TY - JOUR T1 - Complexity-constrained quantum thermodynamics Y1 - 2024 A1 - Anthony Munson A1 - Naga Bhavya Teja Kothakonda A1 - Jonas Haferkamp A1 - Nicole Yunger Halpern A1 - Jens Eisert A1 - Philippe Faist AB -

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

UR - https://arxiv.org/abs/2403.04828 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 - 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 - Efficient learning of ground & thermal states within phases of matter Y1 - 2023 A1 - Emilio Onorati A1 - Cambyse Rouzé A1 - Daniel Stilck França A1 - James D. Watson AB -

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

UR - https://arxiv.org/abs/2301.12946 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 - 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 - Microwave signal processing using an analog quantum reservoir computer Y1 - 2023 A1 - Alen Senanian A1 - Sridhar Prabhu A1 - Vladimir Kremenetski A1 - Saswata Roy A1 - Yingkang Cao A1 - Jeremy Kline A1 - Tatsuhiro Onodera A1 - Logan G. Wright A1 - Xiaodi Wu A1 - Valla Fatemi A1 - Peter L. McMahon AB -

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

UR - https://arxiv.org/abs/2312.16166 ER - TY - JOUR T1 - Non-invertible symmetry-protected topological order in a group-based cluster state Y1 - 2023 A1 - Christopher Fechisin A1 - Nathanan Tantivasadakarn A1 - Victor V. Albert AB -

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

UR - https://arxiv.org/abs/2312.09272 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 - Parallel self-testing of EPR pairs under computational assumptions Y1 - 2023 A1 - Honghao Fu A1 - Daochen Wang A1 - Qi Zhao AB -

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

UR - https://arxiv.org/abs/2201.13430 ER - TY - JOUR T1 - Parallel self-testing of EPR pairs under computational assumptions Y1 - 2023 A1 - Honghao Fu A1 - Daochen Wang A1 - Qi Zhao AB -

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

UR - https://arxiv.org/abs/2201.13430 ER - TY - JOUR T1 - Provably Efficient Learning of Phases of Matter via Dissipative Evolutions Y1 - 2023 A1 - Emilio Onorati A1 - Cambyse Rouzé A1 - Daniel Stilck França A1 - James D. Watson AB -

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

UR - arXiv:2311.07506 Search... 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 - Random Pulse Sequences for Qubit Noise Spectroscopy Y1 - 2023 A1 - Kaixin Huang A1 - Demitry Farfurnik A1 - Alireza Seif A1 - Mohammad Hafezi A1 - Yi-Kai Liu AB -

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

UR - https://arxiv.org/abs/2303.00909 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 - Spin-selective strong light-matter coupling in a 2D hole gas-microcavity system Y1 - 2023 A1 - Daniel G. Suarez-Forero A1 - Deric Weston Session A1 - Mahmoud Jalali Mehrabad A1 - Patrick Knuppel A1 - Stefan Faelt A1 - Werner Wegscheider A1 - Mohammad Hafezi AB -

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

UR - https://arxiv.org/abs/2302.06023 ER - TY - JOUR T1 - Streaming quantum state purification Y1 - 2023 A1 - Andrew M. Childs A1 - Honghao Fu A1 - Debbie Leung A1 - Zhi Li A1 - Maris Ozols A1 - Vedang Vyas AB -

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

UR - https://arxiv.org/abs/2309.16387 ER - TY - JOUR T1 - Time-energy uncertainty relation for noisy quantum metrology JF - PRX Quantum Y1 - 2023 A1 - Faist, Philippe A1 - Woods, Mischa P. A1 - Victor V. Albert A1 - Renes, Joseph M. A1 - Eisert, Jens A1 - Preskill, John KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

VL - 4(4) UR - https://arxiv.org/abs/2207.13707 CP - 040336 U5 - https://journals.aps.org/prxquantum/pdf/10.1103/PRXQuantum.4.040336 ER - TY - JOUR T1 - Verifiable measurement-based quantum random sampling with trapped ions Y1 - 2023 A1 - Martin Ringbauer A1 - Marcel Hinsche A1 - Thomas Feldker A1 - Paul K. Faehrmann A1 - Juani Bermejo-Vega A1 - Claire Edmunds A1 - Lukas Postler A1 - Roman Stricker A1 - Christian D. Marciniak A1 - Michael Meth A1 - Ivan Pogorelov A1 - Rainer Blatt A1 - Philipp Schindler A1 - Jens Eisert A1 - Thomas Monz A1 - Dominik Hangleiter AB -

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

UR - https://arxiv.org/abs/2307.14424 U5 - https://doi.org/10.48550/arXiv.2307.14424 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 - 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 - Computational self-testing of multi-qubit states and measurements Y1 - 2022 A1 - Fu, Honghao A1 - Daochen Wang A1 - Zhao, Qi KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2201.13430 U5 - 10.48550/ARXIV.2201.13430 ER - TY - JOUR T1 - Constant-sized correlations are sufficient to robustly self-test maximally entangled states with unbounded dimension JF - Quantum Y1 - 2022 A1 - Honghao Fu AB -

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

VL - 6 U4 - 614 UR - https://arxiv.org/abs/1911.01494 U5 - https://doi.org/10.22331/q-2022-01-03-614 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 - 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 - Demonstration of three- and four-body interactions between trapped-ion spins Y1 - 2022 A1 - Katz, Or A1 - Feng, Lei A1 - Risinger, Andrew A1 - Monroe, Christopher A1 - Cetina, Marko KW - Atomic Physics (physics.atom-ph) KW - FOS: Physical sciences KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2209.05691 U5 - 10.48550/ARXIV.2209.05691 ER - TY - JOUR T1 - Differentiable Quantum Programming with Unbounded Loops Y1 - 2022 A1 - Fang, Wang A1 - Ying, Mingsheng A1 - Wu, Xiaodi KW - FOS: Computer and information sciences KW - FOS: Physical sciences KW - Machine Learning (cs.LG) KW - Programming Languages (cs.PL) KW - Quantum Physics (quant-ph) AB -

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

UR - https://arxiv.org/abs/2211.04507 U5 - 10.48550/ARXIV.2211.04507 ER - TY - JOUR T1 - Efficient quantum algorithm for nonlinear reaction-diffusion equations and energy estimation Y1 - 2022 A1 - Dong An A1 - Di Fang A1 - Stephen Jordan A1 - Jin-Peng Liu A1 - Guang Hao Low A1 - Jiasu Wang AB -

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

UR - https://arxiv.org/abs/2205.01141 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 - 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 - Isolation and manipulation of a single-donor detector in a silicon quantum dot JF - Phys. Rev. B Y1 - 2022 A1 - Lasek, A. A. A1 - Barnes, C. H. W. A1 - Ferrus, T. AB -

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

VL - 106 U4 - 125423 UR - https://link.aps.org/doi/10.1103/PhysRevB.106.125423 U5 - 10.1103/PhysRevB.106.125423 ER - TY - JOUR T1 - Linear growth of quantum circuit complexity JF - Nat. Phys. Y1 - 2022 A1 - Jonas Haferkamp A1 - Philippe Faist A1 - Naga B. T. Kothakonda A1 - Jens Eisert A1 - Nicole Yunger Halpern AB -

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

U5 - https://doi.org/10.1038/s41567-022-01539-6 ER - TY - JOUR T1 - Quantum computational advantage via high-dimensional Gaussian boson sampling JF - Science Advances Y1 - 2022 A1 - Abhinav Deshpande A1 - Arthur Mehta A1 - Trevor Vincent A1 - Nicolas Quesada A1 - Marcel Hinsche A1 - Marios Ioannou A1 - Lars Madsen A1 - Jonathan Lavoie A1 - Haoyu Qi A1 - Jens Eisert A1 - Dominik Hangleiter A1 - Bill Fefferman A1 - Ish Dhand AB -

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

VL - 8 U4 - eabi7894 UR - https://www.science.org/doi/abs/10.1126/sciadv.abi7894 U5 - 10.1126/sciadv.abi7894 ER - TY - JOUR T1 - Resource theory of quantum uncomplexity JF - Physical Review A Y1 - 2022 A1 - Nicole Yunger Halpern A1 - Naga B. T. Kothakonda A1 - Jonas Haferkamp A1 - Anthony Munson A1 - Jens Eisert A1 - Philippe Faist AB -

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

VL - 106 UR - https://arxiv.org/abs/2110.11371 U5 - 10.1103/physreva.106.062417 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 - 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 - Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation JF - Quantum Y1 - 2022 A1 - Dong An A1 - Di Fang A1 - Lin Lin AB -

