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On the mixed-unitary rank of quantum channels

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arXiv 2020年

作者： Girard, Mark Leung, Debbie Levick, Jeremy Li, Chi-Kwong Paulsen, Vern Poon, Yiu Tung Watrous, John Institute for Quantum Computing University of Waterloo School of Computer Science University of Waterloo Department of Combinatorics & Optimization University of Waterloo Perimeter Institute for Theoretical Physics Waterloo Canada Department of Mathematics & Statistics University of Guelph Department of Mathematics College of William and Mary Department of Pure Mathematics University of Waterloo Department of Mathematics Iowa State University Center for Quantum Computing Peng Cheng Laboratory Canadian Institute for Advanced Research Toronto Canada

In the theory of quantum information, the mixed-unitary quantum channels, for any positive integer dimension n, are those linear maps that can be expressed as a convex combination of conjugations by n × n complex unitary matrices. We consider the mixed-unitary rank of any such channel, which is the minimum number of distinct unitary conjugations required for an expression of this form. We identify several new relationships between the mixed-unitary rank N and the Choi rank r of mixed-unitary channels, the Choi rank being equal to the minimum number of nonzero terms required for a Kraus representation of that channel. Most notably, we prove that the inequality N ≤ r2 − r + 1 is satisfied for every mixed-unitary channel (as is the equality N = 2 when r = 2), and we exhibit the first known examples of mixed-unitary channels for which N > r. Specifically, we prove that there exist mixed-unitary channels having Choi rank d + 1 and mixed-unitary rank 2d for infinitely many positive integers d, including every prime power d. We also examine the mixed-unitary ranks of the mixed-unitary Werner-Holevo channels. Copyright © 2020, The Authors. All rights reserved.

关键词： quantum entanglement

Quenched vs Annealed: Glassiness from SK to SYK

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Physical Review X 2020年第3期10卷 031026-031026页

作者： C. L. Baldwin B. Swingle National Institute of Standards and Technology Gaithersburg Maryland 20899 USA Joint Quantum Institute University of Maryland College Park Maryland 20742 USA Condensed Matter Theory Center University of Maryland College Park Maryland 20742 USA Maryland Center for Fundamental Physics University of Maryland College Park Maryland 20742 USA Joint Institute for Quantum Information and Computer Science University of Maryland College Park Maryland 20742 USA Department of Physics University of Maryland College Park Maryland 20742 USA

We show that any Sachdev-Ye-Kitaev- (SYK) like model with finite-body interactions among local degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: The former model fails to be described by an annealed free energy at low temperature. In this respect, such models more closely resemble spin glasses. We demonstrate this by two means: first, a general theorem proving that the annealed free energy is divergent at low temperature in any model with a tensor product Hilbert space, and second, a replica treatment of two prominent examples which exhibit phase transitions from an “annealed” phase to a “nonannealed” phase as a function of the temperature. We further show that this effect appears only at O(N)th order in a 1/N expansion, even though lower-order terms misleadingly seem to converge. Our results prove that the nonbosonic nature of the particles in the SYK model is an essential ingredient for its physics, highlight connections between local models and spin glasses, and raise important questions as to the role of fermions and/or glassiness in holography.

关键词： quantum gravity quantum statistical mechanics Disordered systems

Cost of quantum entanglement simplified

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arXiv 2020年

作者： Wang, Xin Wilde, Mark M. Institute for Quantum Computing Baidu Research Beijing100193 China Joint Center for Quantum Information and Computer Science University of Maryland College ParkMD20742 United States Hearne Institute for Theoretical Physics Department of Physics and Astronomy Center for Computation and Technology Louisiana State University Baton RougeLA70803 United States

