1
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Endo K, Matsuda Y, Tanaka S, Muramatsu M. Novel real number representations in Ising machines and performance evaluation: Combinatorial random number sum and constant division. PLoS One 2024; 19:e0304594. [PMID: 38870161 PMCID: PMC11175401 DOI: 10.1371/journal.pone.0304594] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2023] [Accepted: 05/14/2024] [Indexed: 06/15/2024] Open
Abstract
Quantum annealing machines are next-generation computers for solving combinatorial optimization problems. Although physical simulations are one of the most promising applications of quantum annealing machines, a method how to embed the target problem into the machines has not been developed except for certain simple examples. In this study, we focus on a method of representing real numbers using binary variables, or quantum bits. One of the most important problems for conducting physical simulation by quantum annealing machines is how to represent the real number with quantum bits. The variables in physical simulations are often represented by real numbers but real numbers must be represented by a combination of binary variables in quantum annealing, such as quadratic unconstrained binary optimization (QUBO). Conventionally, real numbers have been represented by assigning each digit of their binary number representation to a binary variable. Considering the classical annealing point of view, we noticed that when real numbers are represented in binary numbers, there are numbers that can only be reached by inverting several bits simultaneously under the restriction of not increasing a given Hamiltonian, which makes the optimization very difficult. In this work, we propose three new types of real number representation and compared these representations under the problem of solving linear equations. As a result, we found experimentally that the accuracy of the solution varies significantly depending on how the real numbers are represented. We also found that the most appropriate representation depends on the size and difficulty of the problem to be solved and that these differences show a consistent trend for two annealing solvers. Finally, we explain the reasons for these differences using simple models, the minimum required number of simultaneous bit flips, one-way probabilistic bit-flip energy minimization, and simulation of ideal quantum annealing machine.
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Affiliation(s)
- Katsuhiro Endo
- Research Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki Japan
- Quantum Computing Center, Keio University, Yokohama, Kanagawa, Japan
- Graduate School of Science and Technology, Keio University, Yokohama, Kanagawa, Japan
| | - Yoshiki Matsuda
- Fixstars, Tokyo, Japan
- Green Computing System Research Organization, Waseda University, Tokyo, Japan
| | - Shu Tanaka
- Quantum Computing Center, Keio University, Yokohama, Kanagawa, Japan
- Green Computing System Research Organization, Waseda University, Tokyo, Japan
- Department of Applied Physics and Physico-Informatics, Keio University, Yokohama, Kanagawa, Japan
- Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q), Keio University, Tokyo, Japan
| | - Mayu Muramatsu
- Quantum Computing Center, Keio University, Yokohama, Kanagawa, Japan
- Department of Mechanical Engineering, Keio University, Yokohama, Kanagawa, Japan
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2
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Zhao Y, Ma Z, He Z, Liao H, Wang YC, Wang J, Li Y. Quantum annealing of a frustrated magnet. Nat Commun 2024; 15:3495. [PMID: 38664399 PMCID: PMC11045780 DOI: 10.1038/s41467-024-47819-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Accepted: 04/12/2024] [Indexed: 04/28/2024] Open
Abstract
Quantum annealing, which involves quantum tunnelling among possible solutions, has state-of-the-art applications not only in quickly finding the lowest-energy configuration of a complex system, but also in quantum computing. Here we report a single-crystal study of the frustrated magnet α-CoV2O6, consisting of a triangular arrangement of ferromagnetic Ising spin chains without evident structural disorder. We observe quantum annealing phenomena resulting from time-reversal symmetry breaking in a tiny transverse field. Below ~ 1 K, the system exhibits no indication of approaching the lowest-energy state for at least 15 hours in zero transverse field, but quickly converges towards that configuration with a nearly temperature-independent relaxation time of ~ 10 seconds in a transverse field of ~ 3.5 mK. Our many-body simulations show qualitative agreement with the experimental results, and suggest that a tiny transverse field can profoundly enhance quantum spin fluctuations, triggering rapid quantum annealing process from topological metastable Kosterlitz-Thouless phases, at low temperatures.
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Affiliation(s)
- Yuqian Zhao
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Zhaohua Ma
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Zhangzhen He
- State Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, 350002, Fuzhou, China
| | - Haijun Liao
- Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, 100190, Beijing, China
- Songshan Lake Materials Laboratory, 523808, Dongguan, China
| | - Yan-Cheng Wang
- Hangzhou International Innovation Institute, Beihang University, 311115, Hangzhou, China.
