 2012 A1 - Tongcang Li A1 - Gong, Zhe-Xuan A1 - Yin, Zhang-Qi A1 - Quan, H. T. A1 - Yin, Xiaobo A1 - Zhang, Peng A1 - Duan, L.-M. A1 - Zhang, Xiang AB - Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter. VL - 109 U4 - 163001 UR - http://link.aps.org/doi/10.1103/PhysRevLett.109.163001 CP - 16 U5 - 10.1103/PhysRevLett.109.163001 ER - TY - JOUR T1 - Topological Flat Bands from Dipolar Spin Systems JF - Physical Review Letters Y1 - 2012 A1 - Norman Y. Yao A1 - Chris R. Laumann A1 - Alexey V. Gorshkov A1 - Steven D. Bennett A1 - Eugene Demler A1 - Peter Zoller A1 - Mikhail D. Lukin AB - We propose and analyze a physical system that naturally admits two-dimensional topological nearly flat bands. Our approach utilizes an array of three-level dipoles (effective S = 1 spins) driven by inhomogeneous electromagnetic fields. The dipolar interactions produce arbitrary uniform background gauge fields for an effective collection of conserved hardcore bosons, namely, the dressed spin-flips. These gauge fields result in topological band structures, whose bandgap can be larger than the corresponding bandwidth. Exact diagonalization of the full interacting Hamiltonian at half-filling reveals the existence of superfluid, crystalline, and supersolid phases. An experimental realization using either ultra-cold polar molecules or spins in the solid state is considered. VL - 109 UR - http://arxiv.org/abs/1207.4479v3 CP - 26 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.109.266804 ER - TY - JOUR T1 - Casimir force between sharp-shaped conductors JF - Proceedings of the National Academy of Sciences Y1 - 2011 A1 - Mohammad F. Maghrebi A1 - Sahand Jamal Rahi A1 - Thorsten Emig A1 - Noah Graham A1 - Robert L. Jaffe A1 - Mehran Kardar AB - Casimir forces between conductors at the sub-micron scale cannot be ignored in the design and operation of micro-electromechanical (MEM) devices. However, these forces depend non-trivially on geometry, and existing formulae and approximations cannot deal with realistic micro-machinery components with sharp edges and tips. Here, we employ a novel approach to electromagnetic scattering, appropriate to perfect conductors with sharp edges and tips, specifically to wedges and cones. The interaction of these objects with a metal plate (and among themselves) is then computed systematically by a multiple-scattering series. For the wedge, we obtain analytical expressions for the interaction with a plate, as functions of opening angle and tilt, which should provide a particularly useful tool for the design of MEMs. Our result for the Casimir interactions between conducting cones and plates applies directly to the force on the tip of a scanning tunneling probe; the unexpectedly large temperature dependence of the force in these configurations should attract immediate experimental interest. VL - 108 U4 - 6867 - 6871 UR - http://arxiv.org/abs/1010.3223v1 CP - 17 J1 - Proceedings of the National Academy of Sciences U5 - 10.1073/pnas.1018079108 ER - TY - JOUR T1 - Comment on "Foundation of Statistical Mechanics under Experimentally Realistic Conditions" Y1 - 2011 A1 - Zhe-Xuan Gong A1 - L. -M. Duan AB - Reimann [Phys. Rev. Lett. 101, 190403 (2008)] claimed that generic isolated macroscopic quantum system will equilibrate under experimentally realistic conditions by proving a theorem. We here show that the proof is invalid for most many-body systems and is unable to demonstrate equilibration in realistic experiment. UR - http://arxiv.org/abs/1109.4696v1 ER - TY - JOUR T1 - Continuous-variable quantum compressed sensing Y1 - 2011 A1 - Matthias Ohliger A1 - Vincent Nesme A1 - David Gross A1 - Yi-Kai Liu A1 - Jens Eisert AB - We significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a continuous family, and is also applicable to continuous-variable states. As a technical result, this work generalizes quantum compressed sensing to the situation where the measured observables are taken from a so-called tight frame (rather than an orthonormal basis) --- hence covering most realistic measurement scenarios. As an application, we discuss the reconstruction of quantum states of light from homodyne detection and other types of measurements, and we present simulations that show the advantage of the proposed compressed sensing technique over present methods. Finally, we introduce a method to construct a certificate which guarantees the success of the reconstruction with no assumption on the state, and we show how slightly more measurements give rise to "universal" state reconstruction that is highly robust to noise. UR - http://arxiv.org/abs/1111.0853v3 ER - TY - JOUR T1 - d-Wave Superfluidity in Optical Lattices of Ultracold Polar Molecules JF - Physical Review A Y1 - 2011 A1 - Kevin A. Kuns A1 - Ana Maria Rey A1 - Alexey V. Gorshkov AB - Recent work on ultracold polar molecules, governed by a generalization of the t-J Hamiltonian, suggests that molecules may be better suited than atoms for studying d-wave superfluidity due to stronger interactions and larger tunability of the system. We compute the phase diagram for polar molecules in a checkerboard lattice consisting of weakly coupled square plaquettes. In the simplest experimentally realizable case where there is only tunneling and an XX-type spin-spin interaction, we identify the parameter regime where d-wave superfluidity occurs. We also find that the inclusion of a density-density interaction destroys the superfluid phase and that the inclusion of a spin-density or an Ising-type spin-spin interaction can enhance the superfluid phase. We also propose schemes for experimentally realizing the perturbative calculations exhibiting enhanced d-wave superfluidity. VL - 84 UR - http://arxiv.org/abs/1110.5330v2 CP - 6 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.84.063639 ER - TY - JOUR T1 - Dynamics of Overhauser Field under nuclear spin diffusion in a quantum dot JF - New Journal of Physics Y1 - 2011 A1 - Zhe-Xuan Gong A1 - Zhang-qi Yin A1 - L. -M. Duan AB - The coherence of electron spin can be significantly enhanced by locking the Overhauser field from nuclear spins using the nuclear spin preparation. We propose a theoretical model to calculate the long time dynamics of the Overhauser field under intrinsic nuclear spin diffusion in a quantum dot. We obtain a simplified diffusion equation that can be numerically solved and show quantitatively how the Knight shift and the electron-mediated nuclear spin flip-flop affect the nuclear spin diffusion. The results explain several recent experimental observations, where the decay time of Overhauser field is measured under different configurations, including variation of the external magnetic field, the electron spin configuration in a double dot, and the initial nuclear spin polarization rate. VL - 13 U4 - 033036 UR - http://arxiv.org/abs/0912.4322v1 CP - 3 J1 - New J. Phys. U5 - 10.1088/1367-2630/13/3/033036 ER - TY - JOUR T1 - Electromagnetic Casimir Energies of Semi-Infinite Planes JF - EPL (Europhysics Letters) Y1 - 2011 A1 - Mohammad F. Maghrebi A1 - Noah Graham AB - Using recently developed techniques based on