quantum entanglement is a key physical resource in quantum information processing that allows for performing basic quantum tasks such as teleportation and quantum key distribution, which are impossible in the classical world. Ever since the rise of quantum information theory, it has been an open problem to quantify entanglement in an information-theoretically meaningful way. In particular, every previously defined entanglement measure bearing a precise information-theoretic meaning is not known to be efficiently computable, or if it is efficiently computable, then it is not known to have a precise information-theoretic meaning. In this paper, we meet this challenge by introducing an entanglement measure that has a precise information-theoretic meaning as the exact cost required to prepare an entangled state when two distant parties are allowed to perform quantum operations that completely preserve the positivity of the partial transpose. Additionally, this entanglement measure is efficiently computable by means of a semi-definite program, and it bears a number of useful properties such as additivity and faithfulness. Our results bring key insights into the fundamental entanglement structure of arbitrary quantum states, and they can be used directly to assess and quantify the entanglement produced in quantum-physical experiments. Copyright © 2020, The Authors. All rights reserved.

关键词： quantum entanglement

Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions

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Physical Review Letters 2022年第5期128卷 050602-050602页

作者： A. Zabalo M. J. Gullans J. H. Wilson R. Vasseur A. W. W. Ludwig S. Gopalakrishnan David A. Huse J. H. Pixley Department of Physics and Astronomy Center for Materials Theory Rutgers University Piscataway New Jersey 08854 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Joint Center for Quantum Information and Computer Science NIST/University of Maryland College Park Maryland 20742 USA Department of Physics and Astronomy Louisiana State University Baton Rouge Louisiana 70803 USA Center for Computation and Technology Louisiana State University Baton Rouge Louisiana 70803 USA Department of Physics University of Massachusetts Amherst Massachusetts 01003 USA Department of Physics University of California Santa Barbara California 93106 USA Department of Physics The Pennsylvania State University University Park Pennsylvania 16802 USA Department of Physics and Astronomy CUNY College of Staten Island Staten Island New York 10314 USA Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New York New York 10010 USA

Repeated local measurements of quantum many-body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar critical exponents, making it unclear how many distinct universality classes are present. Here, we probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points for (1+1)-dimensional systems. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large on-site Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

关键词： Dynamical phase transitions Nonequilibrium statistical mechanics quantum entanglement quantum measurements

Dynamics in near-threshold J/ψ photoproduction

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Physical Review D 2023年第5期108卷 054018-054018页

作者： D. Winney C. Fernández-Ramírez A. Pilloni A. N. Hiller Blin M. Albaladejo Ł. Bibrzycki N. Hammoud J. Liao V. Mathieu G. Montaña R. J. Perry V. Shastry W. A. Smith A. P. Szczepaniak Guangdong Provincial Key Laboratory of Nuclear Science Institute of Quantum Matter South China Normal University Guangzhou 510006 China Guangdong-Hong Kong Joint Laboratory of Quantum Matter Southern Nuclear Science Computing Center South China Normal University Guangzhou 510006 China Departamento de Física Interdisciplinar Universidad Nacional de Educación a Distancia (UNED) Madrid E-28040 Spain Instituto de Ciencias Nucleares Universidad Nacional Autónoma de México Ciudad de México 04510 Mexico Dipartimento di Scienze Matematiche e Informatiche Scienze Fisiche e Scienze della Terra Università degli Studi di Messina I-98166 Messina Italy INFN Sezione di Catania I-95123 Catania Italy Institute for Theoretical Physics Regensburg University D-93040 Regensburg Germany Institute for Theoretical Physics Tübingen University D-72076 Tübingen Germany Instituto de Física Corpuscular (IFIC) Centro Mixto CSIC-Universidad de Valencia E-46071 Valencia Spain Faculty of Physics and Applied Computer Science AGH University of Krakow PL-30-059 Kraków Poland Institute of Nuclear Physics Polish Academy of Sciences 31-342 Kraków Poland Center for Exploration of Energy and Matter Indiana University Bloomington Indiana 47403 USA Department of Physics Indiana University Bloomington Indiana 47405 USA Departament de Física Quàntica i Astrofísica and Institut de Ciències del Cosmos Universitat de Barcelona Barcelona E-08028 Spain Departamento de Física Teórica Universidad Complutense de Madrid and IPARCOS E-28040 Madrid Spain Theory Center Thomas Jefferson National Accelerator Facility Newport News Virginia 23606 USA Institute of Physics Jan Kochanowski University PL-25-406 Kielce Poland