- Tianmushan Laboratory, 311115, Hangzhou, China.
| | - Junfeng Wang
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China
| | - Yuesheng Li
- Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, 430074, Wuhan, China.
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3
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Calvanese Strinati M, Conti C. Hyperscaling in the Coherent Hyperspin Machine. PHYSICAL REVIEW LETTERS 2024; 132:017301. [PMID: 38242655 DOI: 10.1103/physrevlett.132.017301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Revised: 11/06/2023] [Accepted: 12/06/2023] [Indexed: 01/21/2024]
Abstract
Classical and quantum systems are used to simulate the Ising Hamiltonian, an essential component in large-scale optimization and machine learning. However, as the system size increases, devices like quantum annealers and coherent Ising machines face an exponential drop in their success rate. Here, we introduce a novel approach involving high-dimensional embeddings of the Ising Hamiltonian and a technique called "dimensional annealing" to counteract the decrease in performance. This approach leads to an exponential improvement in the success rate and other performance metrics, slowing down the decline in performance as the system size grows. A thorough examination of convergence dynamics in high-performance computing validates the new methodology. Additionally, we suggest practical implementations using technologies like coherent Ising machines, all-optical systems, and hybrid digital systems. The proposed hyperscaling heuristics can also be applied to other quantum or classical Ising devices by adjusting parameters such as nonlinear gain, loss, and nonlocal couplings.
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Affiliation(s)
| | - Claudio Conti
- Centro Ricerche Enrico Fermi (CREF), Via Panisperna 89a, 00184 Rome, Italy
- Physics Department, Sapienza University of Rome, 00185 Rome, Italy
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4
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King AD, Coraux J, Canals B, Rougemaille N. Magnetic Arctic Circle in a Square Ice Qubit Lattice. PHYSICAL REVIEW LETTERS 2023; 131:166701. [PMID: 37925737 DOI: 10.1103/physrevlett.131.166701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Accepted: 09/15/2023] [Indexed: 11/07/2023]
Abstract
Under certain boundary conditions, the square ice model exhibits a phase separation in which the core of the system is disordered while its outer region remains ordered. This phenomenon, known as the "arctic circle," has been studied theoretically in combinatorial mathematics and statistical mechanics. Here, we realize the physics of the arctic circle experimentally for the first time, using a programmable lattice of superconducting qubits, and investigate its properties under the prism of a highly frustrated magnet. Our work reveals two unexpected properties. First, the disordered spin manifold confined within the arctic curve is a spin liquid whose average spin texture resembles that of an antivortex, i.e., it is a topologically charged Coulomb phase. Second, monopole quasiparticle excitations, which are totally absent in theoretical works, can be isolated in a phase-separated system. Remarkably, a monopole segregation mechanism is observed, in which the monopoles are sorted according to the magnetic charge and magnetic moment they carry, without the application of an external driving force.
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Affiliation(s)
- A D King
- D-Wave Systems, Burnaby, British Columbia V5G 4M9, Canada
| | - J Coraux
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - B Canals
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
| | - N Rougemaille
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble 38000, France
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5
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Pelofske E, Hahn G, Djidjev H. Initial State Encoding via Reverse Quantum Annealing and H-Gain Features. IEEE TRANSACTIONS ON QUANTUM ENGINEERING 2023; 4:3102221. [PMID: 38179578 PMCID: PMC10765165 DOI: 10.1109/tqe.2023.3319586] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/06/2024]
Abstract
Quantum annealing is a specialized type of quantum computation that aims to use quantum fluctuations in order to obtain global minimum solutions of combinatorial optimization problems. Programmable D-Wave quantum annealers are available as cloud computing resources, which allow users low-level access to quantum annealing control features. In this article, we are interested in improving the quality of the solutions returned by a quantum annealer by encoding an initial state into the annealing process. We explore twoD-Wave features that allow one toencode such an initialstate: the reverse annealing (RA) and theh-gain(HG)features.RAaimstorefineaknownsolutionfollowinganannealpathstartingwithaclassical state representing a good solution, going backward to a point where a transverse field is present, and then finishing the annealing process with a forward anneal. The HG feature allows one to put a time-dependent weighting scheme on linear (h ) biases of the Hamiltonian, and we demonstrate that this feature likewise can be used to bias the annealing to start from an initial state. We also consider a hybrid method consisting of a backward phase resembling RA and a forward phase using the HG initial state encoding. Importantly, we investigate the idea of iteratively applying RA and HG to a problem, with the goal of monotonically improving on an initial state that is not optimal. The HG encoding technique is evaluated on a variety of input problems including the edge-weighted maximum cut problem and the vertex-weighted maximum clique problem, demonstrating that the HG technique is a viable alternative to RA for some problems. We also investigate how the iterative procedures perform for both RA and HG initial state encodings on random whole-chip spin glasses with the native hardware connectivity of the D-Wave Chimera and Pegasus chips.
