1
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Danieli C, Yuzbashyan EA, Altshuler BL, Patra A, Flach S. Dynamical chaos in the integrable Toda chain induced by time discretization. CHAOS (WOODBURY, N.Y.) 2024; 34:033107. [PMID: 38437872 DOI: 10.1063/5.0171261] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2023] [Accepted: 01/11/2024] [Indexed: 03/06/2024]
Abstract
We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various symplectic integrators parametrized by the time step τ and measure the Lyapunov time TΛ (inverse of the largest Lyapunov exponent Λ). A key observation is that TΛ is finite whenever τ is finite but diverges when τ→0. We compare the Toda chain results with the nonintegrable Fermi-Pasta-Ulam-Tsingou chain dynamics. In addition, we observe a breakdown of the simulations at times TB≫TΛ due to certain positions and momenta becoming extremely large ("Not a Number"). This phenomenon originates from the periodic driving introduced by symplectic integrators and we also identify the concrete mechanism of the breakdown in the case of the Toda chain.
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Affiliation(s)
- Carlo Danieli
- Physics Department, Sapienza University of Rome, Piazzale Aldo Moro 5, Rome 00185, Italy
| | - Emil A Yuzbashyan
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Boris L Altshuler
- Physics Department, Columbia University, New York, New York 10027, USA
| | - Aniket Patra
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
| | - Sergej Flach
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
- Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Republic of Korea
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2
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Maletskii EA, Iakovlev IA, Mazurenko VV. Quantifying spatiotemporal patterns in classical and quantum systems out of equilibrium. Phys Rev E 2024; 109:024105. [PMID: 38491697 DOI: 10.1103/physreve.109.024105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Accepted: 12/28/2023] [Indexed: 03/18/2024]
Abstract
A rich variety of nonequilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in many-body systems of completely different nature. In this work we provide a solution to this problem by adopting a structural complexity measure to quantify spatiotemporal patterns in the time-dependent digital representation of a system. On the basis of very limited amount of data our approach allows us to distinguish different dynamical regimes and define critical parameters in both classical and quantum systems. By the example of the discrete time crystal realized in nonequilibrium quantum systems we provide a complete low-level characterization of this nontrivial dynamical phase with only processing bitstrings, which can be considered as a valuable alternative to previous studies based on the calculations of qubit correlation functions.
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Affiliation(s)
- E A Maletskii
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, Mira Street 19, 620002 Ekaterinburg, Russia
| | - I A Iakovlev
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, Mira Street 19, 620002 Ekaterinburg, Russia
| | - V V Mazurenko
- Theoretical Physics and Applied Mathematics Department, Ural Federal University, Mira Street 19, 620002 Ekaterinburg, Russia
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3
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Davoudi Z, Mueller N, Powers C. Towards Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States. PHYSICAL REVIEW LETTERS 2023; 131:081901. [PMID: 37683176 DOI: 10.1103/physrevlett.131.081901] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Revised: 02/27/2023] [Accepted: 06/01/2023] [Indexed: 09/10/2023]
Abstract
The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.
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Affiliation(s)
- Zohreh Davoudi
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Niklas Mueller
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Connor Powers
- Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Robust Quantum Simulation, University of Maryland, College Park, Maryland 20742, USA
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4
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Exploring finite temperature properties of materials with quantum computers. Sci Rep 2023; 13:1986. [PMID: 36737662 PMCID: PMC9898567 DOI: 10.1038/s41598-023-28317-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2022] [Accepted: 01/17/2023] [Indexed: 02/05/2023] Open
Abstract
Thermal properties of nanomaterials are crucial to not only improving our fundamental understanding of condensed matter systems, but also to developing novel materials for applications spanning research and industry. Since quantum effects arise at the nano-scale, these systems are difficult to simulate on classical computers. Quantum computers can efficiently simulate quantum many-body systems, yet current quantum algorithms for calculating thermal properties of these systems incur significant computational costs in that they either prepare the full thermal state on the quantum computer, or they must sample a number of pure states from a distribution that grows with system size. Canonical thermal pure quantum (TPQ) states provide a promising path to estimating thermal properties of quantum materials as they neither require preparation of the full thermal state nor require a growing number of samples with system size. Here, we present an algorithm for preparing canonical TPQ states on quantum computers. We compare three different circuit implementations for the algorithm and demonstrate their capabilities in estimating thermal properties of quantum materials. Due to its increasing accuracy with system size and flexibility in implementation, we anticipate that this method will enable finite temperature explorations of relevant quantum materials on near-term quantum computers.