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

VL - 6 U4 - 690 UR - https://arxiv.org/abs/2111.03103v2 U5 - 10.22331/q-2022-04-15-690 ER - TY - JOUR T1 - Topological Edge Mode Tapering Y1 - 2022 A1 - Christopher J. Flower A1 - Sabyasachi Barik A1 - Sunil Mittal A1 - Mohammad Hafezi AB -

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

UR - https://arxiv.org/abs/2206.07056 ER - TY - JOUR T1 - Device-independent Randomness Expansion with Entangled Photons JF - Nat. Phys. Y1 - 2021 A1 - Lynden K. Shalm A1 - Yanbao Zhang A1 - Joshua C. Bienfang A1 - Collin Schlager A1 - Martin J. Stevens A1 - Michael D. Mazurek A1 - Carlos Abellán A1 - Waldimar Amaya A1 - Morgan W. Mitchell A1 - Mohammad A. Alhejji A1 - Honghao Fu A1 - Joel Ornstein A1 - Richard P. Mirin A1 - Sae Woo Nam A1 - Emanuel Knill AB -

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

UR - https://arxiv.org/abs/1912.11158 U5 - https://doi.org/10.1038/s41567-020-01153-4 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 - 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 - 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 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 - The membership problem for constant-sized quantum correlations is undecidable Y1 - 2021 A1 - Honghao Fu A1 - Carl Miller A1 - William Slofstra AB -

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

UR - https://arxiv.org/abs/2101.11087 ER - TY - JOUR T1 - Noise-induced barren plateaus in variational quantum algorithms JF - Nature Communications Y1 - 2021 A1 - Samson Wang A1 - Enrico Fontana A1 - M. Cerezo A1 - Kunal Sharma A1 - Akira Sone A1 - Lukasz Cincio A1 - Patrick J. Coles AB -

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

VL - 12 U4 - 6961 U5 - https://doi.org/10.1038/s41467-021-27045-6 ER - TY - JOUR T1 - Observation of a prethermal discrete time crystal Y1 - 2021 A1 - Antonis Kyprianidis A1 - Francisco Machado A1 - William Morong A1 - Patrick Becker A1 - Kate S. Collins A1 - Dominic V. Else A1 - Lei Feng A1 - Paul W. Hess A1 - Chetan Nayak A1 - Guido Pagano A1 - Norman Y. Yao A1 - Christopher Monroe AB -

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

UR - https://arxiv.org/abs/2102.01695 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 - Quantum Computational Supremacy via High-Dimensional Gaussian Boson Sampling Y1 - 2021 A1 - Abhinav Deshpande A1 - Arthur Mehta A1 - Trevor Vincent A1 - Nicolas Quesada A1 - Marcel Hinsche A1 - Marios Ioannou A1 - Lars Madsen A1 - Jonathan Lavoie A1 - Haoyu Qi A1 - Jens Eisert A1 - Dominik Hangleiter A1 - Bill Fefferman A1 - Ish Dhand AB -

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

UR - https://arxiv.org/abs/2102.12474 ER - TY - JOUR T1 - Resource theory of quantum uncomplexity Y1 - 2021 A1 - Nicole Yunger Halpern A1 - Naga B. T. Kothakonda A1 - Jonas Haferkamp A1 - Anthony Munson A1 - Jens Eisert A1 - Philippe Faist AB -

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

UR - https://arxiv.org/abs/2110.11371 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 - 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 - Approximate recovery and relative entropy I. general von Neumann subalgebras Y1 - 2020 A1 - Thomas Faulkner A1 - Stefan Hollands A1 - Brian Swingle A1 - Yixu Wang AB -

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

UR - https://arxiv.org/abs/2006.08002 ER - TY - JOUR T1 - Approximate recovery and relative entropy I. general von Neumann subalgebras Y1 - 2020 A1 - Thomas Faulkner A1 - Stefan Hollands A1 - Brian Swingle A1 - Yixu Wang AB -

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

UR - https://arxiv.org/abs/2006.08002 ER - TY - JOUR T1 - Collisions of room-temperature helium with ultracold lithium and the van der Waals bound state of HeLi JF - Phys. Rev. A Y1 - 2020 A1 - Constantinos Makrides A1 - Daniel S Barker A1 - James A Fedchak A1 - Julia Scherschligt A1 - Stephen Eckel A1 - Eite Tiesinga AB -

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

VL - 101 CP - 012702 U5 - https://doi.org/10.1103/PhysRevA.101.012702 ER - TY - JOUR T1 - Continuous symmetries and approximate quantum error correction JF - Phys. Rev. X Y1 - 2020 A1 - Philippe Faist A1 - Sepehr Nezami A1 - Victor V. Albert A1 - Grant Salton A1 - Fernando Pastawski A1 - Patrick Hayden A1 - John Preskill AB -

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

VL - 10 UR - https://arxiv.org/abs/1902.07714 CP - 041018 U5 - https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.041018 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 - Efficient randomness certification by quantum probability estimation JF - Phys. Rev. Research Y1 - 2020 A1 - Yanbao Zhang A1 - Honghao Fu A1 - Emanuel Knill AB -

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

VL - 2 CP - 013016 U5 - https://doi.org/10.1103/PhysRevResearch.2.013016 ER - TY - JOUR T1 - Experimental Low-Latency Device-Independent Quantum Randomness JF - Phys. Rev. Lett. Y1 - 2020 A1 - Yanbao Zhang A1 - Lynden K. Shalm A1 - Joshua C. Bienfang A1 - Martin J. Stevens A1 - Michael D. Mazurek A1 - Sae Woo Nam A1 - Carlos Abellán A1 - Waldimar Amaya A1 - Morgan W. Mitchell A1 - Honghao Fu A1 - Carl Miller A1 - Alan Mink A1 - Emanuel Knill AB -

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

VL - 124 UR - https://arxiv.org/abs/1812.07786 CP - 010505 U5 - https://doi.org/10.1103/PhysRevLett.124.010505 ER - TY - JOUR T1 - More of the Bulk from Extremal Area Variations JF - Classical and Quantum Gravity Y1 - 2020 A1 - Ning Bao A1 - ChunJun Cao A1 - Sebastian Fischetti A1 - Jason Pollack A1 - Yibo Zhong AB -

It was shown recently, building on work of Alexakis, Balehowksy, and Nachman that the geometry of (some portion of) a manifold with boundary is uniquely fixed by the areas of a foliation of two-dimensional disk-shaped surfaces anchored to the boundary. In the context of AdS/CFT, this implies that (a portion of) a four-dimensional bulk geometry can be fixed uniquely from the entanglement entropies of disk-shaped boundary regions, subject to several constraints. In this Note, we loosen some of these constraints, in particular allowing for the bulk foliation of extremal surfaces to be local and removing the constraint of disk topology; these generalizations ensure uniqueness of more of the deep bulk geometry by allowing for e.g. surfaces anchored on disconnected asymptotic boundaries, or HRT surfaces past a phase transition. We also explore in more depth the generality of the local foliation requirement, showing that even in a highly dynamical geometry like AdS-Vaidya it is satisfied.

VL - 38 U4 - 047001 UR - https://arxiv.org/abs/2009.07850 CP - 4 U5 - https://iopscience.iop.org/article/10.1088/1361-6382/abcfd0/pdf 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 - A note on blind contact tracing at scale with applications to the COVID-19 pandemic Y1 - 2020 A1 - Jack K. Fitzsimons A1 - Atul Mantri A1 - Robert Pisarczyk A1 - Tom Rainforth A1 - Zhikuan Zhao AB -

The current COVID-19 pandemic highlights the utility of contact tracing, when combined with case isolation and social distancing, as an important tool for mitigating the spread of a disease [1]. Contact tracing provides a mechanism of identifying individuals with a high likelihood of previous exposure to a contagious disease, allowing additional precautions to be put in place to prevent continued transmission. Here we consider a cryptographic approach to contact tracing based on secure two-party computation (2PC). We begin by considering the problem of comparing a set of location histories held by two parties to determine whether they have come within some threshold distance while at the same time maintaining the privacy of the location histories. We propose a solution to this problem using pre-shared keys, adapted from an equality testing protocol due to Ishai et al [2]. We discuss how this protocol can be used to maintain privacy within practical contact tracing scenarios, including both app-based approaches and approaches which leverage location history held by telecoms and internet service providers. We examine the efficiency of this approach and show that existing infrastructure is sufficient to support anonymised contact tracing at a national level.