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Affiliation(s)
- Elijah Pelofske
- CCS-3 Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545 USA
| | - Georg Hahn
- Harvard T. H. Chan School of Public Health, Harvard University, Boston, MA 02115 USA
| | - Hristo Djidjev
- CCS-3 Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545 USA
- Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, 1040 Sofia, Bulgaria
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6
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King AD, Raymond J, Lanting T, Harris R, Zucca A, Altomare F, Berkley AJ, Boothby K, Ejtemaee S, Enderud C, Hoskinson E, Huang S, Ladizinsky E, MacDonald AJR, Marsden G, Molavi R, Oh T, Poulin-Lamarre G, Reis M, Rich C, Sato Y, Tsai N, Volkmann M, Whittaker JD, Yao J, Sandvik AW, Amin MH. Quantum critical dynamics in a 5,000-qubit programmable spin glass. Nature 2023; 617:61-66. [PMID: 37076625 DOI: 10.1038/s41586-023-05867-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 02/20/2023] [Indexed: 04/21/2023]
Abstract
Experiments on disordered alloys1-3 suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Owing to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quantum optimization4-13. Here we achieve this goal by realizing quantum-critical spin-glass dynamics on thousands of qubits with a superconducting quantum annealer. We first demonstrate quantitative agreement between quantum annealing and time evolution of the Schrödinger equation in small spin glasses. We then measure dynamics in three-dimensional spin glasses on thousands of qubits, for which classical simulation of many-body quantum dynamics is intractable. We extract critical exponents that clearly distinguish quantum annealing from the slower stochastic dynamics of analogous Monte Carlo algorithms, providing both theoretical and experimental support for large-scale quantum simulation and a scaling advantage in energy optimization.
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Affiliation(s)
- Andrew D King
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada.
| | - Jack Raymond
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | | | - Alex Zucca
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | | | - Kelly Boothby
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Sara Ejtemaee
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Colin Enderud
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | | | | | | | | | - Reza Molavi
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Travis Oh
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | - Mauricio Reis
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Chris Rich
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Yuki Sato
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Nicholas Tsai
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | - Mark Volkmann
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | - Jason Yao
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada
| | | | - Mohammad H Amin
- D-Wave Quantum Inc., Burnaby, British Columbia, Canada.
- Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada.
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7
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Sandt R, Spatschek R. Efficient low temperature Monte Carlo sampling using quantum annealing. Sci Rep 2023; 13:6754. [PMID: 37185931 PMCID: PMC10130176 DOI: 10.1038/s41598-023-33828-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 04/19/2023] [Indexed: 05/17/2023] Open
Abstract
Quantum annealing is an efficient technology to determine ground state configurations of discrete binary optimization problems, described through Ising Hamiltonians. Here we show that-at very low computational cost-finite temperature properties can be calculated. The approach is most efficient at low temperatures, where conventional approaches like Metropolis Monte Carlo sampling suffer from high rejection rates and therefore large statistical noise. To demonstrate the general approach, we apply it to spin glasses and Ising chains.
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Affiliation(s)
- Roland Sandt
- Structure and Function of Materials, Institute of Energy and Climate Research, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany.
| | - Robert Spatschek
- Structure and Function of Materials, Institute of Energy and Climate Research, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany
- JARA-ENERGY, 52425, Jülich, Germany
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8
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Sandt R, Le Bouar Y, Spatschek R. Quantum annealing for microstructure equilibration with long-range elastic interactions. Sci Rep 2023; 13:6036. [PMID: 37055543 PMCID: PMC10102158 DOI: 10.1038/s41598-023-33232-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 04/10/2023] [Indexed: 04/15/2023] Open
Abstract
We demonstrate the use and benefits of quantum annealing approaches for the determination of equilibrated microstructures in shape memory alloys and other materials with long-range elastic interaction between coherent grains and their different martensite variants and phases. After a one dimensional illustration of the general approach, which requires to formulate the energy of the system in terms of an Ising Hamiltonian, we use distant dependent elastic interactions between grains to predict the variant selection for different transformation eigenstrains. The results and performance of the computations are compared to classical algorithms, demonstrating that the new approach can lead to a significant acceleration of the simulations. Beyond a discretization using simple cuboidal elements, also a direct representation of arbitrary microstructures is possible, allowing fast simulations with currently up to several thousand grains.