scattering theory, we find the electromagnetic Casimir energy for geometries involving semi-infinite planes, a case that is of particular interest in the design of microelectromechanical devices. We obtain both approximate analytic formulae and exact results requiring only modest numerical computation. Using these results, we analyze the effects of edges and orientation on the Casimir energy. We also demonstrate the accuracy, simplicity, and utility of our approximation scheme, which is based on a multiple reflection expansion. VL - 95 U4 - 14001 UR - http://arxiv.org/abs/1102.1486v1 CP - 1 J1 - EPL U5 - 10.1209/0295-5075/95/14001 ER - TY - JOUR T1 - Interferometry with Synthetic Gauge Fields JF - Physical Review A Y1 - 2011 A1 - Brandon M. Anderson A1 - J. M. Taylor A1 - Victor M. Galitski AB - We propose a compact atom interferometry scheme for measuring weak, time-dependent accelerations. Our proposal uses an ensemble of dilute trapped bosons with two internal states that couple to a synthetic gauge field with opposite charges. The trapped gauge field couples spin to momentum to allow time dependent accelerations to be continuously imparted on the internal states. We generalize this system to reduce noise and estimate the sensitivity of such a system to be S~10^-7 m / s^2 / Hz^1/2. VL - 83 UR - http://arxiv.org/abs/1008.3910v2 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.83.031602 ER - TY - JOUR T1 - Light storage in an optically thick atomic ensemble under conditions of electromagnetically induced transparency and four-wave mixing JF - Physical Review A Y1 - 2011 A1 - Nathaniel B. Phillips A1 - Alexey V. Gorshkov A1 - Irina Novikova AB - We study the modification of a traditional electromagnetically induced transparency (EIT) stored light technique that includes both EIT and four-wave mixing (FWM) in an ensemble of hot Rb atoms. The standard treatment of light storage involves the coherent and reversible mapping of one photonic mode onto a collective spin coherence. It has been shown that unwanted, competing processes such as four-wave mixing are enhanced by EIT and can significantly modify the signal optical pulse propagation. We present theoretical and experimental evidence to indicate that while a Stokes field is indeed detected upon retrieval of the signal field, any information originally encoded in a seeded Stokes field is not independently preserved during the storage process. We present a simple model that describes the propagation dynamics of the fields and the impact of FWM on the spin wave. VL - 83 UR - http://arxiv.org/abs/1103.2131v1 CP - 6 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.83.063823 ER - TY - JOUR T1 - Photon-Photon Interactions via Rydberg Blockade JF - Physical Review Letters Y1 - 2011 A1 - Alexey V. Gorshkov A1 - Johannes Otterbach A1 - Michael Fleischhauer A1 - Thomas Pohl A1 - Mikhail D. Lukin AB - We develop the theory of light propagation under the conditions of electromagnetically induced transparency (EIT) in systems involving strongly interacting Rydberg states. Taking into account the quantum nature and the spatial propagation of light, we analyze interactions involving few-photon pulses. We demonstrate that this system can be used for the generation of nonclassical states of light including trains of single photons with an avoided volume between them, for implementing photon-photon quantum gates, as well as for studying many-body phenomena with strongly correlated photons. VL - 107 UR - http://arxiv.org/abs/1103.3700v1 CP - 13 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.107.133602 ER - TY - JOUR T1 - Quantum Magnetism with Polar Alkali Dimers JF - Physical Review A Y1 - 2011 A1 - Alexey V. Gorshkov A1 - Salvatore R. Manmana A1 - Gang Chen A1 - Eugene Demler A1 - Mikhail D. Lukin A1 - Ana Maria Rey AB - We show that dipolar interactions between ultracold polar alkali dimers in optical lattices can be used to realize a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. The model features long-range spin-spin interactions J_z and J_perp of XXZ type, long-range density-density interaction V, and long-range density-spin interaction W, all of which can be controlled in both magnitude and sign independently of each other and of the tunneling t. The "spin" is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional (orbital) degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. The presented system is expected to exhibit exotic physics and to provide insights into strongly correlated phenomena in condensed matter systems. Realistic experimental imperfections are discussed. VL - 84 UR - http://arxiv.org/abs/1106.1655v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.84.033619 ER - TY - JOUR T1 - Quantum magnetism with polar alkali-metal dimers JF - Phys. Rev. A Y1 - 2011 A1 - Alexey V. Gorshkov A1 - Manmana, S R A1 - Chen, G A1 - Demler, E A1 - Lukin, M D A1 - Rey, A M VL - 84 U4 - 033619 UR - http://link.aps.org/abstract/PRA/v84/e033619/ ER - TY - JOUR T1 - Resolved atomic interaction sidebands in an optical clock transition JF - Physical Review Letters Y1 - 2011 A1 - Michael Bishof A1 - Yige Lin A1 - Matthew D. Swallows A1 - Alexey V. Gorshkov A1 - Jun Ye A1 - Ana Maria Rey AB - We report the observation of resolved atomic interaction sidebands (ISB) in the ${}^{87}$Sr optical clock transition when atoms at microkelvin temperatures are confined in a two-dimensional (2D) optical lattice. The ISB are a manifestation of the strong interactions that occur between atoms confined in a quasi-one-dimensional geometry and disappear when the confinement is relaxed along one dimension. The emergence of ISB is linked to the recently observed suppression of collisional frequency shifts in [1]. At the current temperatures, the ISB can be resolved but are broad. At lower temperatures, ISB are predicted to be substantially narrower and usable as powerful spectroscopic tools in strongly interacting alkaline-earth gases. VL - 106 UR - http://arxiv.org/abs/1102.1016v2 CP - 25 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.106.250801 ER - TY - JOUR T1 - Robust Quantum State Transfer in Random Unpolarized Spin Chains JF - Physical Review Letters Y1 - 2011 A1 - Norman Y. Yao A1 - Liang Jiang A1 - Alexey V. Gorshkov A1 - Zhe-Xuan Gong A1 - Alex Zhai A1 - L. -M. Duan A1 - Mikhail D. Lukin AB - We propose and analyze a new approach for quantum state transfer between remote spin qubits. Specifically, we demonstrate that coherent quantum coupling between remote qubits can be achieved via certain classes of random, unpolarized (infinite temperature) spin chains. Our method is robust to coupling strength disorder and does not require manipulation or control over individual spins. In principle, it can be used to attain perfect state transfer over arbitrarily long range via purely Hamiltonian evolution and may be particularly applicable in a solid-state quantum information processor. As an example, we demonstrate that it can be used to attain strong coherent coupling between Nitrogen-Vacancy centers separated by micrometer distances at room temperature. Realistic imperfections