UR - https://arxiv.org/abs/2004.05116 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 - Probing XY phase transitions in a Josephson junction array with tunable frustration Y1 - 2020 A1 - R. Cosmic A1 - K. Kawabata A1 - Y. Ashida A1 - H. Ikegami A1 - S. Furukawa A1 - P. Patil A1 - J. M. Taylor A1 - Y. Nakamura AB -

The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations. These transitions have been extensively studied in the context of two-dimensional XY models -- coupled compasses -- and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U(1)] and discrete chiral (Z2) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U(1) part.

UR - https://arxiv.org/abs/2001.07877 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 - 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 - 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 - 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 - Momentum-space entanglement after a quench in one-dimensional disordered fermionic systems Y1 - 2019 A1 - Rex Lundgren A1 - Fangli Liu A1 - Pontus Laurell A1 - Gregory A. Fiete AB -

We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type of dynamics that occurs depends on whether or not the Fermi level of the initial state is near the energy of the delocalized states present in these models. If the Fermi level of the initial state is near the energy of the delocalized states, we observe an interesting slow logarithmic-like growth of the momentum-space entanglement entropy followed by an eventual saturation. Otherwise, the momentum-space entanglement entropy is found to rapidly saturate. We also find that the momentum-space entanglement spectrum reveals the presence of delocalized states in these models for long times after the quench and the many-body entanglement gap decays logarithmically in time when the Fermi level is near the energy of the delocalized states.

UR - https://arxiv.org/abs/1909.05140 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 - 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 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 - Quantum Wasserstein Generative Adversarial Networks JF - Advances in Neural Information Processing Systems (NIPS) Y1 - 2019 A1 - Shouvanik Chakrabarti A1 - Yiming Huang A1 - Tongyang Li A1 - Soheil Feizi A1 - Xiaodi Wu AB -

The study of quantum generative models is well-motivated, not only because of its importance in quantum machine learning and quantum chemistry but also because of the perspective of its implementation on near-term quantum machines. Inspired by previous studies on the adversarial training of classical and quantum generative models, we propose the first design of quantum Wasserstein Generative Adversarial Networks (WGANs), which has been shown to improve the robustness and the scalability of the adversarial training of quantum generative models even on noisy quantum hardware. Specifically, we propose a definition of the Wasserstein semimetric between quantum data, which inherits a few key theoretical merits of its classical counterpart. We also demonstrate how to turn the quantum Wasserstein semimetric into a concrete design of quantum WGANs that can be efficiently implemented on quantum machines. Our numerical study, via classical simulation of quantum systems, shows the more robust and scalable numerical performance of our quantum WGANs over other quantum GAN proposals. As a surprising application, our quantum WGAN has been used to generate a 3-qubit quantum circuit of ~50 gates that well approximates a 3-qubit 1-d Hamiltonian simulation circuit that requires over 10k gates using standard techniques.

VL - 32 UR - https://arxiv.org/abs/1911.00111 U5 - https://papers.nips.cc/paper/8903-quantum-wasserstein-generative-adversarial-networks.pdf ER - TY - JOUR T1 - Towards Bulk Metric Reconstruction from Extremal Area Variations Y1 - 2019 A1 - Ning Bao A1 - ChunJun Cao A1 - Sebastian Fischetti A1 - Cynthia Keeler AB -

The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show that in four bulk dimensions, the entanglement entropies of boundary regions of disk topology uniquely fix the bulk metric in any region foliated by the corresponding HRT surfaces. More generally, for a bulk of any dimension , knowledge of the (variations of the) areas of two-dimensional boundary-anchored extremal surfaces of disk topology uniquely fixes the bulk metric wherever these surfaces reach. This result is covariant and not reliant on any symmetry assumptions; its applicability thus includes regions of strong dynamical gravity such as the early-time interior of black holes formed from collapse. While we only show uniqueness of the metric, the approach we present provides a clear path towards an\textit {explicit} spacetime metric reconstruction.

UR - https://arxiv.org/abs/1904.04834 ER - TY - JOUR T1 - Demonstration of Bayesian quantum game on an ion trap quantum computer Y1 - 2018 A1 - Neal Solmeyer A1 - Norbert M. Linke A1 - Caroline Figgatt A1 - Kevin A. Landsman A1 - Radhakrishnan Balu A1 - George Siopsis A1 - Christopher Monroe AB -

We demonstrate a Bayesian quantum game on an ion trap quantum computer with five qubits. The players share an entangled pair of qubits and perform rotations on their qubit as the strategy choice. Two five-qubit circuits are sufficient to run all 16 possible strategy choice sets in a game with four possible strategies. The data are then parsed into player types randomly in order to combine them classically into a Bayesian framework. We exhaustively compute the possible strategies of the game so that the experimental data can be used to solve for the Nash equilibria of the game directly. Then we compare the payoff at the Nash equilibria and location of phase-change-like transitions obtained from the experimental data to the theory, and study how it changes as a function of the amount of entanglement.

UR - https://arxiv.org/abs/1802.08116 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 - Local randomness: Examples and application JF - Phys. Rev. A Y1 - 2018 A1 - Honghao Fu A1 - Carl Miller AB -

When two players achieve a superclassical score at a nonlocal game, their outputs must contain intrinsic randomness. This fact has many useful implications for quantum cryptography. Recently it has been observed [C. Miller and Y. Shi, Quantum Inf. Computat. 17, 0595 (2017)] that such scores also imply the existence of local randomness—that is, randomness known to one player but not to the other. This has potential implications for cryptographic tasks between two cooperating but mistrustful players. In the current paper we bring this notion toward practical realization, by offering near-optimal bounds on local randomness for the CHSH game, and also proving the security of a cryptographic application of local randomness (single-bit certified deletion).

U4 - 032324 UR - https://arxiv.org/abs/1708.04338 CP - 97 U5 - https://doi.org/10.1103/PhysRevA.97.032324 ER - TY - JOUR T1 - Machine learning assisted readout of trapped-ion qubits JF - J. Phys. B: At. Mol. Opt. Phys. Y1 - 2018 A1 - Alireza Seif A1 - Kevin A. Landsman A1 - Norbert M. Linke A1 - Caroline Figgatt A1 - C. Monroe A1 - Mohammad Hafezi AB -

We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30\% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.

VL - 51 UR - https://arxiv.org/abs/1804.07718 U5 - https://doi.org/10.1088/1361-6455/aad62b 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 - Parallel Entangling Operations on a Universal Ion Trap Quantum Computer Y1 - 2018 A1 - C. Figgatt A1 - A. Ostrander A1 - N. M. Linke A1 - K. A. Landsman A1 - D. Zhu A1 - D. Maslov A1 - C. Monroe AB -

The circuit model of a quantum computer consists of sequences of gate operations between quantum bits (qubits), drawn from a universal family of discrete operations. The ability to execute parallel entangling quantum gates offers clear efficiency gains in numerous quantum circuits as well as for entire algorithms such as Shor's factoring algorithm and quantum simulations. In cases such as full adders and multiple-control Toffoli gates, parallelism can provide an exponential improvement in overall execution time. More importantly, quantum gate parallelism is essential for the practical fault-tolerant error correction of qubits that suffer from idle errors. The implementation of parallel quantum gates is complicated by potential crosstalk, especially between qubits fully connected by a common-mode bus, such as in Coulomb-coupled trapped atomic ions or cavity-coupled superconducting transmons. Here, we present the first experimental results for parallel 2-qubit entangling gates in an array of fully-connected trapped ion qubits. We demonstrate an application of this capability by performing a 1-bit full addition operation on a quantum computer using a depth-4 quantum circuit. These results exploit the power of highly connected qubit systems through classical control techniques, and provide an advance toward speeding up quantum circuits and achieving fault tolerance with trapped ion quantum computers.

UR - https://arxiv.org/abs/1810.11948 ER - TY - JOUR T1 - Quantum Channel Simulation and the Channel's Smooth Max-Information Y1 - 2018 A1 - Kun Fang A1 - Xin Wang A1 - Marco Tomamichel A1 - Mario Berta AB -

We study the general framework of quantum channel simulation, that is, the ability of a quantum channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the channel's smooth max-information, which can be seen as a one-shot generalization of the mutual information of a quantum channel. We provide an exact operational interpretation of the channel's smooth max-information as the one-shot quantum simulation cost under no-signalling assisted codes. Third, we derive the asymptotic equipartition property of the channel's smooth max-information, i.e., it converges to the quantum mutual information of the channel in the independent and identically distributed asymptotic limit. This implies the quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various quantum channels.

