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arXiv 2021年

作者： Jain, Rahul Kundu, Srijita Centre for Quantum Technologies Department of Computer Science National University of Singapore MajuLab UMI 3654 Singapore Institute for Quantum Computing University of Waterloo Canada

We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity of an l-player predicate V. In particular we show that for a distribution p that is product across the input sets of the l players, the success probability of any entanglement-assisted quantum communication protocol for computing n copies of V, whose communication is o(log(eff∗(V, p)) · n), goes down exponentially in n. Here eff∗(V, p) is a distributional version of the quantum efficiency or partition bound introduced by Laplante, Lerays and Roland (2012), which is a lower bound on the distributional quantum communication complexity of computing a single copy of V with respect to p. For a two-input boolean function f, the best result for interactive quantum communication complexity known previously was due to Sherstov (2018), who showed a direct product theorem in terms of the generalized discrepancy, which is a lower bound on communication. Our lower bound on non-distributional communication complexity is in terms of maxproduct p eff∗(V, p), and there is no known relationship between this and the generalized discrepancy. But we define a distributional version of the generalized discrepancy bound and can show that for a given p, eff∗(V, p) upper bounds it. Moreover, unlike Sherstov’s result, our result works for two-input functions or relations whose outputs are non-boolean as well, and is a strong direct product theorem for functions or relations whose quantum communication complexity is characterized by eff∗(Vf, p) for a product p. Applying our direct product theorem for small communication and techniques related to eff∗, we show that it is possible to do device-independent (DI) quantum cryptography without the assumption that devices do not leak any information. First, we analyze the parallel DI quantum key distribution protocol given by Jain, Miller and Shi (2020), and show that when the protocol is carried out with devices that are compatible with n copie

关键词： quantum cryptography

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Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost

arXiv

引用

arXiv 2023年

作者： An, Dong Liu, Jin-Peng Lin, Lin Joint Center for Quantum Information and Computer Science University of Maryland MD20742 United States Department of Mathematics University of California BerkeleyCA94720 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA02139 United States Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Challenge Institute for Quantum Computation University of California BerkeleyCA94720 United States

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving non-unitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters. Copyright © 2023, The Authors. All rights reserved.

关键词： Hamiltonians

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Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions

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Physical Review Research 2023年第4期5卷 043092-043092页

作者： Ievgen I. Arkhipov Adam Miranowicz Franco Nori Şahin K. Özdemir Fabrizio Minganti Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS Faculty of Science Palacký University 17. listopadu 12 771 46 Olomouc Czech Republic Theoretical Quantum Physics Laboratory Cluster for Pioneering Research RIKEN Wakoshi Saitama 351-0198 Japan Quantum Information Physics Theory Research Team Quantum Computing Center RIKEN Wakoshi Saitama 351-0198 Japan Institute of Spintronics and Quantum Information Faculty of Physics Adam Mickiewicz University 61-614 Poznań Poland Physics Department The University of Michigan Ann Arbor Michigan 48109-1040 USA Department of Engineering Science and Mechanics and Materials Research Institute (MRI) The Pennsylvania State University University Park Pennsylvania 16802 USA Institute of Physics Ecole Polytechnique Fédérale de Lausanne (EPFL) CH-1015 Lausanne Switzerland Center for Quantum Science and Engineering Ecole Polytechnique Fédérale de Lausanne (EPFL) CH-1015 Lausanne Switzerland