and decoherence effects are analyzed. VL - 106 UR - http://arxiv.org/abs/1011.2762v2 CP - 4 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.106.040505 ER - TY - JOUR T1 - Spatial separation in a thermal mixture of ultracold $^174$Yb and $^87$Rb atoms JF - Physical Review A Y1 - 2011 A1 - Florian Baumer A1 - Frank Münchow A1 - Axel Görlitz A1 - Stephen E. Maxwell A1 - Paul S. Julienne A1 - Eite Tiesinga AB - We report on the observation of unusually strong interactions in a thermal mixture of ultracold atoms which cause a significant modification of the spatial distribution. A mixture of $^{87}$Rb and $^{174}$Yb with a temperature of a few $\mu$K is prepared in a hybrid trap consisting of a bichromatic optical potential superimposed on a magnetic trap. For suitable trap parameters and temperatures, a spatial separation of the two species is observed. We infer that the separation is driven by a large interaction strength between $^{174}$Yb and $^{87}$Rb accompanied by a large three-body recombination rate. Based on this assumption we have developed a diffusion model which reproduces our observations. VL - 83 UR - http://arxiv.org/abs/1104.1722v1 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.83.040702 ER - TY - JOUR T1 - Spectroscopy of dipolar fermions in 2D pancakes and 3D lattices JF - Physical Review A Y1 - 2011 A1 - Kaden R. A. Hazzard A1 - Alexey V. Gorshkov A1 - Ana Maria Rey AB - Motivated by ongoing measurements at JILA, we calculate the recoil-free spectra of dipolar interacting fermions, for example ultracold heteronuclear molecules, in a one-dimensional lattice of two-dimensional pancakes, spectroscopically probing transitions between different internal (e.g., rotational) states. We additionally incorporate p-wave interactions and losses, which are important for reactive molecules such as KRb. Moreover, we consider other sources of spectral broadening: interaction-induced quasiparticle lifetimes and the different polarizabilities of the different rotational states used for the spectroscopy. Although our main focus is molecules, some of the calculations are also useful for optical lattice atomic clocks. For example, understanding the p-wave shifts between identical fermions and small dipolar interactions coming from the excited clock state are necessary to reach future precision goals. Finally, we consider the spectra in a deep 3D lattice and show how they give a great deal of information about static correlation functions, including \textit{all} the moments of the density correlations between nearby sites. The range of correlations measurable depends on spectroscopic resolution and the dipole moment. VL - 84 UR - http://arxiv.org/abs/1106.1718v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.84.033608 ER - TY - JOUR T1 - Spectroscopy of dipolar fermions in layered two-dimensional and three-dimensional lattices JF - Phys. Rev. A Y1 - 2011 A1 - Hazzard, K R A A1 - Alexey V. Gorshkov A1 - Rey, A M VL - 84 U4 - 033608 UR - http://link.aps.org/abstract/PRA/v84/e033608/ ER - TY - JOUR T1 - Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules JF - Physical Review Letters Y1 - 2011 A1 - Alexey V. Gorshkov A1 - Salvatore R. Manmana A1 - Gang Chen A1 - Jun Ye A1 - Eugene Demler A1 - Mikhail D. Lukin A1 - Ana Maria Rey AB - By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. In addition to XXZ spin exchange, the model features density-density interactions and novel density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method (DMRG) to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the t-J-V-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally. VL - 107 UR - http://arxiv.org/abs/1106.1644v1 CP - 11 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.107.115301 ER - TY - JOUR T1 - Adiabatic preparation of many-body states in optical lattices JF - Physical Review A Y1 - 2010 A1 - Anders S. Sorensen A1 - Ehud Altman A1 - Michael Gullans A1 - J. V. Porto A1 - Mikhail D. Lukin A1 - Eugene Demler AB - We analyze a technique for the preparation of low entropy many body states of atoms in optical lattices based on adiabatic passage. In particular, we show that this method allows preparation of strongly correlated states as stable highest energy states of Hamiltonians that have trivial ground states. As an example, we analyze the generation of antiferromagnetically ordered states by adiabatic change of a staggered field acting on the spins of bosonic atoms with ferromagnetic interactions. VL - 81 UR - http://arxiv.org/abs/0906.2567v3 CP - 6 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.81.061603 ER - TY - JOUR T1 - Dynamic Nuclear Polarization in Double Quantum Dots JF - Physical Review Letters Y1 - 2010 A1 - Michael Gullans A1 - J. J. Krich A1 - J. M. Taylor A1 - H. Bluhm A1 - B. I. Halperin A1 - C. M. Marcus A1 - M. Stopa A1 - A. Yacoby A1 - M. D. Lukin AB - We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identified, including the build up of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states," and the elimination of the difference field. We show that in the case of unequal dots, build up of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, build up of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process. VL - 104 UR - http://arxiv.org/abs/1003.4508v2 CP - 22 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.104.226807 ER - TY - JOUR T1 - Efficient quantum state tomography JF - Nature Communications Y1 - 2010 A1 - Marcus Cramer A1 - Martin B. Plenio A1 - Steven T. Flammia A1 - David Gross A1 - Stephen D. Bartlett A1 - Rolando Somma A1 - Olivier Landon-Cardinal A1 - Yi-Kai Liu A1 - David Poulin AB - Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger systems it becomes infeasible because the number of quantum measurements and the amount of computation required to process them grows exponentially in the system size. Here we show that we can do exponentially better than direct state tomography for a wide range of quantum states, in particular those that are well approximated by a matrix product state ansatz. We present two schemes for tomography in 1-D quantum systems and touch on generalizations. One scheme requires unitary operations on a constant number of subsystems, while the other requires only local measurements together with more elaborate post-processing. Both schemes rely only on a linear number of experimental operations and classical postprocessing that is polynomial in the system size. A further strength of the methods is that the accuracy of the reconstructed states can be rigorously certified without any a priori assumptions. VL - 1 U4 - 149 UR - http://arxiv.org/abs/1101.4366v1 CP - 9 J1 - Nat Comms U5 - 10.1038/ncomms1147 ER - TY - JOUR T1 - Far-field optical imaging and manipulation of individual spins with nanoscale resolution JF - Nature Phys. Y1 - 2010 A1 - Maurer, P C A1 - Maze, J R A1 - Stanwix, P L A1 - Jiang, L A1 - Alexey V. Gorshkov A1 - Zibrov, A A A1 - Harke, B A1 - Hodges, J S A1 - Zibrov, A S A1 - Yacoby, A A1 - Twitchen, D A1 - Hell, S W A1 - Walsworth, R L A1 - Lukin, M D VL - 6 U4 - 912 UR - http://www.nature.com/nphys/journal/v6/n11/abs/nphys1774.html ER - TY - JOUR T1 - Fast Entanglement Distribution with Atomic Ensembles and Fluorescent Detection JF - Physical Review A Y1 - 2010 A1 - Jonatan B. Brask A1 - Liang Jiang A1 - Alexey V. Gorshkov A1 - Vladan Vuletic A1 - Anders S. Sorensen A1 - Mikhail D. Lukin AB - Quantum repeaters based on atomic ensemble quantum memories are promising candidates for achieving scalable distribution of entanglement over long distances. Recently, important experimental progress has been made towards their implementation. However, the entanglement rates and scalability of current approaches are limited by relatively low retrieval and single-photon detector efficiencies. We propose a scheme, which makes use of fluorescent detection of stored excitations to significantly increase the efficiency of connection and hence the rate. Practical performance and possible experimental realizations of the new protocol are discussed. VL - 81 UR - http://arxiv.org/abs/0907.3839v2 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.81.020303 ER - TY - JOUR T1 - Feshbach Resonances in Ultracold Gases JF - Reviews of Modern Physics Y1 - 2010 A1 - Cheng Chin A1 - Rudolf Grimm A1 - Paul Julienne A1 - Eite Tiesinga AB - Feshbach resonances are the essential tool to control the interaction between atoms in ultracold quantum gases. They have found numerous experimental applications, opening up the way to important breakthroughs. This Review broadly covers the phenomenon of Feshbach resonances in ultracold gases and their main applications. This includes the theoretical background and models for the description of Feshbach resonances, the experimental methods to find and characterize the resonances, a discussion of the main properties of resonances in various atomic species and mixed atomic species systems, and an overview of key experiments with atomic Bose-Einstein condensates, degenerate Fermi gases, and ultracold molecules. VL - 82 U4 - 1225 - 1286 UR - http://arxiv.org/abs/0812.1496v2 CP - 2 J1 - Rev. Mod. Phys. U5 - 10.1103/RevModPhys.82.1225 ER - TY - JOUR T1 - Heavy fermions in an optical lattice JF - Physical Review A Y1 - 2010 A1 - Michael Foss-Feig A1 - Michael Hermele A1 - Victor Gurarie A1 - Ana Maria Rey AB - We employ a mean-field theory to study ground-state properties and transport of a two-dimensional gas of ultracold alklaline-earth metal atoms governed by the Kondo Lattice Hamiltonian plus a parabolic confining potential. In a homogenous system this mean-field theory is believed to give a qualitatively correct description of heavy fermion metals and Kondo insulators: it reproduces the Kondo-like scaling of the quasiparticle mass in the former, and the same scaling of the excitation gap in the latter. In order to understand ground-state properties in a trap we extend this mean-field theory via local-density approximation. We find that the Kondo insulator gap manifests as a shell structure in the trapped density profile. In addition, a strong signature of the large Fermi surface expected for heavy fermion systems survives the confinement, and could be probed in time-of-flight experiments. From a full self-consistent diagonalization of the mean-field theory we are able to study dynamics in the trap. We find that the mass enhancement of quasiparticle excitations in the heavy Fermi liquid phase manifests as slowing of the dipole oscillations that result from a sudden displacement of the trap center. VL - 82 UR - http://arxiv.org/abs/1007.5083v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.82.053624 ER - TY - JOUR T1 - Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain JF - Physical Review Letters Y1 - 2010 A1 - Alexey V. Gorshkov A1 - Johannes Otterbach A1 - Eugene Demler A1 - Michael Fleischhauer A1 - Mikhail D. Lukin AB - 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. VL - 105 UR - http://arxiv.org/abs/1001.0968v3 CP - 6 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.105.060502 ER - TY - JOUR T1 - QMA-complete problems for stoquastic Hamiltonians and Markov matrices JF - Physical Review A Y1 - 2010 A1 - Stephen P. Jordan A1 - David Gosset A1 - Peter J. Love AB - We show that finding the lowest eigenvalue of a 3-local symmetric stochastic matrix is QMA-complete. We also show that finding the highest energy of a stoquastic Hamiltonian is QMA-complete and that adiabatic quantum computation using certain excited states of a stoquastic Hamiltonian is universal. We also show that adiabatic evolution in the ground state of a stochastic frustration free Hamiltonian is universal. Our results give a new QMA-complete problem arising in the classical setting of Markov chains, and new adiabatically universal Hamiltonians that arise in many physical systems. VL - 81 UR - http://arxiv.org/abs/0905.4755v2 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.81.032331 ER - TY - JOUR T1 - Quantum state tomography via compressed sensing JF - Physical Review Letters Y1 - 2010 A1 - David Gross A1 - Yi-Kai Liu A1 - Steven T. Flammia A1 - Stephen Becker A1 - Jens Eisert AB - We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rd log^2 d) measurement settings, compared to standard methods that require d^2 settings. Our methods have several features that make them amenable to experimental implementation: they require only simple Pauli measurements, use fast convex optimization, are stable against noise, and can be applied to states that are only approximately low-rank. The acquired data can be used to certify that the state is indeed close to pure, so no a priori assumptions are needed. We present both theoretical bounds and numerical simulations. VL - 105 UR - http://arxiv.org/abs/0909.3304v4 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.105.150401 ER - TY - JOUR T1 - Temperature driven structural phase transition for trapped ions and its experimental detection JF - Physical Review Letters Y1 - 2010 A1 - Zhe-Xuan Gong A1 - G. -D. Lin A1 - L. -M. Duan AB - A Wigner crystal formed with trapped ion can undergo structural phase transition, which is determined only by the mechanical conditions on a classical level. Instead of this classical result, we show that through consideration of quantum and thermal fluctuation, a structural phase transition can be solely driven by change of the system's temperature. We determine a finite-temperature phase diagram for trapped ions using the renormalization group method and the path integral formalism, and propose an experimental scheme to observe the predicted temperature-driven structural phase transition, which is well within the reach of the current ion trap technology. VL - 105 UR - http://arxiv.org/abs/1009.0089v1 CP - 26 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.105.265703 ER - TY - JOUR T1 - Thesis: Novel Systems and Methods for Quantum Communication, Quantum Computation, and Quantum Simulation JF - Harvard University Physics Department Y1 - 2010 A1 - Alexey V. Gorshkov VL - Ph.D. Thesis ER - TY - JOUR T1 - Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms JF - Nature Phys. Y1 - 2010 A1 - Alexey V. Gorshkov A1 - Hermele, M