UR - https://arxiv.org/abs/1807.05354 ER - TY - JOUR T1 - Quantum Supremacy and the Complexity of Random Circuit Sampling Y1 - 2018 A1 - Adam Bouland A1 - Bill Fefferman A1 - Chinmay Nirkhe A1 - Umesh Vazirani AB -

A critical milestone on the path to useful quantum computers is quantum supremacy - a demonstration of a quantum computation that is prohibitively hard for classical computers. A leading near-term candidate, put forth by the Google/UCSB team, is sampling from the probability distributions of randomly chosen quantum circuits, which we call Random Circuit Sampling (RCS). In this paper we study both the hardness and verification of RCS. While RCS was defined with experimental realization in mind, we show complexity theoretic evidence of hardness that is on par with the strongest theoretical proposals for supremacy. Specifically, we show that RCS satisfies an average-case hardness condition - computing output probabilities of typical quantum circuits is as hard as computing them in the worst-case, and therefore #P-hard. Our reduction exploits the polynomial structure in the output amplitudes of random quantum circuits, enabled by the Feynman path integral. In addition, it follows from known results that RCS satisfies an anti-concentration property, making it the first supremacy proposal with both average-case hardness and anti-concentration. 

UR - https://arxiv.org/abs/1803.04402 ER - TY - JOUR T1 - Robust two-qubit gates in a linear ion crystal using a frequency-modulated driving force JF - Physical Review Letters Y1 - 2018 A1 - Pak Hong Leung A1 - Kevin A. Landsman A1 - Caroline Figgatt A1 - Norbert M. Linke A1 - Christopher Monroe A1 - Kenneth R. Brown AB -

In an ion trap quantum computer, collective motional modes are used to entangle two or more qubits in order to execute multi-qubit logical gates. Any residual entanglement between the internal and motional states of the ions will result in decoherence errors, especially when there are many spectator ions in the crystal. We propose using a frequency-modulated (FM) driving force to minimize such errors and implement it experimentally. In simulation, we obtained an optimized FM gate that can suppress decoherence to less than 10−4 and is robust against a frequency drift of more than ±1 kHz. The two-qubit gate was tested in a five-qubit trapped ion crystal, with 98.3(4)% fidelity for a Mølmer-Sørensen entangling gate and 98.6(7)% for a controlled-not (CNOT) gate. We also show an optimized FM two-qubit gate for 17 ions, proving the scalability of our method.

VL - 120 U4 - 020501 UR - https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.020501 CP - 2 U5 - 10.1103/PhysRevLett.120.020501 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 - Verified Quantum Information Scrambling Y1 - 2018 A1 - Kevin A. Landsman A1 - Caroline Figgatt A1 - Thomas Schuster A1 - Norbert M. Linke A1 - Beni Yoshida A1 - Norman Y. Yao A1 - Christopher Monroe AB -

Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and more recently has emerged as a powerful tool for characterizing chaos in black holes. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, since scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here, we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous litmus test for scrambling while projecting potential circuit errors into an ancillary observable. We engineer quantum scrambling processes through a tunable 3-qubit unitary operation as part of a 7-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically ∼80%, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

UR - https://arxiv.org/abs/1806.02807 ER - TY - JOUR T1 - Complete 3-Qubit Grover Search on a Programmable Quantum Computer JF - Nature Communications, accepted Y1 - 2017 A1 - C. Figgatt A1 - Dmitri Maslov A1 - K. A. Landsman A1 - N. M. Linke A1 - S. Debnath A1 - Christopher Monroe AB -

Searching large databases is an important problem with broad applications. The Grover search algorithm provides a powerful method for quantum computers to perform searches with a quadratic speedup in the number of required database queries over classical computers. It is an optimal search algorithm for a quantum computer, and has further applications as a subroutine for other quantum algorithms. Searches with two qubits have been demonstrated on a variety of platforms and proposed for others, but larger search spaces have only been demonstrated on a non-scalable NMR system. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. The algorithm is performed for all 8 possible single-result oracles and all 28 possible two-result oracles. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state-marking scheme required to perform a classical search. All quantum solutions are shown to outperform their classical counterparts. We also report the first implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.

UR - https://arxiv.org/abs/1703.10535 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 - Development of a new UHV/XHV pressure standard (cold atom vacuum standard) JF - Metrologia Y1 - 2017 A1 - Julia Scherschligt A1 - James A Fedchak A1 - Daniel S Barker A1 - Stephen Eckel A1 - Nikolai Klimov A1 - Constantinos Makrides A1 - Eite Tiesinga AB -

The National Institute of Standards and Technology has recently begun a program to develop a primary pressure standard that is based on ultra-cold atoms, covering a pressure range of 1 x 10-6 to 1 x 10-10 Pa and possibly lower. These pressures correspond to the entire ultra-high vacuum range and extend into the extreme-high vacuum. This cold-atom vacuum standard (CAVS) is both a primary standard and absolute sensor of vacuum. The CAVS is based on the loss of cold, sensor atoms (such as the alkali-metal lithium) from a magnetic trap due to collisions with the background gas (primarily H2) in the vacuum. The pressure is determined from a thermally-averaged collision cross section, which is a fundamental atomic property, and the measured loss rate. The CAVS is primary because it will use collision cross sections determined from ab initio calculations for the Li + H2 system. Primary traceability is transferred to other systems of interest using sensitivity coefficients.

VL - 54 UR - https://arxiv.org/abs/1801.10120 CP - 6 U5 - https://doi.org/10.1088/1681-7575/aa8a7b 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 - 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 - Generic T1 - Experimental Comparison of Two Quantum Computing Architectures T2 - Proceedings of the National Academy of Sciences Y1 - 2017 A1 - N.M. Linke A1 - Dmitri Maslov A1 - Martin Roetteler A1 - S. Debnath A1 - C. Figgatt A1 - K. A. Landsman A1 - K. Wright A1 - Christopher Monroe AB -

We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device [1] with limited connectivity, and the other is a fully connected trapped-ion system [2]. Even though the two systems have different native quantum interactions, both can be programmed in a way that is blind to the underlying hardware, thus allowing the first comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that employ more connectivity clearly benefit from a better connected system of qubits. While the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that co-designing particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.

JA - Proceedings of the National Academy of Sciences VL - 114 U4 - 3305-3310 UR - http://www.pnas.org/content/114/13/3305 U5 - 10.1073/pnas.1618020114 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 - 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 - On the readiness of quantum optimization machines for industrial applications Y1 - 2017 A1 - Alejandro Perdomo-Ortiz A1 - Alexander Feldman A1 - Asier Ozaeta A1 - Sergei V. Isakov A1 - Zheng Zhu A1 - Bryan O'Gorman A1 - Helmut G. Katzgraber A1 - Alexander Diedrich A1 - Hartmut Neven A1 - Johan de Kleer A1 - Brad Lackey A1 - Rupak Biswas AB -

There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for near-term quantum annealers.

UR - https://arxiv.org/abs/1708.09780 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 - 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 - A Complete Characterization of Unitary Quantum Space Y1 - 2016 A1 - Bill Fefferman A1 - Cedric Yen-Yu Lin AB - We give two complete characterizations of unitary quantum space-bounded classes. The first is based on the Matrix Inversion problem for well-conditioned matrices. We show that given the size-n efficient encoding of a 2O(k(n))×2O(k(n)) well-conditioned matrix H, approximating a particular entry of H−1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation. In particular, the problem of computing entries of H−1 for an explicit well-conditioned n×n matrix H is complete for unitary quantum logspace. We then show that the problem of approximating to high precision the least eigenvalue of a positive semidefinite matrix H, encoded as a circuit, gives a second characterization of unitary quantum space complexity. In the process we also establish an equivalence between unitary quantum space-bounded classes and certain QMA proof systems. As consequences, we establish that QMA with exponentially small completeness-soundness gap is equal to PSPACE, that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian. UR - http://arxiv.org/abs/1604.01384 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 - Demonstration of a small programmable quantum computer with atomic qubits JF - Nature Y1 - 2016 A1 - S. Debnath A1 - N. M. Linke A1 - C. Figgatt A1 - K. A. Landsman A1 - K. Wright A1 - C. Monroe AB -

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here, we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully-connected set of gate operations that are native to the hardware and have a mean fidelity of 98 %. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa (DJ) and Bernstein-Vazirani (BV) algorithms with average success rates of 95 % and 90 %, respectively. We also perform a coherent quantum Fourier transform (QFT) on five trappedion qubits for phase estimation and period finding with average fidelities of 62 % and 84 %, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

VL - 536 U4 - 63-66 UR - http://www.nature.com/nature/journal/v536/n7614/full/nature18648.html CP - 7614 U5 - 10.1038/nature18648 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 - 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 - Pure-state tomography with the expectation value of Pauli operators JF - Physical Review A Y1 - 2016 A1 - Xian Ma A1 - Tyler Jackson A1 - Hui Zhou A1 - Jianxin Chen A1 - Dawei Lu A1 - Michael D. Mazurek A1 - Kent A.G. Fisher A1 - Xinhua Peng A1 - David Kribs A1 - Kevin J. Resch A1 - Zhengfeng Ji A1 - Bei Zeng A1 - Raymond Laflamme AB -

We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary n-qubit pure state among all quantum states. We show that only 11 Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with 16 measurements, and only 31 Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with 64 measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.