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5
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Miessen A, Ollitrault PJ, Tacchino F, Tavernelli I. Quantum algorithms for quantum dynamics. NATURE COMPUTATIONAL SCIENCE 2023; 3:25-37. [PMID: 38177956 DOI: 10.1038/s43588-022-00374-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2021] [Accepted: 11/12/2022] [Indexed: 01/06/2024]
Abstract
Among the many computational challenges faced across different disciplines, quantum-mechanical systems pose some of the hardest ones and offer a natural playground for the growing field of quantum technologies. In this Perspective, we discuss quantum algorithmic solutions for quantum dynamics, reporting on the latest developments and offering a viewpoint on their potential and current limitations. We present some of the most promising areas of application and identify possible research directions for the coming years.
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Affiliation(s)
| | - Pauline J Ollitrault
- IBM Quantum, IBM Research - Zurich, Rüschlikon, Switzerland
- QC Ware, Palo Alto, CA, USA
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6
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Sahimi M, Tahmasebi P. The Potential of Quantum Computing for Geoscience. Transp Porous Media 2022. [DOI: 10.1007/s11242-022-01855-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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7
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Oh S, Kais S. Statistical Properties of Bit Strings Sampled from Sycamore Random Quantum Circuits. J Phys Chem Lett 2022; 13:7469-7475. [PMID: 35939529 DOI: 10.1021/acs.jpclett.2c02045] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Quantum supremacy has been recently reported for random circuit sampling on the Sycamore processor with 53 qubits. Here, we analyze the statistical properties of bit strings sampled from random quantum circuits. In contrast to classical random bit strings, bit strings sampled from Sycamore random circuits give rise to heat maps with stripe patterns at specific qubits, have more bit 1 than 0, and do not pass the NIST random number tests. The difference between the Sycamore bit strings and classical random bit strings is also demonstrated by the Marchenko-Pastur distribution and the Girko circular law of random matrices. The calculation of Wasserstein distances shows that the Sycamore bit strings are farther from bit strings sampled from Haar-measure random quantum circuits than classical random bit strings. Our results show that random matrices and Wasserstein distances could be used to analyze the performance of quantum computers.
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Affiliation(s)
- Sangchul Oh
- Department of Chemistry, Department of Physics and Astronomy, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
| | - Sabre Kais
- Department of Chemistry, Department of Physics and Astronomy, and Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, United States
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8
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Layden D. First-Order Trotter Error from a Second-Order Perspective. PHYSICAL REVIEW LETTERS 2022; 128:210501. [PMID: 35687468 DOI: 10.1103/physrevlett.128.210501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Accepted: 05/02/2022] [Indexed: 06/15/2023]
Abstract
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near term are the simplest, which use the Trotter formula and its higher-order variants to approximate the dynamics of interest. The approximation error of these algorithms is often poorly understood, even in the most basic and topical cases where the target Hamiltonian decomposes into two realizable terms: H=H_{1}+H_{2}. Recent studies have reported anomalously low approximation error with unexpected scaling in such cases, which they attribute to quantum interference between the errors from different steps of the algorithm. Here, we provide a simpler picture of these effects by relating the Trotter formula to its second-order variant for such H=H_{1}+H_{2} cases. Our method generalizes state-of-the-art error bounds without the technical caveats of prior studies, and elucidates how each part of the total error arises from the underlying quantum circuit. We compare our bound to the true error numerically, and find a close match over many orders of magnitude in the simulation parameters. Our findings further reduce the required circuit depth for the least experimentally demanding quantum simulation algorithms, and illustrate a useful method for bounding simulation error more broadly.