A1 - Gurarie, V A1 - Xu, C A1 - Julienne, P S A1 - Ye, J A1 - Zoller, P A1 - Demler, E A1 - Lukin, M D A1 - Rey, A M VL - 6 U4 - 289 UR - http://www.nature.com/nphys/journal/v6/n4/abs/nphys1535.html ER - TY - JOUR T1 - Alkaline-Earth-Metal Atoms as Few-Qubit Quantum Registers JF - Physical Review Letters Y1 - 2009 A1 - Alexey V. Gorshkov A1 - Ana Maria Rey A1 - Andrew J. Daley A1 - Martin M. Boyd A1 - Jun Ye A1 - Peter Zoller A1 - Mikhail D. Lukin AB - We propose and analyze a novel approach to quantum information processing, in which multiple qubits can be encoded and manipulated using electronic and nuclear degrees of freedom associated with individual alkaline-earth atoms trapped in an optical lattice. Specifically, we describe how the qubits within each register can be individually manipulated and measured with sub-wavelength optical resolution. We also show how such few-qubit registers can be coupled to each other in optical superlattices via conditional tunneling to form a scalable quantum network. Finally, potential applications to quantum computation and precision measurements are discussed. VL - 102 UR - http://arxiv.org/abs/0812.3660v2 CP - 11 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.102.110503 ER - TY - JOUR T1 - Many-Body Treatment of the Collisional Frequency Shift in Fermionic Atoms JF - Phys. Rev. Lett. Y1 - 2009 A1 - Rey, A M A1 - Alexey V. Gorshkov A1 - Rubbo, C VL - 103 U4 - 260402 UR - http://link.aps.org/abstract/PRL/v103/e260402/ ER - TY - JOUR T1 - Number Fluctuations and Energy Dissipation in Sodium Spinor Condensates JF - Physical Review Letters Y1 - 2009 A1 - Yingmei Liu A1 - Eduardo Gomez A1 - Stephen E. Maxwell A1 - Lincoln D. Turner A1 - Eite Tiesinga A1 - Paul D. Lett AB - We characterize fluctuations in atom number and spin populations in F=1 sodium spinor condensates. We find that the fluctuations enable a quantitative measure of energy dissipation in the condensate. The time evolution of the population fluctuations shows a maximum. We interpret this as evidence of a dissipation-driven separatrix crossing in phase space. For a given initial state, the critical time to the separatrix crossing is found to depend exponentially on the magnetic field and linearly on condensate density. This crossing is confirmed by tracking the energy of the spinor condensate as well as by Faraday rotation spectroscopy. We also introduce a phenomenological model that describes the observed dissipation with a single coefficient. VL - 102 UR - http://arxiv.org/abs/0906.2110v1 CP - 22 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.102.225301 ER - TY - JOUR T1 - Realization of Coherent Optically Dense Media via Buffer-Gas Cooling JF - Physical Review A Y1 - 2009 A1 - Tao Hong A1 - Alexey V. Gorshkov A1 - David Patterson A1 - Alexander S. Zibrov A1 - John M. Doyle A1 - Mikhail D. Lukin A1 - Mara G. Prentiss AB - We demonstrate that buffer-gas cooling combined with laser ablation can be used to create coherent optical media with high optical depth and low Doppler broadening that offers metastable states with low collisional and motional decoherence. Demonstration of this generic technique opens pathways to coherent optics with a large variety of atoms and molecules. We use helium buffer gas to cool 87Rb atoms to below 7 K and slow atom diffusion to the walls. Electromagnetically induced transparency (EIT) in this medium allows for 50% transmission in a medium with initial OD >70 and for slow pulse propagation with large delay-bandwidth products. In the high-OD regime, we observe high-contrast spectrum oscillations due to efficient four-wave mixing. VL - 79 UR - http://arxiv.org/abs/0805.1416v2 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.79.013806 ER - TY - JOUR T1 - Slow light propagation and amplification via electromagnetically induced transparency and four-wave mixing in an optically dense atomic vapor JF - J. Mod. Opt. Y1 - 2009 A1 - Phillips, N B A1 - Alexey V. Gorshkov A1 - Novikova, I VL - 56 U4 - 1916 UR - http://www.informaworld.com/smpp/content db=all content=a913545405 ER - TY - JOUR T1 - Anyonic interferometry and protected memories in atomic spin lattices JF - Nature Physics Y1 - 2008 A1 - Liang Jiang A1 - Gavin K. Brennen A1 - Alexey V. Gorshkov A1 - Klemens Hammerer A1 - Mohammad Hafezi A1 - Eugene Demler A1 - Mikhail D. Lukin A1 - Peter Zoller AB - Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations. VL - 4 U4 - 482 - 488 UR - http://arxiv.org/abs/0711.1365v1 CP - 6 J1 - Nat Phys U5 - 10.1038/nphys943 ER - TY - JOUR T1 - Coherent Quantum Optical Control with Subwavelength Resolution JF - Physical Review Letters Y1 - 2008 A1 - Alexey V. Gorshkov A1 - Liang Jiang A1 - Markus Greiner A1 - Peter Zoller A1 - Mikhail D. Lukin AB - We suggest a new method for quantum optical control with nanoscale resolution. Our method allows for coherent far-field manipulation of individual quantum systems with spatial selectivity that is not limited by the wavelength of radiation and can, in principle, approach a few nanometers. The selectivity is enabled by the nonlinear atomic response, under the conditions of Electromagnetically Induced Transparency, to a control beam with intensity vanishing at a certain location. Practical performance of this technique and its potential applications to quantum information science with cold atoms, ions, and solid-state qubits are discussed. VL - 100 UR - http://arxiv.org/abs/0706.3879v2 CP - 9 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.100.093005 ER - TY - JOUR T1 - Efficient scheme for one-way quantum computing in thermal cavities JF - International Journal of Theoretical Physics Y1 - 2008 A1 - Wen-Xing Yang A1 - Zhe-Xuan Gong AB - We propose a practical scheme for one-way quantum computing based on efficient generation of 2D cluster state in thermal cavities. We achieve a controlled-phase gate that is neither sensitive to cavity decay nor to thermal field by adding a strong classical field to the two-level atoms. We show that a 2D cluster state can be generated directly by making every two atoms collide in an array of cavities, with numerically calculated parameters and appropriate operation sequence that can be easily achieved in practical Cavity QED experiments. Based on a generated cluster state in Box$^{(4)}$ configuration, we then implement Grover's search algorithm for four database elements in a very simple way as an example of one-way quantum computing. VL - 47 U4 - 2997 - 3004 UR - http://arxiv.org/abs/0704.2297v1 CP - 11 J1 - Int J Theor Phys U5 - 10.1007/s10773-008-9734-x ER - TY - JOUR T1 - Optimal light storage in atomic vapor JF - Physical Review A Y1 - 2008 A1 - Nathaniel B. Phillips A1 - Alexey V. Gorshkov A1 - Irina Novikova AB - We study procedures for the optimization of efficiency of light storage and retrieval based on the dynamic form of electromagnetically induced transparency (EIT) in warm Rb vapor. We present a detailed analysis of two recently demonstrated optimization protocols: a time-reversal-based iteration procedure, which finds the optimal input signal pulse shape for any given control field, and