VL - 93 U4 - 032140 UR - http://arxiv.org/abs/1601.05379 CP - 3 U5 - http://dx.doi.org/10.1103/PhysRevA.93.032140 ER - TY - JOUR T1 - Quantum Merlin Arthur with Exponentially Small Gap Y1 - 2016 A1 - Bill Fefferman A1 - Cedric Yen-Yu Lin AB - We study the complexity of QMA proof systems with inverse exponentially small promise gap. We show that this class can be exactly characterized by PSPACE, the class of problems solvable with a polynomial amount of memory. As applications we show that a "precise" version of the Local Hamiltonian problem is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states is not as powerful as the ability to prepare the ground state of general Local Hamiltonians. UR - http://arxiv.org/abs/1601.01975 ER - TY - JOUR T1 - On Quantum Obfuscation Y1 - 2016 A1 - Gorjan Alagic A1 - Bill Fefferman AB - Encryption of data is fundamental to secure communication in the modern world. Beyond encryption of data lies obfuscation, i.e., encryption of functionality. It is well-known that the most powerful means of obfuscating classical programs, so-called ``black-box obfuscation',' is provably impossible [Barak et al '12]. However, several recent results have yielded candidate schemes that satisfy a definition weaker than black-box, and yet still have numerous applications. In this work, we initialize the rigorous study of obfuscating programs via quantum-mechanical means. We define notions of quantum obfuscation which encompass several natural variants. The input to the obfuscator can describe classical or quantum functionality, and the output can be a circuit description or a quantum state. The obfuscator can also satisfy one of a number of obfuscation conditions: black-box, information-theoretic black-box, indistinguishability, and best possible; the last two conditions come in three variants: perfect, statistical, and computational. We discuss many applications, including CPA-secure quantum encryption, quantum fully-homomorphic encryption, and public-key quantum money. We then prove several impossibility results, extending a number of foundational papers on classical obfuscation to the quantum setting. We prove that quantum black-box obfuscation is impossible in a setting where adversaries can possess more than one output of the obfuscator. In particular, generic transformation of quantum circuits into black-box-obfuscated quantum circuits is impossible. We also show that statistical indistinguishability obfuscation is impossible, up to an unlikely complexity-theoretic collapse. Our proofs involve a new tool: chosen-ciphertext-secure encryption of quantum data, which was recently shown to be possible assuming quantum-secure one-way functions exist [Alagic et al '16]. UR - http://arxiv.org/abs/1602.01771 ER - TY - JOUR T1 - A Quantum Version of Schöning's Algorithm Applied to Quantum 2-SAT JF - Quantum Information and Computation Y1 - 2016 A1 - Edward Farhi A1 - Shelby Kimmel A1 - Kristan Temme AB -

We study a quantum algorithm that consists of a simple quantum Markov process, and we analyze its behavior on restricted versions of Quantum 2-SAT. We prove that the algorithm solves this decision problem with high probability for n qubits, L clauses, and promise gap c in time O(n^2 L^2 c^{-2}). If the Hamiltonian is additionally polynomially gapped, our algorithm efficiently produces a state that has high overlap with the satisfying subspace. The Markov process we study is a quantum analogue of Sch\"oning's probabilistic algorithm for k-SAT.

VL - 16 UR - http://arxiv.org/abs/1603.06985 CP - 13-14 ER - TY - JOUR T1 - Space-Efficient Error Reduction for Unitary Quantum Computations JF - 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) Y1 - 2016 A1 - Bill Fefferman A1 - Hirotada Kobayashi A1 - Cedric Yen-Yu Lin A1 - Tomoyuki Morimae A1 - Harumichi Nishimura AB -

This paper develops general space-efficient methods for error reduction for unitary quantum computation. Consider a polynomial-time quantum computation with completeness c and soundnesss, either with or without a witness (corresponding to QMA and BQP, respectively). To convert this computation into a new computation with error at most 2p, the most space-efficient method known requires extra workspace of O(plog1cs) qubits. This space requirement is too large for scenarios like logarithmic-space quantum computations. This paper presents error-reduction methods for unitary quantum computations (i.e., computations without intermediate measurements) that require extra workspace of just O(logpcs) qubits. This in particular gives the first methods of strong amplification for logarithmic-space unitary quantum computations with two-sided bounded error. This also leads to a number of consequences in complexity theory, such as the uselessness of quantum witnesses in bounded-error logarithmic-space unitary quantum computations, the PSPACE upper bound for QMA with exponentially-small completeness-soundness gap, and strong amplification for matchgate computations.

VL - 55 U4 - 14:1--14:14 SN - 978-3-95977-013-2 UR - http://drops.dagstuhl.de/opus/volltexte/2016/6297 U5 - http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.14 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 - 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 - 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 - Entangling two transportable neutral atoms via local spin exchange JF - Nature Y1 - 2015 A1 - A. M. Kaufman A1 - B. J. Lester A1 - Michael Foss-Feig A1 - M. L. Wall A1 - A. M. Rey A1 - C. A. Regal AB - To advance quantum information science a constant pursuit is the search for physical systems that meet the stringent requirements for creating and preserving quantum entanglement. In atomic physics, robust two-qubit entanglement is typically achieved by strong, long-range interactions in the form of Coulomb interactions between ions or dipolar interactions between Rydberg atoms. While these interactions allow fast gates, atoms subject to these interactions must overcome the associated coupling to the environment and cross-talk among qubits. Local interactions, such as those requiring significant wavefunction overlap, can alleviate these detrimental effects yet present a new challenge: To distribute entanglement, qubits must be transported, merged for interaction, and then isolated for storage and subsequent operations. Here we show how, via a mobile optical tweezer, it is possible to prepare and locally entangle two ultracold neutral atoms, and then separate them while preserving their entanglement. While ultracold neutral atom experiments have measured dynamics consistent with spin entanglement, we are now able to demonstrate two-particle coherence via application of a local gradient and parity measurements; this new entanglement-verification protocol could be applied to arbitrary spin-entangled states of spatially-separated atoms. The local entangling operation is achieved via ultracold spin-exchange interactions, and quantum tunneling is used to combine and separate atoms. Our toolset provides a framework for dynamically entangling remote qubits via local operations within a large-scale quantum register. VL - 527 U4 - 208-211 UR - http://arxiv.org/abs/1507.05586 U5 - 10.1038/nature16073 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 - 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 - Observation of optomechanical buckling phase transitions Y1 - 2015 A1 - Haitan Xu A1 - Utku Kemiktarak A1 - Jingyun Fan A1 - Stephen Ragole A1 - John Lawall A1 - J. M. Taylor AB -

Correlated phases of matter provide long-term stability for systems as diverse as solids, magnets, and potential exotic quantum materials. Mechanical systems, such as relays and buckling transition spring switches can yield similar stability by exploiting non-equilibrium phase transitions. Curiously, in the optical domain, observations of such phase transitions remain elusive. However, efforts to integrate optical and mechanical systems -- optomechanics -- suggest that a hybrid approach combining the quantum control of optical systems with the engineerability of mechanical systems may provide a new avenue for such explorations. Here we report the first observation of the buckling of an optomechanical system, in which transitions between stable mechanical states corresponding to both first- and second-order phase transitions are driven by varying laser power and detuning. Our results enable new applications in photonics and, given rapid progress in pushing optomechanical systems into the quantum regime, the potential for explorations of quantum phase transitions.