Finite simplex lattice models are used in different branches of science, e.g., in condensed-matter physics, when studying frustrated magnetic systems and non-Hermitian localization phenomena; or in chemistry, when describing experiments with mixtures. An n-simplex represents the simplest possible polytope in n dimensions, e.g., a line segment, a triangle, and a tetrahedron in one, two, and three dimensions, respectively. In this work, we show that various fully solvable, in general non-Hermitian, n-simplex lattice models with open boundaries can be constructed from the high-order field-moments space of quadratic bosonic systems. Namely, we demonstrate that such n-simplex lattices can be formed by a dimensional reduction of highly degenerate iterated polytope chains in (k>n)-dimensions, which naturally emerge in the field-moments space. Our findings indicate that the field-moments space of bosonic systems provides a versatile platform for simulating real-space n-simplex lattices exhibiting non-Hermitian phenomena, and it yields valuable insights into the structure of many-body systems exhibiting similar complexity. Among a variety of practical applications, these simplex structures can offer a physical setting for implementing the discrete fractional Fourier transform, an indispensable tool for both quantum and classical signal processing.

关键词： Complex systems Dissipative dynamics Lattice dynamics Nonlinear optics quantum optics Lattice models in statistical physics Lattices Non-Hermitian systems PT-symmetry Lattice models in condensed matter

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Causal and Noncausal Revivals of Information: A New Regime of Non-Markovianity in quantum Stochastic Processes

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PRX quantum 2025年第2期6卷 020316-020316页

作者： Francesco Buscemi Rajeev Gangwar Kaumudibikash Goswami Himanshu Badhani Tanmoy Pandit Brij Mohan Siddhartha Das Manabendra Nath Bera Department of Mathematical Informatics Nagoya University Furo-cho Chikusa-ku 464-8601 Nagoya Japan Department of Physical Sciences Indian Institute of Science Education and Research (IISER) Mohali Punjab 140306 India QICI Quantum Information and Computation Initiative Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong The Institute of Mathematical Sciences C. I. T. Campus Taramani Chennai 600113 India Homi Bhabha National Institute Training School Complex Anushakti Nagar Mumbai 400094 India Center for Security Theory and Algorithmic Research (CSTAR) Centre for Quantum Science and Technology (CQST) International Institute of Information Technology Hyderabad Gachibowli Telangana 500032 India Fritz Haber Research Center for Molecular Dynamics Hebrew University of Jerusalem Jerusalem 9190401 Israel

The study of information revivals, witnessing the violation of certain data-processing inequalities, has provided an important paradigm in the study of non-Markovian quantum stochastic processes. Although often used interchangeably, we argue here that the notions of “revivals” and “backflows,” i.e., flows of information from the environment back into the system, are distinct: an information revival can occur without any backflow ever taking place. In this paper, we examine in detail the phenomenon of noncausal revivals and relate them to the theory of short Markov chains and squashed non-Markovianity. We also provide an operational condition, in terms of system-only degrees of freedom, to witness the presence of genuine backflow that cannot be explained by noncausal revivals. As a byproduct, we demonstrate that focusing on processes with genuine backflows, while excluding those with only noncausal revivals, resolves the issue of nonconvexity of Markovianity, thus enabling the construction of a convex resource theory of genuine quantum non-Markovianity.

关键词： Markov chains

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What is Nonclassical about Uncertainty Relations?

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Physical Review Letters 2022年第24期129卷 240401-240401页

作者： Lorenzo Catani Matthew Leifer Giovanni Scala David Schmid Robert W. Spekkens Electrical Engineering and Computer Science Department Technische Universität Berlin 10587 Berlin Germany Institute for Quantum Studies and Schmid College of Science and Technology Chapman University One University Drive Orange California 92866 USA International Centre for Theory of Quantum Technologies University of Gdansk 80-308 Gdansk Poland Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo Ontario Canada N2L 2Y5

Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered to be a way in which it entails a departure from the classical worldview. However, this perspective is undermined by the fact that there exist operational theories which exhibit nontrivial uncertainty relations but which are consistent with the classical worldview insofar as they admit of a generalized-noncontextual ontological model. This prompts the question of what aspects of uncertainty relations, if any, cannot be realized in this way and so constitute evidence of genuine nonclassicality. We here consider uncertainty relations describing the tradeoff between the predictability of a pair of binary-outcome measurements (e.g., measurements of Pauli X and Pauli Z observables in quantum theory). We show that, for a class of theories satisfying a particular symmetry property, the functional form of this predictability tradeoff is constrained by noncontextuality to be below a linear curve. Because qubit quantum theory has the relevant symmetry property, the fact that its predictability tradeoff describes a section of a circle is a violation of this noncontextual bound, and therefore constitutes an example of how the functional form of an uncertainty relation can witness contextuality. We also deduce the implications for a selected group of operational foils to quantum theory and consider the generalization to three measurements.