a procedure based on the calculation of an optimal control field for any given signal pulse shape. We verify that the two procedures are consistent with each other, and that they both independently achieve the maximum memory efficiency for any given optical depth. We observe good agreement with theoretical predictions for moderate optical depths (<25), while at higher optical depths the experimental efficiency falls below the theoretically predicted values. We identify possible effects responsible for this reduction in memory efficiency. VL - 78 UR - http://arxiv.org/abs/0805.3348v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.78.023801 ER - TY - JOUR T1 - Optimal light storage with full pulse shape control JF - Physical Review A Y1 - 2008 A1 - Irina Novikova A1 - Nathaniel B. Phillips A1 - Alexey V. Gorshkov AB - We experimentally demonstrate optimal storage and retrieval of light pulses of arbitrary shape in atomic ensembles. By shaping auxiliary control pulses, we attain efficiencies approaching the fundamental limit and achieve precise retrieval into any predetermined temporal profile. Our techniques, demonstrated in warm Rb vapor, are applicable to a wide range of systems and protocols. As an example, we present their potential application to the creation of optical time-bin qubits and to controlled partial retrieval. VL - 78 UR - http://arxiv.org/abs/0805.1927v1 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.78.021802 ER - TY - JOUR T1 - Optimal light storage with full pulse-shape control JF - Phys. Rev. A Y1 - 2008 A1 - Novikova, I A1 - Phillips, N B A1 - Alexey V. Gorshkov VL - 78 U4 - 021802(R) UR - http://link.aps.org/abstract/PRA/v78/e021802/ ER - TY - JOUR T1 - Optimizing Slow and Stored Light for Multidisciplinary Applications JF - Proc. SPIE Y1 - 2008 A1 - Klein, M A1 - Xiao, Y A1 - Alexey V. Gorshkov A1 - M Hohensee A1 - C D Leung A1 - M R Browning A1 - Phillips, D F A1 - Novikova, I A1 - Walsworth, R L VL - 6904 U4 - 69040C UR - http://spie.org/x648.xml?product_id=772216&Search_Origin=QuickSearch&Search_Results_URL=http://spie.org/x1636.xml&Alternate_URL=http://spie.org/x18509.xml&Alternate_URL_Name=timeframe&Alternate_URL_Value=Exhibitors&UseJavascript=1&Please_Wait_URL=http://s ER - TY - JOUR T1 - Photon storage in Lambda-type optically dense atomic media. IV. Optimal control using gradient ascent JF - Physical Review A Y1 - 2008 A1 - Alexey V. Gorshkov A1 - Tommaso Calarco A1 - Mikhail D. Lukin A1 - Anders S. Sorensen AB - 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. VL - 77 UR - http://arxiv.org/abs/0710.2698v2 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.77.043806 ER - TY - JOUR T1 - Suppression of Inelastic Collisions Between Polar Molecules With a Repulsive Shield JF - Phys. Rev. Lett. Y1 - 2008 A1 - Alexey V. Gorshkov A1 - Rabl, P A1 - Pupillo, G A1 - Micheli, A A1 - Zoller, P A1 - Lukin, M D A1 - Büchler, H P VL - 101 U4 - 073201 UR - http://link.aps.org/abstract/PRL/v101/e073201/ ER - TY - JOUR T1 - Multi-photon Entanglement: From Quantum Curiosity to Quantum Computing and Quantum Repeaters JF - Proc. SPIE Y1 - 2007 A1 - Walther, P A1 - Eisaman, M D A1 - Nemiroski, A A1 - Alexey V. Gorshkov A1 - Zibrov, A S A1 - Zeilinger, A A1 - Lukin, M D VL - 6664 U4 - 66640G UR - http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG00666400000166640G000001&idtype=cvips&gifs=Yes&bproc=volrange&scode=6600%20-%206699 ER - TY - JOUR T1 - Optimal control of light pulse storage and retrieval JF - Physical Review Letters Y1 - 2007 A1 - Irina Novikova A1 - Alexey V. Gorshkov A1 - David F. Phillips A1 - Anders S. Sorensen A1 - Mikhail D. Lukin A1 - Ronald L. Walsworth AB - We demonstrate experimentally a procedure to obtain the maximum efficiency for the storage and retrieval of light pulses in atomic media. The procedure uses time reversal to obtain optimal input signal pulse-shapes. Experimental results in warm Rb vapor are in good agreement with theoretical predictions and demonstrate a substantial improvement of efficiency. This optimization procedure is applicable to a wide range of systems. VL - 98 UR - http://arxiv.org/abs/quant-ph/0702266v1 CP - 24 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.98.243602 ER - TY - JOUR T1 - Optimization of slow and stored light in atomic vapor JF - Proc. SPIE Y1 - 2007 A1 - Novikova, I A1 - Alexey V. Gorshkov A1 - Phillips, D F A1 - Xiao, Y A1 - Klein, M A1 - Walsworth, R L VL - 6482 U4 - 64820M UR - http://spiedigitallibrary.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG00648200000164820M000001&idtype=cvips&gifs=Yes&bproc=volrange&scode=6400%20-%206499 ER - TY - JOUR T1 - Photon storage in Lambda-type optically dense atomic media. I. Cavity model JF - Physical Review A Y1 - 2007 A1 - Alexey V. Gorshkov A1 - Axel Andre A1 - Mikhail D. Lukin A1 - Anders S. Sorensen AB - 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. VL - 76 UR - http://arxiv.org/abs/quant-ph/0612082v2 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.76.033804 ER - TY - JOUR T1 - Photon storage in Lambda-type optically dense atomic media. II. Free-space model JF - Physical Review A Y1 - 2007 A1 - Alexey V. Gorshkov A1 - Axel Andre A1 - Mikhail D. Lukin A1 - Anders S. Sorensen AB - 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)]. VL - 76 UR - http://arxiv.org/abs/quant-ph/0612083v2 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.76.033805 ER - TY - JOUR T1 - Photon storage in Lambda-type optically dense atomic media. III. Effects of inhomogeneous broadening JF - Physical Review A Y1 - 2007 A1 - Alexey V. Gorshkov A1 - Axel Andre A1 - Mikhail D. Lukin A1 - Anders S. Sorensen AB - 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. VL - 76 UR - http://arxiv.org/abs/quant-ph/0612084v2 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.76.033806 ER - TY - JOUR T1 - Practical scheme for quantum dense coding between three parties using microwave radiation in trapped ions JF - Journal of Physics B: Atomic, Molecular and Optical Physics Y1 - 2007 A1 - Wen-Xing Yang A1 - Zhe-Xuan Gong AB - 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. VL - 40 U4 - 1245 - 1252 UR - http://arxiv.org/abs/quant-ph/0702062v1 CP - 6 J1 - J. Phys. B: At. Mol. Opt. Phys. U5 - 10.1088/0953-4075/40/6/014 ER - TY - JOUR T1 - Signatures of incoherence in a quantum information processor Y1 - 2007 A1 - Michael K. Henry A1 - Alexey V. Gorshkov A1 - Yaakov S. Weinstein A1 - Paola Cappellaro A1 - Joseph Emerson A1 - Nicolas Boulant A1 - Jonathan S. Hodges A1 - Chandrasekhar Ramanathan A1 - Timothy F. Havel A1 - Rudy Martinez A1 - David G. Cory AB - Incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. While many incoherent processes appear decoherent, there are important differences. The distribution functions underlying incoherent processes are either static or slowly varying with respect to control operations and so the errors introduced by these distributions are refocusable. The observation and control of incoherence in small Hilbert spaces is well known. Here we explore incoherence during an entangling operation, such as is relevant in quantum