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Affiliation(s)
- David Layden
- IBM Quantum, Almaden Research Center, San Jose, California 95120, USA
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9
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Zhu Q, Cao S, Chen F, Chen MC, Chen X, Chung TH, Deng H, Du Y, Fan D, Gong M, Guo C, Guo C, Guo S, Han L, Hong L, Huang HL, Huo YH, Li L, Li N, Li S, Li Y, Liang F, Lin C, Lin J, Qian H, Qiao D, Rong H, Su H, Sun L, Wang L, Wang S, Wu D, Wu Y, Xu Y, Yan K, Yang W, Yang Y, Ye Y, Yin J, Ying C, Yu J, Zha C, Zhang C, Zhang H, Zhang K, Zhang Y, Zhao H, Zhao Y, Zhou L, Lu CY, Peng CZ, Zhu X, Pan JW. Quantum computational advantage via 60-qubit 24-cycle random circuit sampling. Sci Bull (Beijing) 2022; 67:240-245. [DOI: 10.1016/j.scib.2021.10.017] [Citation(s) in RCA: 18] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2021] [Revised: 10/18/2021] [Accepted: 10/19/2021] [Indexed: 11/29/2022]
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10
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Mi X, Ippoliti M, Quintana C, Greene A, Chen Z, Gross J, Arute F, Arya K, Atalaya J, Babbush R, Bardin JC, Basso J, Bengtsson A, Bilmes A, Bourassa A, Brill L, Broughton M, Buckley BB, Buell DA, Burkett B, Bushnell N, Chiaro B, Collins R, Courtney W, Debroy D, Demura S, Derk AR, Dunsworth A, Eppens D, Erickson C, Farhi E, Fowler AG, Foxen B, Gidney C, Giustina M, Harrigan MP, Harrington SD, Hilton J, Ho A, Hong S, Huang T, Huff A, Huggins WJ, Ioffe LB, Isakov SV, Iveland J, Jeffrey E, Jiang Z, Jones C, Kafri D, Khattar T, Kim S, Kitaev A, Klimov PV, Korotkov AN, Kostritsa F, Landhuis D, Laptev P, Lee J, Lee K, Locharla A, Lucero E, Martin O, McClean JR, McCourt T, McEwen M, Miao KC, Mohseni M, Montazeri S, Mruczkiewicz W, Naaman O, Neeley M, Neill C, Newman M, Niu MY, O'Brien TE, Opremcak A, Ostby E, Pato B, Petukhov A, Rubin NC, Sank D, Satzinger KJ, Shvarts V, Su Y, Strain D, Szalay M, Trevithick MD, Villalonga B, White T, Yao ZJ, Yeh P, Yoo J, Zalcman A, Neven H, Boixo S, Smelyanskiy V, Megrant A, Kelly J, Chen Y, Sondhi SL, Moessner R, Kechedzhi K, Khemani V, Roushan P. Time-Crystalline Eigenstate Order on a Quantum Processor. Nature 2021; 601:531-536. [PMID: 34847568 PMCID: PMC8791837 DOI: 10.1038/s41586-021-04257-w] [Citation(s) in RCA: 33] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 11/17/2021] [Indexed: 11/10/2022]
Abstract
Quantum many-body systems display rich phase structure in their low-temperature equilibrium states1. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases2–8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC)7,9–15. Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order7,16,17. In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states7,9,10. Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors. A study establishes a scalable approach to engineer and characterize a many-body-localized discrete time crystal phase on a superconducting quantum processor.
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Affiliation(s)
- Xiao Mi
- Google Research, Mountain View, CA, USA
| | - Matteo Ippoliti
- Department of Physics, Stanford University, Stanford, CA, USA
| | | | | | | | | | | | | | | | | | - Joseph C Bardin
- Google Research, Mountain View, CA, USA.,Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA, USA
| | | | | | | | - Alexandre Bourassa
- Google Research, Mountain View, CA, USA.,Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Alan Ho
- Google Research, Mountain View, CA, USA
| | | | | | | | | | - L B Ioffe
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | | | | | - Seon Kim
- Google Research, Mountain View, CA, USA
| | | | | | - Alexander N Korotkov
- Google Research, Mountain View, CA, USA.,Department of Electrical and Computer Engineering, University of California, Riverside, CA, USA
| | | | | | | | - Joonho Lee
- Google Research, Mountain View, CA, USA.,Department of Chemistry, Columbia University, New York, NY, 10027, USA
| | - Kenny Lee
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | - Matt McEwen
- Google Research, Mountain View, CA, USA.,Department of Physics, University of California, Santa Barbara, CA, USA
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Yuan Su
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | | | - Ping Yeh
- Google Research, Mountain View, CA, USA
| | | | | | | | | | | | | | | | - Yu Chen
- Google Research, Mountain View, CA, USA
| | - S L Sondhi
- Department of Physics, Princeton University, Princeton, NJ, USA.,Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford, OX1 3PU, United Kingdom
| | - Roderich Moessner
- Max-Planck-Institut für Physik komplexer Systeme, 01187, Dresden, Germany
| | | | - Vedika Khemani
- Department of Physics, Stanford University, Stanford, CA, USA.