The study of J/ψ photoproduction at low energies has consequences for the understanding of multiple aspects of nonperturbative QCD, ranging from mechanical properties of the proton to the binding inside nuclei and the existence of hidden-charm pentaquarks. Factorization of the photon-cc¯ and nucleon dynamics or vector meson dominance are often invoked to justify these studies. Alternatively, open-charm intermediate states have been proposed as the dominant mechanism underlying J/ψ photoproduction. As the latter violates this factorization, it is important to estimate the relevance of such contributions. We analyze the latest differential and integrated photoproduction cross sections from the GlueX and J/ψ−007 experiments. We show that the data can be adequately described by a small number of partial waves, which we parametrize with generic models enforcing low-energy unitarity. The results suggest a non-negligible contribution from open-charm intermediate states. Furthermore, most of the models present an elastic scattering length incompatible with previous extractions based on vector meson dominance and thus call into question its applicability to heavy mesons. Our results indicate a wide array of physics possibilities that are compatible with present data and need to be disentangled.

关键词： Hadron production Hadrons Quarkonia

QuaSiMo: A composable library to program hybrid workflows for quantum simulation

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arXiv 2021年

作者： Nguyen, Thien Bassman, Lindsay Lotshaw, Phillip C. Lyakh, Dmitry McCaskey, Alexander Leyton-Ortega, Vicente Pooser, Raphael Elwasif, Wael Humble, Travis S. de Jong, Wibe A. Computer Science & Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States National Center for Computational Sciences Oak Ridge National Laboratory Oak RidgeTN37831 United States Computer Science and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Quantum Computing Institute Oak Ridge National Laboratory Oak RidgeTN37831 United States

We present a composable design scheme for the development of hybrid quantum/classical algorithms and workflows for applications of quantum simulation. Our object-oriented approach is based on constructing an expressive set of common data structures and methods that enable programming of a broad variety of complex hybrid quantum simulation applications. The abstract core of our scheme is distilled from the analysis of the current quantum simulation algorithms. Subsequently, it allows a synthesis of new hybrid algorithms and workflows via the extension, specialization, and dynamic customization of the abstract core classes defined by our design. We implement our design scheme using the hardware-agnostic programming language QCOR into the QuaSiMo library. To validate our implementation, we test and show its utility on commercial quantum processors from IBM and Rigetti, running some prototypical quantum simulations. Copyright © 2021, The Authors. All rights reserved.

关键词： quantum chemistry

Simulating quantum chaos on a quantum computer

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arXiv 2021年

作者： Anand, Amit Srivastava, Sanchit Gangopadhyay, Sayan Ghose, Shohini Department of Mechanical Engineering Indian Institute of Engineering Science And Technology West Bengal Shibpur Howrah711103 India School of Physics Indian Institute of Science Education and Research Kerala Thiruvananthapuram695551 India Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics and Computer Science Wilfrid Laurier University WaterlooONN2L 3C5 Canada

We show that currently available noisy intermediate-scale quantum (NISQ) computers can be used for versatile quantum simulations of chaotic systems. We introduce a novel classical-quantum hybrid approach for exploring the dynamics of the chaotic quantum kicked top (QKT) on a universal quantum computer. The programmability of this approach allows us to experimentally explore the complete range of QKT chaoticity parameter regimes inaccessible to previous studies. Furthermore, the number of gates in our simulation does not increase with the number of kicks, thus making it possible to study the QKT evolution for arbitrary number of kicks without fidelity loss. Using a publicly accessible NISQ computer (IBMQ), we observe periodicities in the evolution of the 2-qubit QKT, as well as signatures of chaos in the time-averaged 2-qubit entanglement. We also demonstrate a connection between entanglement and delocalization in the 2-qubit QKT, confirming theoretical predictions. © 2021, CC BY-NC-ND.