UR - http://arxiv.org/abs/1510.04971v1 ER - TY - JOUR T1 - The Power of Quantum Fourier Sampling Y1 - 2015 A1 - Bill Fefferman A1 - Chris Umans AB - A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer, unless the PH collapses. Aaronson and Arkhipov take this further by considering a distribution that can be sampled efficiently by linear optical quantum computation, that under two feasible conjectures, cannot even be approximately sampled classically within bounded total variation distance, unless the PH collapses. In this work we use Quantum Fourier Sampling to construct a class of distributions that can be sampled by a quantum computer. We then argue that these distributions cannot be approximately sampled classically, unless the PH collapses, under variants of the Aaronson and Arkhipov conjectures. In particular, we show a general class of quantumly sampleable distributions each of which is based on an "Efficiently Specifiable" polynomial, for which a classical approximate sampler implies an average-case approximation. This class of polynomials contains the Permanent but also includes, for example, the Hamiltonian Cycle polynomial, and many other familiar #P-hard polynomials. Although our construction, unlike that proposed by Aaronson and Arkhipov, likely requires a universal quantum computer, we are able to use this additional power to weaken the conjectures needed to prove approximate sampling hardness results. UR - http://arxiv.org/abs/1507.05592v1 ER - TY - JOUR T1 - Quantum vs Classical Proofs and Subset Verification Y1 - 2015 A1 - Bill Fefferman A1 - Shelby Kimmel AB - We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only classical witnesses, cannot verify certain properties of subsets given implicitly via an oracle. We use this framework to prove an oracle separation between QCMA and QMA using an ``in-place'' permutation oracle, making the first progress on this question since Aaronson and Kuperberg in 2007. We also use the framework to prove a particularly simple standard oracle separation between QCMA and AM. UR - http://arxiv.org/abs/1510.06750 ER - TY - JOUR T1 - Different Strategies for Optimization Using the Quantum Adiabatic Algorithm Y1 - 2014 A1 - Elizabeth Crosson A1 - Edward Farhi A1 - Cedric Yen-Yu Lin A1 - Han-Hsuan Lin A1 - Peter Shor AB - We present the results of a numerical study, with 20 qubits, of the performance of the Quantum Adiabatic Algorithm on randomly generated instances of MAX 2-SAT with a unique assignment that maximizes the number of satisfied clauses. The probability of obtaining this assignment at the end of the quantum evolution measures the success of the algorithm. Here we report three strategies which consistently increase the success probability for the hardest instances in our ensemble: decreasing the overall evolution time, initializing the system in excited states, and adding a random local Hamiltonian to the middle of the evolution. UR - http://arxiv.org/abs/1401.7320v1 ER - TY - JOUR T1 - Hong-Ou-Mandel atom interferometry in tunnel-coupled optical tweezers JF - Science Y1 - 2014 A1 - A. M. Kaufman A1 - B. J. Lester A1 - C. M. Reynolds A1 - M. L. Wall A1 - Michael Foss-Feig A1 - K. R. A. Hazzard A1 - A. M. Rey A1 - C. A. Regal AB - The quantum statistics of atoms is typically observed in the behavior of an ensemble via macroscopic observables. However, quantum statistics modifies the behavior of even two particles, inducing remarkable consequences that are at the heart of quantum science. Here we demonstrate near-complete control over all the internal and external degrees of freedom of two laser-cooled 87Rb atoms trapped in two optical tweezers. This full controllability allows us to implement a massive-particle analog of a Hong-Ou-Mandel interferometer where atom tunneling plays the role of a photon beamsplitter. We use the interferometer to probe the effect of quantum statistics on the two-atom dynamics under tunable initial conditions, chosen to adjust the degree of atomic indistinguishability. Our work thereby establishes laser-cooled atoms in optical tweezers as a new route to bottom-up engineering of scalable, low-entropy quantum systems. VL - 345 U4 - 306 - 309 UR - http://arxiv.org/abs/1312.7182v2 CP - 6194 J1 - Science U5 - 10.1126/science.1250057 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 - Quantum correlations and entanglement in far-from-equilibrium spin systems JF - Physical Review A Y1 - 2014 A1 - Kaden R. A. Hazzard A1 - Mauritz van den Worm A1 - Michael Foss-Feig A1 - Salvatore R. Manmana A1 - Emanuele Dalla Torre A1 - Tilman Pfau A1 - Michael Kastner A1 - Ana Maria Rey AB - By applying complementary analytic and numerical methods, we investigate the dynamics of spin-$1/2$ XXZ models with variable-range interactions in arbitrary dimensions. The dynamics we consider is initiated from uncorrelated states that are easily prepared in experiments, and can be equivalently viewed as either Ramsey spectroscopy or a quantum quench. Our primary focus is the dynamical emergence of correlations and entanglement in these far-from-equilibrium interacting quantum systems: we characterize these correlations by the entanglement entropy, concurrence, and squeezing, which are inequivalent measures of entanglement corresponding to different quantum resources. In one spatial dimension, we show that the time evolution of correlation functions manifests a non-perturbative dynamic singularity. This singularity is characterized by a universal power-law exponent that is insensitive to small perturbations. Explicit realizations of these models in current experiments using polar molecules, trapped ions, Rydberg atoms, magnetic atoms, and alkaline-earth and alkali atoms in optical lattices, along with the relative merits and limitations of these different systems, are discussed. VL - 90 UR - http://arxiv.org/abs/1406.0937v1 CP - 6 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.90.063622 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 - 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 - When the asymptotic limit offers no advantage in the local-operations-and-classical-communication paradigm JF - Phys. Rev. A Y1 - 2014 A1 - Honghao Fu A1 - Debbie Leung A1 - Laura Mancinska AB -

We consider bipartite LOCC, the class of operations implementable by local quantum operations and classical communication between two parties. Surprisingly, there are operations that can be approximated to arbitrary precision but are impossible to implement exactly if only a finite number of messages are exchanged. This significantly complicates the analysis of what can or cannot be approximated with LOCC. Toward alleviating this problem, we exhibit two scenarios in which allowing vanishing error does not help. The first scenario is implementation of projective measurements with product measurement operators. The second scenario is the discrimination of unextendable product bases on two three-dimensional systems.