关键词： quantum foundations quantum theory

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Efficient product formulas for commutators and applications to quantum simulation

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Physical Review Research 2022年第1期4卷 013191-013191页

作者： Yu-An Chen Andrew M. Childs Mohammad Hafezi Zhang Jiang Hwanmun Kim Yijia Xu Google Quantum AI 340 Main Street Venice California 90291 USA Department of Physics and Joint Quantum Institute NIST/University of Maryland College Park Maryland 20742 USA Condensed Matter Theory Center University of Maryland College Park Maryland 20472 USA Joint Center for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA Department of Computer Science University of Maryland College Park Maryland 20742 USA Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 USA Departments of Electrical and Computer Engineering and Institute for Research in Electronics and Applied Physics University of Maryland College Park Maryland 20742 USA Institute for Physical Science and Technology University of Maryland College Park Maryland 20742 USA

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

关键词： Fractional quantum Hall effect quantum algorithms quantum computation quantum control quantum simulation Abstract algebra

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Near-Linear Time Approximations for Cut Problems via Fair Cuts

arXiv

引用

arXiv 2022年

作者： Li, Jason Nanongkai, Danupon Panigrahi, Debmalya Saranurak, Thatchaphol Simons Institute for Theory of Computing UC Berkeley United States Max Planck Institute for Informatics University of Copenhagen KTH Denmark Department of Computer Science Duke University United States University of Michigan Ann Arbor United States

We introduce the notion of fair cuts as an approach to leverage approximate (s, t)-mincut (equivalently (s, t)-maxflow) algorithms in undirected graphs to obtain near-linear time approximation algorithms for several cut problems. Informally, for any α ≥ 1, an α-fair (s, t)-cut is an (s, t)-cut such that there exists an (s, t)-flow that uses 1/α fraction of the capacity of every edge in the cut. (So, any α-fair cut is also an α-approximate mincut, but not vice-versa.) We give an algorithm for (1 + ∊)-fair (s, t)-cut in Õ(m∊)-time, thereby matching the best runtime for (1 + ∊)-approximate (s, t)-mincut [Peng, SODA'16]. We then demonstrate the power of this approach by showing that this result almost immediately leads to several applications: • the first nearly-linear time (1+∊)-approximation algorithm that computes all-pairs maxflow values (by constructing an approximate Gomory-Hu tree). Prior to our work, such a result was not known even for the special case of Steiner mincut [Dinitz and Vainstein, STOC'94;Cole and Hariharan, STOC'03];• the first almost-linear-work subpolynomial-depth parallel algorithms for computing (1+∊)-approximations for all-pairs maxflow values (again via an approximate Gomory-Hu tree) in unweighted graphs;• the first near-linear time expander decomposition algorithm that works even when the expansion parameter is polynomially small;this subsumes previous incomparable algorithms [Nanongkai and Saranurak, FOCS'17;Wulff-Nilsen, FOCS'17;Saranurak and Wang, SODA'19]. © 2022, CC BY.