关键词： Chaotic systems

quantum error mitigation for rotation-symmetric bosonic codes with symmetry expansion

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Physical Review A 2025年第6期111卷 062402-062402页

作者： Suguru Endo Yasunari Suzuki Kento Tsubouchi Rui Asaoka Kaoru Yamamoto Yuichiro Matsuzaki Yuuki Tokunaga NTT Computer and Data Science Laboratories NTT Corporation Musashino 180-8585 Tokyo Japan Department of Applied Physics University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-8656 Japan Research Center for Emerging Computing Technologies National Institute of Advanced Industrial Science and Technology (AIST) Central2 1-1-1 Umezono Tsukuba Ibaraki 305-8568 Japan NEC-AIST Quantum Technology Cooperative Research Laboratory National Institute of Advanced Industrial Science and Technology (AIST) Tsukuba Ibaraki 305-8568 Japan

The rotation symmetric bosonic code (RSBC) is a unified framework of practical bosonic codes that have rotation symmetries, such as cat codes and binomial codes. While cat and binomial codes achieve the breakeven point in which the coherence time of the encoded qubits exceeds that of unencoded qubits, the state preparation fidelity needs to be improved for practical quantum computing. Concerning this problem, we investigate the framework of symmetry expansion, a class of quantum error mitigation that virtually projects the state onto the noise-free symmetric subspace by exploiting the system's intrinsic symmetries and postprocessing of measurement outcomes. Although symmetry expansion has been limited to error mitigation of quantum states immediately before measurement, we successfully generalize symmetry expansion for state preparation. Then, we consider two types of stabilization: photon number and phase stabilization. Photon number stabilization can be performed by leveraging the rotation operators. On the other hand, the phase errors can be suppressed via the extension towards phase direction by leveraging the recently proposed projective squeezing method. To implement our method, we use an ancilla qubit and a randomly generated controlled gate between the bosonic code states and the ancilla qubit. Our novel error mitigation method will significantly enhance computation accuracy in the near-term bosonic quantum computing.

关键词： Qubits

The Wiedemann-Franz law in doped Mott insulators without quasiparticles

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arXiv 2022年

作者： Wang, Wen O. Ding, Jixun K. Schattner, Yoni Huang, Edwin W. Moritz, Brian Devereaux, Thomas P. Department of Applied Physics Stanford University StanfordCA94305 United States Stanford Institute for Materials and Energy Sciences SLAC National Accelerator Laboratory 2575 Sand Hill Road Menlo ParkCA94025 United States Department of Physics Stanford University StanfordCA94305 United States AWS Center for Quantum Computing PasadenaCA91125 United States Department of Physics Institute of Condensed Matter Theory University of Illinois at Urbana-Champaign UrbanaIL61801 United States Department of Physics and Astronomy University of Notre Dame Notre DameIN46556 United States Stavropoulos Center for Complex Quantum Matter University of Notre Dame Notre DameIN46556 United States Department of Materials Science and Engineering Stanford University StanfordCA94305 United States Geballe Laboratory for Advanced Materials Stanford University StanfordCA94305 United States

Many metallic quantum materials display anomalous transport phenomena that defy a Fermi liquid description. Here, we use numerical methods to calculate thermal and charge transport in the doped Hubbard model and observe a cross-over separating high- and low-temperature behaviors. Distinct from the behavior at high temperatures, the Lorenz number L becomes weakly doping dependent and less sensitive to parameters at low temperatures. At the lowest numerically accessible temperatures, L roughly approaches the Wiedemann-Franz constant L0, even in a doped Mott insulator that lacks well-defined quasiparticles. Decomposing the energy current operator indicates a compensation between kinetic and potential contributions, which may help to clarify the interpretation of transport experiments beyond Boltzmann theory in strongly correlated metals. Copyright © 2022, The Authors. All rights reserved.

关键词： Mott insulators