information processing. As expected, it is more difficult to separate incoherence and decoherence over such processes. However, by studying the fidelity decay under a cyclic entangling map we are able to identify distinctive experimental signatures of incoherence. This result is demonstrated both through numerical simulations and experimentally in a three qubit nuclear magnetic resonance implementation. UR - http://arxiv.org/abs/0705.3666v2 ER - TY - JOUR T1 - Simple scheme for implementing the Deutsch-Jozsa algorithm in thermal cavity JF - Journal of Physics A: Mathematical and Theoretical Y1 - 2007 A1 - Wen-Xing Yang A1 - Zhe-Xuan Gong AB - We present a simple scheme to implement the Deutsch-Jozsa algorithm based on two-atom interaction in a thermal cavity. The photon-number-dependent parts in the evolution operator are canceled with the strong resonant classical field added. As a result, our scheme is immune to thermal field, and does not require the cavity to remain in the vacuum state throughout the procedure. Besides, large detuning between the atoms and the cavity is not necessary neither, leading to potential speed up of quantum operation. Finally, we show by numerical simulation that the proposed scheme is equal to demonstrate the Deutsch-Jozsa algorithm with high fidelity. VL - 40 U4 - 155 - 161 UR - http://arxiv.org/abs/quant-ph/0611225v2 CP - 1 J1 - J. Phys. A: Math. Theor. U5 - 10.1088/1751-8113/40/1/009 ER - TY - JOUR T1 - Universal Approach to Optimal Photon Storage in Atomic Media JF - Physical Review Letters Y1 - 2007 A1 - Alexey V. Gorshkov A1 - Axel Andre A1 - Michael Fleischhauer A1 - Anders S. Sorensen A1 - Mikhail D. Lukin AB - We present a universal physical picture for describing storage and retrieval of photon wave packets in a Lambda-type atomic medium. This physical picture encompasses a variety of different approaches to pulse storage ranging from adiabatic reduction of the photon group velocity and pulse-propagation control via off-resonant Raman fields to photon-echo based techniques. Furthermore, we derive an optimal control strategy for storage and retrieval of a photon wave packet of any given shape. All these approaches, when optimized, yield identical maximum efficiencies, which only depend on the optical depth of the medium. VL - 98 UR - http://arxiv.org/abs/quant-ph/0604037v3 CP - 12 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.98.123601 ER - TY - JOUR T1 - Effective error-suppression scheme for reversible quantum computer Y1 - 2006 A1 - Zhe-Xuan Gong AB - We construct a new error-suppression scheme that makes use of the adjoint of reversible quantum algorithms. For decoherence induced errors such as depolarization, it is presented that provided the depolarization error probability is less than 1, our scheme can exponentially reduce the final output error rate to zero using a number of cycles, and the output state can be coherently sent to another stage of quantum computation process. Besides, experimental set-ups via optical approach have been proposed using Grover's search algorithm as an example. Some further discussion on the benefits and limitations of the scheme is given in the end. UR - http://arxiv.org/abs/quant-ph/0608152v4 ER - TY - JOUR T1 - Mean-field treatment of the damping of the oscillations of a 1D Bose gas in an optical lattice JF - Physical Review A Y1 - 2006 A1 - Julio Gea-Banacloche A1 - Ana Maria Rey A1 - Guido Pupillo A1 - Carl J. Williams A1 - Charles W. Clark AB - We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. We expect this irregular motion to result from the well-known dynamical instability exhibited by the mean-field theory for these systems. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally-observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices. VL - 73 UR - http://arxiv.org/abs/cond-mat/0410677v4 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.73.013605 ER - TY - JOUR T1 - Multichannel quantum-defect theory for slow atomic collisions JF - Physical Review A Y1 - 2005 A1 - Bo Gao A1 - Eite Tiesinga A1 - Carl J. Williams A1 - Paul S. Julienne AB - We present a multichannel quantum-defect theory for slow atomic collisions that takes advantages of the analytic solutions for the long-range potential, and both the energy and the angular-momentum insensitivities of the short-range parameters. The theory provides an accurate and complete account of scattering processes, including shape and Feshbach resonances, in terms of a few parameters such as the singlet and the triplet scattering lengths. As an example, results for $^{23}$Na-$^{23}$Na scattering are presented and compared close-coupling calculations. VL - 72 UR - http://arxiv.org/abs/physics/0508060v1 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.72.042719 ER - TY - JOUR T1 - Adiabatic association of ultracold molecules via magnetic field tunable interactions JF - Journal of Physics B: Atomic, Molecular and Optical Physics Y1 - 2004 A1 - Krzysztof Goral A1 - Thorsten Koehler A1 - Simon A. Gardiner A1 - Eite Tiesinga A1 - Paul S. Julienne AB - We consider in detail the situation of applying a time dependent external magnetic field to a 87Rb atomic Bose-Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of T. Koehler and K. Burnett [Phys. Rev. A 65, 033601 (2002)] to study the efficiency of the association of molecules in a 87Rb Bose-Einstein condensate during a linear passage of the magnetic field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau-Zener, configuration interaction, and two level mean field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose-Einstein condensed gas, provided that the magnetic field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic field strength, and identify the Landau-Zener coefficient determined by F.H. Mies et al. [Phys. Rev. A 61, 022721 (2000)] as the main parameter that controls the efficiency. VL - 37 U4 - 3457 - 3500 UR - http://arxiv.org/abs/cond-mat/0312178v5 CP - 17 J1 - J. Phys. B: At. Mol. Opt. Phys. U5 - 10.1088/0953-4075/37/17/006 ER - TY - JOUR T1 - Quantum information processing using localized ensembles of nuclear spins Y1 - 2004 A1 - J. M. Taylor A1 - G. Giedke A1 - H. Christ A1 - B. Paredes A1 - J. I. Cirac A1 - P. Zoller A1 - M. D. Lukin A1 - A. Imamoglu AB - We describe a technique for quantum information processing based on localized en sembles of nuclear spins. A qubit is identified as the presence or absence of a collective excitation of a mesoscopic ensemble of nuclear spins surrounding a single quantum dot. All single and two-qubit operations can be effected using hyperfine interactions and single-electron spin rotations, hence the proposed scheme avoids gate errors arising from entanglement between spin and orbital degrees of freedom. Ultra-long coherence times of nuclear spins suggest that this scheme could be particularly well suited for applications where long lived memory is essential. UR - http://arxiv.org/abs/cond-mat/0407640v2 ER - TY - JOUR T1 - Quantum key distribution with 1.25 Gbps clock synchronization JF - Optics Express Y1 - 2004 A1 - J. C. Bienfang A1 - A. J. Gross A1 - A. Mink