VL - 89 CP - 052310 U5 - https://doi.org/10.1103/PhysRevA.89.052310 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 - Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence JF - New Journal of Physics Y1 - 2013 A1 - Michael Foss-Feig A1 - Kaden R A Hazzard A1 - John J Bollinger A1 - Ana Maria Rey A1 - Charles W Clark AB - Ising models, and the physical systems described by them, play a central role in generating entangled states for use in quantum metrology and quantum information. In particular, ultracold atomic gases, trapped ion systems, and Rydberg atoms realize long-ranged Ising models, which even in the absence of a transverse field can give rise to highly non-classical dynamics and long-range quantum correlations. In the first part of this paper, we present a detailed theoretical framework for studying the dynamics of such systems driven (at time t=0) into arbitrary unentangled non-equilibrium states, thus greatly extending and unifying the work of Ref. [1]. Specifically, we derive exact expressions for closed-time-path ordered correlation functions, and use these to study experimentally relevant observables, e.g. Bloch vector and spin-squeezing dynamics. In the second part, these correlation functions are then used to derive closed-form expressions for the dynamics of arbitrary spin-spin correlation functions in the presence of both T_1 (spontaneous spin relaxation/excitation) and T_2 (dephasing) type decoherence processes. Even though the decoherence is local, our solution reveals that the competition between Ising dynamics and T_1 decoherence gives rise to an emergent non-local dephasing effect, thereby drastically amplifying the degradation of quantum correlations. In addition to identifying the mechanism of this deleterious effect, our solution points toward a scheme to eliminate it via measurement-based coherent feedback. VL - 15 U4 - 113008 UR - http://arxiv.org/abs/1306.0172v1 CP - 11 J1 - New J. Phys. U5 - 10.1088/1367-2630/15/11/113008 ER - TY - JOUR T1 - Far from equilibrium quantum magnetism with ultracold polar molecules JF - Physical Review Letters Y1 - 2013 A1 - Kaden R. A. Hazzard A1 - Salvatore R. Manmana A1 - Michael Foss-Feig A1 - Ana Maria Rey AB - Recent theory has indicated how to emulate tunable models of quantum magnetism with ultracold polar molecules. Here we show that present molecule optical lattice experiments can accomplish three crucial goals for quantum emulation, despite currently being well below unit filling and not quantum degenerate. The first is to verify and benchmark the models proposed to describe these systems. The second is to prepare correlated and possibly useful states in well-understood regimes. The third is to explore many-body physics inaccessible to existing theoretical techniques. Our proposal relies on a non-equilibrium protocol that can be viewed either as Ramsey spectroscopy or an interaction quench. It uses only routine experimental tools available in any ultracold molecule experiment. VL - 110 UR - http://arxiv.org/abs/1209.4076v1 CP - 7 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.110.075301 ER - TY - JOUR T1 - Non-equilibrium dynamics of Ising models with decoherence: an exact solution JF - Physical Review A Y1 - 2013 A1 - Michael Foss-Feig A1 - Kaden R. A. Hazzard A1 - John J. Bollinger A1 - Ana Maria Rey AB - The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics: Decoherence can degrade correlations, but can also give rise to a variety of rich dynamical and steady-state behaviors. We obtain an exact analytic solution for the non-equilibrium dynamics of Ising models with arbitrary interactions and subject to the most general form of local Markovian decoherence. Our solution shows that decoherence affects the relaxation of observables more than predicted by single-particle considerations. It also reveals a dynamical phase transition, specifically a Hopf bifurcation, which is absent at the single-particle level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems. VL - 87 UR - http://arxiv.org/abs/1209.5795v2 CP - 4 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.87.042101 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 - On Beating the Hybrid Argument JF - Proceedings, ITCS Y1 - 2012 A1 - Bill Fefferman A1 - Ronen Shaltiel A1 - Christopher Umans A1 - Emanuele Viola AB - The hybrid argument allows one to relate the distinguishability of a distribution (from uniform) to the predictability of individual bits given a prefix. The argument incurs a loss of a factor k equal to the bit-length of the distributions: -distinguishability implies only /k-predictability. This paper studies the consequences of avoiding this loss – what we call “beating the hybrid argument” – and develops new proof techniques that circumvent the loss in certain natural settings. Specifically, we obtain the following results: 1. We give an instantiation of the Nisan-Wigderson generator (JCSS ’94) that can be broken by quantum computers, and that is o(1)-unpredictable against AC0 . This is not enough to imply indistinguishability via the hybrid argument because of the hybrid-argument loss; nevertheless, we conjecture that this generator indeed fools AC0 , and we prove this statement for a simplified version of the problem. Our conjecture implies the existence of an oracle relative to which BQP is not in the PH, a longstanding open problem. 2. We show that the “INW” generator by Impagliazzo, Nisan, and Wigderson (STOC ’94) with seed length O(log n log log n) produces a distribution that is 1/ log n-unpredictable against poly-logarithmic width (general) read-once oblivious branching programs. Thus avoiding the hybrid-argument loss would lead to a breakthrough in generators against small space. 3. We study pseudorandom generators obtained from a hard function by repeated sampling. We identify a property of functions, “resamplability,” that allows us to beat the hybrid argument, leading to new pseudorandom generators for AC0 [p] and similar classes. Although the generators have sub-linear stretch, they represent the best-known generators for these classes. Thus we establish that “beating” or bypassing the hybrid argument would have two significant consequences in complexity, and we take steps toward that goal by developing techniques that indeed beat the hybrid argument in related (but simpler) settings, leading to best-known PRGs for certain complexity classes. VL - 9 U4 - 809-843 UR - http://users.cms.caltech.edu/~umans/papers/FSUV10.pdf ER - TY - JOUR T1 - The equilibrium states of open quantum systems in the strong coupling regime JF - Physical Review E Y1 - 2012 A1 - Y. Subasi A1 - C. H. Fleming A1 - J. M. Taylor A1 - B. L. Hu AB - In this work we investigate the late-time stationary states of open quantum systems coupled to a thermal reservoir in the strong coupling regime. In general such systems do not necessarily relax to a Boltzmann distribution if the coupling to the thermal reservoir is non-vanishing or equivalently if the relaxation timescales are finite. Using a variety of non-equilibrium formalisms valid for non-Markovian processes, we show that starting from a product state of the closed system = system + environment, with the environment in its thermal state, the open system which results from coarse graining the environment will evolve towards an equilibrium state at late-times. This state can be expressed as the reduced state of the closed system thermal state at the temperature of the environment. For a linear (harmonic) system and environment, which is exactly solvable, we are able to show in a rigorous way that all multi-time correlations of the open system evolve towards those of the closed system thermal state. Multi-time correlations are especially relevant in the non-Markovian regime, since they cannot be generated by the dynamics of the single-time correlations. For more general systems, which cannot be exactly solved, we are able to provide a general proof that all single-time correlations of the open system evolve to those of the closed system thermal state, to first order in the relaxation rates. For the special case of a zero-temperature reservoir, we are able to explicitly construct the reduced closed system thermal state in terms of the environmental correlations. VL - 86 UR - http://arxiv.org/abs/1206.2707v1 CP - 6 J1 - Phys. Rev. E U5 - 10.1103/PhysRevE.86.061132 ER - TY - JOUR T1 - Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice JF - Physical Review Letters Y1 - 2012 A1 - Amodsen Chotia A1 - Brian Neyenhuis A1 - Steven A. Moses A1 - Bo Yan A1 - Jacob P. Covey A1 - Michael Foss-Feig A1 - Ana Maria Rey A1 - Deborah S. Jin A1 - Jun Ye AB - We have realized long-lived ground-state polar molecules in a 3D optical lattice, with a lifetime of up to 25 s, which is limited only by off-resonant scattering of the trapping light. Starting from a 2D optical lattice, we observe that the lifetime increases dramatically as a small lattice potential is added along the tube-shaped lattice traps. The 3D optical lattice also dramatically increases the lifetime for weakly bound Feshbach molecules. For a pure gas of Feshbach molecules, we observe a lifetime of >20 s in a 3D optical lattice; this represents a 100-fold improvement over previous results. This lifetime is also limited by off-resonant scattering, the rate of which is related to the size of the Feshbach molecule. Individually trapped Feshbach molecules in the 3D lattice can be converted to pairs of K and Rb atoms and back with nearly 100% efficiency. VL - 108 UR - http://arxiv.org/abs/1110.4420v1 CP - 8 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.108.080405 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 - 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 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 - A Spectral Algorithm for Latent Dirichlet Allocation JF - Algorithmica Y1 - 2012 A1 - Animashree Anandkumar A1 - Dean P. Foster A1 - Daniel Hsu A1 - Sham M. Kakade A1 - Yi-Kai Liu AB - The problem of topic modeling can be seen as a generalization of the clustering problem, in that it posits that observations are generated due to multiple latent factors (e.g., the words in each document are generated as a mixture of several active topics, as opposed to just one). This increased representational power comes at the cost of a more challenging unsupervised learning problem of estimating the topic probability vectors (the distributions over words for each topic), when only the words are observed and the corresponding topics are hidden. We provide a simple and efficient learning procedure that is guaranteed to recover the parameters for a wide class of mixture models, including the popular latent Dirichlet allocation (LDA) model. For LDA, the procedure correctly recovers both the topic probability vectors and the prior over the topics, using only trigram statistics (i.e., third order moments, which may be estimated with documents containing just three words). The method, termed Excess Correlation Analysis (ECA), is based on a spectral decomposition of low order moments (third and fourth order) via two singular value decompositions (SVDs). Moreover, the algorithm is scalable since the SVD operations are carried out on $k\times k$ matrices, where $k$ is the number of latent factors (e.g. the number of topics), rather than in the $d$-dimensional observed space (typically $d \gg k$). U4 - 193-214 UR - http://arxiv.org/abs/1204.6703v4 ER - TY - JOUR T1 - Steady-state many-body entanglement of hot reactive fermions JF - Physical Review Letters Y1 - 2012 A1 - Michael Foss-Feig A1 - Andrew J. Daley A1 - James K. Thompson A1 - Ana Maria Rey AB - Entanglement