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11
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Wu Y, Bao WS, Cao S, Chen F, Chen MC, Chen X, Chung TH, Deng H, Du Y, Fan D, Gong M, Guo C, Guo C, Guo S, Han L, Hong L, Huang HL, Huo YH, Li L, Li N, Li S, Li Y, Liang F, Lin C, Lin J, Qian H, Qiao D, Rong H, Su H, Sun L, Wang L, Wang S, Wu D, Xu Y, Yan K, Yang W, Yang Y, Ye Y, Yin J, Ying C, Yu J, Zha C, Zhang C, Zhang H, Zhang K, Zhang Y, Zhao H, Zhao Y, Zhou L, Zhu Q, Lu CY, Peng CZ, Zhu X, Pan JW. Strong Quantum Computational Advantage Using a Superconducting Quantum Processor. PHYSICAL REVIEW LETTERS 2021; 127:180501. [PMID: 34767433 DOI: 10.1103/physrevlett.127.180501] [Citation(s) in RCA: 105] [Impact Index Per Article: 35.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Accepted: 08/26/2021] [Indexed: 06/13/2023]
Abstract
Scaling up to a large number of qubits with high-precision control is essential in the demonstrations of quantum computational advantage to exponentially outpace the classical hardware and algorithmic improvements. Here, we develop a two-dimensional programmable superconducting quantum processor, Zuchongzhi, which is composed of 66 functional qubits in a tunable coupling architecture. To characterize the performance of the whole system, we perform random quantum circuits sampling for benchmarking, up to a system size of 56 qubits and 20 cycles. The computational cost of the classical simulation of this task is estimated to be 2-3 orders of magnitude higher than the previous work on 53-qubit Sycamore processor [Nature 574, 505 (2019)NATUAS0028-083610.1038/s41586-019-1666-5. We estimate that the sampling task finished by Zuchongzhi in about 1.2 h will take the most powerful supercomputer at least 8 yr. Our work establishes an unambiguous quantum computational advantage that is infeasible for classical computation in a reasonable amount of time. The high-precision and programmable quantum computing platform opens a new door to explore novel many-body phenomena and implement complex quantum algorithms.
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Affiliation(s)
- Yulin Wu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Wan-Su Bao
- Henan Key Laboratory of Quantum Information and Cryptography, Zhengzhou 450000, China
| | - Sirui Cao
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Fusheng Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Ming-Cheng Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Xiawei Chen
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Tung-Hsun Chung
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Hui Deng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yajie Du
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Daojin Fan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Ming Gong
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Cheng Guo
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Chu Guo
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Shaojun Guo
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Lianchen Han
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | | | - He-Liang Huang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
- Henan Key Laboratory of Quantum Information and Cryptography, Zhengzhou 450000, China
| | - Yong-Heng Huo
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Liping Li
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Na Li
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Shaowei Li
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yuan Li
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Futian Liang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Chun Lin
- Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
| | - Jin Lin
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Haoran Qian
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Dan Qiao
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Hao Rong
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Hong Su
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Lihua Sun
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Liangyuan Wang
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Shiyu Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Dachao Wu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yu Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Kai Yan
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | | | - Yang Yang
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Yangsen Ye
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jianghan Yin
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Chong Ying
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jiale Yu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Chen Zha
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Cha Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Haibin Zhang
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Kaili Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yiming Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Han Zhao
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
| | - Youwei Zhao
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Liang Zhou
- QuantumCTek Co., Ltd., Hefei 230026, China
| | - Qingling Zhu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Cheng-Zhi Peng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Xiaobo Zhu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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