A1 - B. J. Hershman A1 - A. Nakassis A1 - X. Tang A1 - R. Lu A1 - D. H. Su A1 - Charles W Clark A1 - Carl J. Williams A1 - E. W. Hagley A1 - Jesse Wen AB - We have demonstrated the exchange of sifted quantum cryptographic key over a 730 meter free-space link at rates of up to 1.0 Mbps, two orders of magnitude faster than previously reported results. A classical channel at 1550 nm operates in parallel with a quantum channel at 845 nm. Clock recovery techniques on the classical channel at 1.25 Gbps enable quantum transmission at up to the clock rate. System performance is currently limited by the timing resolution of our silicon avalanche photodiode detectors. With improved detector resolution, our technique will yield another order of magnitude increase in performance, with existing technology. VL - 12 U4 - 2011 UR - http://arxiv.org/abs/quant-ph/0405097v1 CP - 9 J1 - Opt. Express U5 - 10.1364/OPEX.12.002011 ER - TY - JOUR T1 - Spatial search and the Dirac equation JF - Physical Review A Y1 - 2004 A1 - Andrew M. Childs A1 - Jeffrey Goldstone AB - We consider the problem of searching a d-dimensional lattice of N sites for a single marked location. We present a Hamiltonian that solves this problem in time of order sqrt(N) for d>2 and of order sqrt(N) log(N) in the critical dimension d=2. This improves upon the performance of our previous quantum walk search algorithm (which has a critical dimension of d=4), and matches the performance of a corresponding discrete-time quantum walk algorithm. The improvement uses a lattice version of the Dirac Hamiltonian, and thus requires the introduction of spin (or coin) degrees of freedom. VL - 70 UR - http://arxiv.org/abs/quant-ph/0405120v1 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.70.042312 ER - TY - JOUR T1 - Spatial search by quantum walk JF - Physical Review A Y1 - 2004 A1 - Andrew M. Childs A1 - Jeffrey Goldstone AB - Grover's quantum search algorithm provides a way to speed up combinatorial search, but is not directly applicable to searching a physical database. Nevertheless, Aaronson and Ambainis showed that a database of N items laid out in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search algorithm based on a continuous time quantum walk on a graph. The case of the complete graph gives the continuous time search algorithm of Farhi and Gutmann, and other previously known results can be used to show that sqrt(N) speedup can also be achieved on the hypercube. We show that full sqrt(N) speedup can be achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the algorithm does not provide substantial speedup. VL - 70 UR - http://arxiv.org/abs/quant-ph/0306054v2 CP - 2 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.70.022314 ER - TY - JOUR T1 - Exponential algorithmic speedup by quantum walk Y1 - 2002 A1 - Andrew M. Childs A1 - Richard Cleve A1 - Enrico Deotto A1 - Edward Farhi A1 - Sam Gutmann A1 - Daniel A. Spielman AB - We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our oracular setting. We then show how this quantum walk can be used to solve our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve this problem with high probability in subexponential time. UR - http://arxiv.org/abs/quant-ph/0209131v2 J1 - Proc. 35th ACM Symposium on Theory of Computing (STOC 2003) U5 - 10.1145/780542.780552 ER - TY - JOUR T1 - Quantum search by measurement JF - Physical Review A Y1 - 2002 A1 - Andrew M. Childs A1 - Enrico Deotto A1 - Edward Farhi A1 - Jeffrey Goldstone A1 - Sam Gutmann A1 - Andrew J. Landahl AB - We propose a quantum algorithm for solving combinatorial search problems that uses only a sequence of measurements. The algorithm is similar in spirit to quantum computation by adiabatic evolution, in that the goal is to remain in the ground state of a time-varying Hamiltonian. Indeed, we show that the running times of the two algorithms are closely related. We also show how to achieve the quadratic speedup for Grover's unstructured search problem with only two measurements. Finally, we discuss some similarities and differences between the adiabatic and measurement algorithms. VL - 66 UR - http://arxiv.org/abs/quant-ph/0204013v1 CP - 3 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.66.032314 ER - TY - JOUR T1 - An example of the difference between quantum and classical random walks JF - Quantum Information Processing Y1 - 2001 A1 - Andrew M. Childs A1 - Edward Farhi A1 - Sam Gutmann AB - In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph, propagation between a particular pair of nodes is exponentially faster in the quantum case. VL - 1 U4 - 35 - 43 UR - http://arxiv.org/abs/quant-ph/0103020v1 CP - 1/2 J1 - Quantum Information Processing 1 U5 - 10.1023/A:1019609420309 ER - TY - JOUR T1 - Finding cliques by quantum adiabatic evolution Y1 - 2000 A1 - Andrew M. Childs A1 - Edward Farhi A1 - Jeffrey Goldstone A1 - Sam Gutmann AB - Quantum adiabatic evolution provides a general technique for the solution of combinatorial search problems on quantum computers. We present the results of a numerical study of a particular application of quantum adiabatic evolution, the problem of finding the largest clique in a random graph. An n-vertex random graph has each edge included with probability 1/2, and a clique is a completely connected subgraph. There is no known classical algorithm that finds the largest clique in a random graph with high probability and runs in a time polynomial in n. For the small graphs we are able to investigate (n <= 18), the quantum algorithm appears to require only a quadratic run time. UR - http://arxiv.org/abs/quant-ph/0012104v1 J1 - Quantum Information and Computation 2 ER - TY - JOUR T1 - On Galilean connections and the first jet bundle Y1 - 1999 A1 - James D. E. Grant A1 - Brad Lackey AB - We express the first jet bundle of curves in Euclidean space as homogeneous spaces associated to a Galilean-type group. Certain Cartan connections on a manifold with values in the Lie algebra of the Galilean group are characterized as geometries associated to systems of second order ordinary differential equations. We show these Cartan connections admit a form of normal coordinates, and that in these normal coordinates the geodesic equations of the connection are second order ordinary differential equations. We then classify such connections by some of their torsions, extending a classical theorem of Chern involving the geometry associated to a system of second order differential equations. UR - http://arxiv.org/abs/math/9909148v1 J1 - Central European Journal of Mathematics 10.5 (2012): 1889-1895 ER - TY - JOUR T1 - Revised Proof of the Uniqueness Theorem for 'No Collapse' Interpretations of Quantum Mechanics Y1 - 1999 A1 - Jeffrey Bub A1 - Rob Clifton A1 - Sheldon Goldstein AB - We show that the Bub-Clifton uniqueness theorem for 'no collapse' interpretations of quantum mechanics (Studies in the History and Philosophy of Modern Physics 27, 181-219 (1996)) can be proved without the 'weak separability' assumption. UR - http://arxiv.org/abs/quant-ph/9910097v1 J1 - Studies in History and Philosophy of Modern Physics 31 (2000) 95 ER -