is typically created via systematic intervention in the time evolution of an initially unentangled state, which can be achieved by coherent control, carefully tailored non-demolition measurements, or dissipation in the presence of properly engineered reservoirs. In this paper we show that two-component Fermi gases at ~\mu K temperatures naturally evolve, in the presence of reactive two-body collisions, into states with highly entangled (Dicke-type) spin wavefunctions. The entanglement is a steady-state property that emerges---without any intervention---from uncorrelated initial states, and could be used to improve the accuracy of spectroscopy in experiments with fermionic alkaline earth atoms or fermionic groundstate molecules. VL - 109 UR - http://arxiv.org/abs/1207.4741v1 CP - 23 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.109.230501 ER - TY - JOUR T1 - Direct Fidelity Estimation from Few Pauli Measurements JF - Physical Review Letters Y1 - 2011 A1 - Steven T. Flammia A1 - Yi-Kai Liu AB - We describe a simple method for certifying that an experimental device prepares a desired quantum state rho. Our method is applicable to any pure state rho, and it provides an estimate of the fidelity between rho and the actual (arbitrary) state in the lab, up to a constant additive error. The method requires measuring only a constant number of Pauli expectation values, selected at random according to an importance-weighting rule. Our method is faster than full tomography by a factor of d, the dimension of the state space, and extends easily and naturally to quantum channels. VL - 106 UR - http://arxiv.org/abs/1104.4695v3 CP - 23 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.106.230501 ER - TY - JOUR T1 - Phase diagram of the Bose Kondo-Hubbard model JF - Physical Review A Y1 - 2011 A1 - Michael Foss-Feig A1 - Ana Maria Rey AB - We study a bosonic version of the Kondo lattice model with an on-site repulsion in the conduction band, implemented with alkali atoms in two bands of an optical lattice. Using both weak and strong-coupling perturbation theory, we find that at unit filling of the conduction bosons the superfluid to Mott insulator transition should be accompanied by a magnetic transition from a ferromagnet (in the superfluid) to a paramagnet (in the Mott insulator). Furthermore, an analytic treatment of Gutzwiller mean-field theory reveals that quantum spin fluctuations induced by the Kondo exchange cause the otherwise continuous superfluid to Mott-insulator phase transition to be first order. We show that lattice separability imposes a serious constraint on proposals to exploit excited bands for quantum simulations, and discuss a way to overcome this constraint in the context of our model by using an experimentally realized non-separable lattice. A method to probe the first-order nature of the transition based on collapses and revivals of the matter-wave field is also discussed. VL - 84 UR - http://arxiv.org/abs/1103.0245v2 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.84.053619 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 - 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 - 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 - Probing the Kondo Lattice Model with Alkaline Earth Atoms JF - Physical Review A Y1 - 2010 A1 - Michael Foss-Feig A1 - Michael Hermele A1 - Ana Maria Rey AB - We study transport properties of alkaline-earth atoms governed by the Kondo Lattice Hamiltonian plus a harmonic confining potential, and suggest simple dynamical probes of several different regimes of the phase diagram that can be implemented with current experimental techniques. In particular, we show how Kondo physics at strong coupling, low density, and in the heavy fermion phase is manifest in the dipole oscillations of the conduction band upon displacement of the trap center. VL - 81 UR - http://arxiv.org/abs/0912.4762v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.81.051603 ER - TY - JOUR T1 - Pseudorandom generators and the BQP vs. PH problem Y1 - 2010 A1 - Bill Fefferman A1 - Christopher Umans AB - It is a longstanding open problem to devise an oracle relative to which BQP does not lie in the Polynomial-Time Hierarchy (PH). We advance a natural conjecture about the capacity of the Nisan-Wigderson pseudorandom generator [NW94] to fool AC_0, with MAJORITY as its hard function. Our conjecture is essentially that the loss due to the hybrid argument (which is a component of the standard proof from [NW94]) can be avoided in this setting. This is a question that has been asked previously in the pseudorandomness literature [BSW03]. We then make three main contributions: (1) We show that our conjecture implies the existence of an oracle relative to which BQP is not in the PH. This entails giving an explicit construction of unitary matrices, realizable by small quantum circuits, whose row-supports are "nearly-disjoint." (2) We give a simple framework (generalizing the setting of Aaronson [A10]) in which any efficiently quantumly computable unitary gives rise to a distribution that can be distinguished from the uniform distribution by an efficient quantum algorithm. When applied to the unitaries we construct, this framework yields a problem that can be solved quantumly, and which forms the basis for the desired oracle. (3) We prove that Aaronson's "GLN conjecture" [A10] implies our conjecture; our conjecture is thus formally easier to prove. The GLN conjecture was recently proved false for depth greater than 2 [A10a], but it remains open for depth 2. If true, the depth-2 version of either conjecture would imply an oracle relative to which BQP is not in AM, which is itself an outstanding open problem. Taken together, our results have the following interesting interpretation: they give an instantiation of the Nisan-Wigderson generator that can be broken by quantum computers, but not by the relevant modes of classical computation, if our conjecture is true. UR - http://arxiv.org/abs/1007.0305v3 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 - Geometric-Phase-Effect Tunnel-Splitting Oscillations in Single-Molecule Magnets with Fourth-Order Anisotropy Induced by Orthorhombic Distortion JF - EPL (Europhysics Letters) Y1 - 2009 A1 - Michael Foss-Feig A1 - Jonathan R. Friedman AB - We analyze the interference between tunneling paths that occurs for a spin system with both fourth-order and second-order transverse anisotropy. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is increased, the tunnel splitting is modulated, with zeros occurring periodically. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field. VL - 86 U4 - 27002 UR - http://arxiv.org/abs/0809.2289v2 CP - 2 J1 - Europhys. Lett. U5 - 10.1209/0295-5075/86/27002 ER - TY - JOUR T1 - Perturbative Gadgets at Arbitrary Orders JF - Physical Review A Y1 - 2008 A1 - Stephen P. Jordan A1 - Edward Farhi AB - Adiabatic quantum algorithms are often most easily formulated using many-body interactions. However, experimentally available interactions are generally two-body. In 2004, Kempe, Kitaev, and Regev introduced perturbative gadgets, by which arbitrary three-body effective interactions can be obtained using Hamiltonians consisting only of two-body interactions. These three-body effective interactions arise from the third order in perturbation theory. Since their introduction, perturbative gadgets have become a standard tool in the theory of quantum computation. Here we construct generalized gadgets so that one can directly obtain arbitrary k-body effective interactions from two-body Hamiltonians. These effective interactions arise from the kth order in perturbation theory. VL - 77 UR - http://arxiv.org/abs/0802.1874v4 CP - 6 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.77.062329 ER - TY - JOUR T1 - The Power of Unentanglement Y1 - 2008 A1 - Scott Aaronson A1 - Salman Beigi A1 - Andrew Drucker A1 - Bill Fefferman A1 - Peter Shor AB - The class QMA(k), introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give any evidence that k quantum proofs are more powerful than one? Does QMA(k)=QMA(2) for k>=2? Can QMA(k) protocols be amplified to exponentially small error? In this paper, we make progress on all of the above questions. First, we give a protocol by which a verifier can be convinced that a 3SAT formula of size n is satisfiable, with constant soundness, given ~O(sqrt(n)) unentangled quantum witnesses with O(log n) qubits each. Our protocol relies on the existence of very short PCPs. Second, we show that assuming a weak version of the Additivity Conjecture from quantum information theory, any QMA(2) protocol can be amplified to exponentially small error, and QMA(k)=QMA(2) for all k>=2. Third, we prove the nonexistence of "perfect disentanglers" for simulating multiple Merlins with one. UR - http://arxiv.org/abs/0804.0802v2 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 - Error correcting codes for adiabatic quantum computation JF - Physical Review A Y1 - 2006 A1 - Stephen P. Jordan A1 - Edward Farhi A1 - Peter W. Shor AB - Recently, there has been growing interest in using adiabatic quantum computation as an architecture for experimentally realizable quantum computers. One of the reasons for this is the idea that the energy gap should provide some inherent resistance to noise. It is now known that universal quantum computation can be achieved adiabatically using 2-local Hamiltonians. The energy gap in these Hamiltonians scales as an inverse polynomial in the problem size. Here we present stabilizer codes which can be used to produce a constant energy gap against 1-local and 2-local noise. The corresponding fault-tolerant universal Hamiltonians are 4-local and 6-local respectively, which is the optimal result achievable within this framework. VL - 74 UR - http://arxiv.org/abs/quant-ph/0512170v3 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.74.052322 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 - `Flat Phase' Loading of a Bose-Einstein Condensate into an Optical Lattice JF - Physical Review A Y1 - 2002 A1 - Shlomo E. Sklarz A1 - Inbal Friedler A1 - David J. Tannor A1 - Yehuda B. Band A1 - Carl J. Williams AB - It has been proposed that the adiabatic loading of a Bose-Einstein Condensate (BEC) into an optical lattice via the Mott-insulator transition can be used to initialize a quantum computer [D. Jaksch, {\it et al.}, Phys. Rev. Lett. {\bf 81}, 3108 (1998)]. The loading of a BEC into the lattice without causing band excitation is readily achievable; however, unless one switches on an optical lattice very slowly, the optical lattice causes a phase to accumulate across the condensate. We show analytically and numerically that a cancellation of this effect is possible by adjusting the harmonic trap force-constant of the magnetic trap appropriately, thereby facilitating quick loading of an optical lattice for quantum computing purposes. A simple analytical theory is developed for a non-stationary BEC in a harmonic trap. VL - 66 UR - http://arxiv.org/abs/physics/0209071v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.66.053620 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 - Robustness of adiabatic quantum computation JF - Physical Review A Y1 - 2001 A1 - Andrew M. Childs A1 - Edward Farhi A1 - John Preskill AB - We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic computation against two kinds of errors, unitary control errors and decoherence, and we study this robustness using numerical simulations of the algorithm. VL - 65 UR - http://arxiv.org/abs/quant-ph/0108048v1 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.65.012322 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 -