关键词： Approximation algorithms

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Flat Band Generation through Interlayer Geometric Frustration in Intercalated Transition Metal Dichalcogenides

arXiv

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arXiv 2024年

作者： Peng, Yawen He, Ren Li, Peng Zhdanovich, Sergey Michiardi, Matteo Gorovikov, Sergey Zonno, Marta Damascelli, Andrea Miao, Guo-Xing Institute for Quantum Computing Department of Electrical and Computer Engineering University of Waterloo WaterlooONN2L3G1 Canada Quantum Matter Institute University of British Columbia VancouverBCV6T 1Z4 Canada Canadian Light Source Inc. 44 Innovation Boulevard SaskatoonSKS7N 2V3 Canada School of Electronic Science and Engineering University of Electronic Science and Technology of China Chengdu China

Electronic flat bands can lead to rich many-body quantum phases by quenching the electron’s kinetic energy and enhancing many-body correlation. The reduced bandwidth can be realized by either destructive quantum interference in frustrated lattices, or by generating heavy band folding with avoided band crossing in Moiré superlattices. Here we propose a general approach to introduce flat bands into widely studied transition metal dichalcogenide (TMD) materials by dilute intercalation. A flat band with vanishing dispersion is observed by angle-resolved photoemission spectroscopy (ARPES) over the entire momentum space in intercalated Mn1/4TaS2. Polarization dependent ARPES measurements combined with symmetry analysis reveals the orbital characters of the flat band. Supercell tight-binding simulations suggest that such flat bands arising from destructive interference between Mn and Ta on S through hopping pathways, are ubiquitous in a range of TMD families as well as for different intercalation configurations. Our findings establish a new material platform to manipulate flat band structures and explore their corresponding emergent correlated properties. © 2024, CC BY.

关键词： Kinetic energy

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Fault-Tolerant quantum Memory using Low-Depth Random Circuit Codes

arXiv

引用

arXiv 2023年

作者： Nelson, Jon Bentsen, Gregory Flammia, Steven T. Gullans, Michael J. Joint Center for Quantum Information and Computer Science NIST University of Maryland College ParkMD20742 United States Martin A. Fisher School of Physics Brandeis University WalthamMA02465 United States AWS Center for Quantum Computing PasadenaCA91125 United States IQIM California Institute of Technology PasadenaCA91125 United States

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. [1]. 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. Copyright © 2023, The Authors. All rights reserved.

关键词： Tensors

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An Automata-Theoretic Approach to Synthesizing Binarized Neural Networks

arXiv

引用

arXiv 2023年

作者： Tao, Ye Liu, Wanwei Song, Fu Liang, Zhen Wang, Ji Zhu, Hongxu College of Computer Science and Technology National University of Defense Technology China School of Information Science and Technology ShanghaiTech University China Institute of Software Chinese Academy of Sciences University of Chinese Academy of Sciences China Automotive Software Innovation Center China Institute for Quantum Information State Key Laboratory for High Performance Computing National University of Defense Technology China

Deep neural networks, (DNNs, a.k.a. NNs), have been widely used in various tasks and have been proven to be successful. However, the accompanied expensive computing and storage costs make the deployments in resource-constrained devices a significant concern. To solve this issue, quantization has emerged as an effective way to reduce the costs of DNNs with little accuracy degradation by quantizing floating-point numbers to low-width fixed-point representations. Quantized neural networks (QNNs) have been developed, with binarized neural networks (BNNs) restricted to binary values as a special case. Another concern about neural networks is their vulnerability and lack of interpretability. Despite the active research on trustworthy of DNNs, few approaches have been proposed to QNNs. To this end, this paper presents an automata-theoretic approach to synthesizing BNNs that meet designated properties. More specifically, we define a temporal logic, called BLTL, as the specification language. We show that each BLTL formula can be transformed into an automaton on finite words. To deal with the state-explosion problem, we provide a tableau-based approach in real implementation. For the synthesis procedure, we utilize SMT solvers to detect the existence of a model (i.e., a BNN) in the construction process. Notably, synthesis provides a way to determine the hyper-parameters of the network before training. Moreover, we experimentally evaluate our approach and demonstrate its effectiveness in improving the individual fairness and local robustness of BNNs while maintaining accuracy to a great extent. Copyright © 2023, The Authors. All rights reserved.

关键词： Deep neural networks

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