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Affiliation(s)
- Roland Sandt
- Structure and Function of Materials, Institute of Energy and Climate Research, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany.
| | - Yann Le Bouar
- Université Paris-Saclay, ONERA, CNRS, Laboratoire d'Etude des Microstructures, 92320, Châtillon, France
| | - Robert Spatschek
- Structure and Function of Materials, Institute of Energy and Climate Research, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany
- JARA-ENERGY, 52425, Jülich, Germany
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9
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Sinha A. Development of research network on Quantum Annealing Computation and Information using Google Scholar data. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210413. [PMID: 36463919 DOI: 10.1098/rsta.2021.0413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2022] [Accepted: 09/08/2022] [Indexed: 06/17/2023]
Abstract
We build and analyse the network of 100 top-cited nodes (research papers and books from Google Scholar; the strength or citation of the nodes range from about 44 000 up to 100) starting in early 1980 until last year. These searched publications (papers and books) are based on Quantum Annealing Computation and Information categorized into four different sets: (A) Quantum/Transverse Field Spin Glass Model, (B) Quantum Annealing, (C) Quantum Adiabatic Computation and (D) Quantum Computation Information in the title or abstract of the searched publications. We fitted the growth in the annual number of publication ([Formula: see text]) in each of these four categories, A-D, to the form [Formula: see text] where [Formula: see text] denotes the time in years. We found the scaling time [Formula: see text] to be of the order of about 10 years for categories A and C, whereas [Formula: see text] is of the order of about 5 years for categories B and D. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Antika Sinha
- Department of Computer Science, Asutosh College, Kolkata, West Bengal 700026, India
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10
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Rajak A, Suzuki S, Dutta A, Chakrabarti BK. Quantum annealing: an overview. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210417. [PMID: 36463923 DOI: 10.1098/rsta.2021.0417] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 08/22/2022] [Indexed: 06/17/2023]
Abstract
In this review, after providing the basic physical concept behind quantum annealing (or adiabatic quantum computation), we present an overview of some recent theoretical as well as experimental developments pointing to the issues which are still debated. With a brief discussion on the fundamental ideas of continuous and discontinuous quantum phase transitions, we discuss the Kibble-Zurek scaling of defect generation following a ramping of a quantum many body system across a quantum critical point. In the process, we discuss associated models, both pure and disordered, and shed light on implementations and some recent applications of the quantum annealing protocols. Furthermore, we discuss the effect of environmental coupling on quantum annealing. Some possible ways to speed up the annealing protocol in closed systems are elaborated upon: we especially focus on the recipes to avoid discontinuous quantum phase transitions occurring in some models where energy gaps vanish exponentially with the system size. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Atanu Rajak
- Department of Physics, Presidency University, Kolkata 700073, India
| | - Sei Suzuki
- Department of Liberal Arts, Saitama Medical University, Moroyama, Saitama 350-0495, Japan
| | - Amit Dutta
- Indian Institute of Technology Kanpur, Kanpur 208016, India
| | - Bikas K Chakrabarti
- Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India
- Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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11
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Lotshaw PC, Xu H, Khalid B, Buchs G, Humble TS, Banerjee A. Simulations of frustrated Ising Hamiltonians using quantum approximate optimization. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210414. [PMID: 36463920 PMCID: PMC9719794 DOI: 10.1098/rsta.2021.0414] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2022] [Accepted: 09/15/2022] [Indexed: 06/17/2023]
Abstract
Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground-state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements ([Formula: see text]) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Phillip C. Lotshaw
- Quantum Information Sciences Section, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - Hanjing Xu
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, USA
| | - Bilal Khalid
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, USA
- Quantum Science Center, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette - 47907, USA
| | - Gilles Buchs
- Quantum Information Sciences Section, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
- Quantum Science Center, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA
| | - Travis S. Humble
- Quantum Information Sciences Section, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
- Quantum Science Center, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA
| | - Arnab Banerjee
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, IN 47907, USA
- Quantum Science Center, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA
- Department of Physics and Astronomy, Purdue University, West Lafayette - 47907, USA
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12
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Yarkoni S, Raponi E, Bäck T, Schmitt S. Quantum annealing for industry applications: introduction and review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:104001. [PMID: 36001953 DOI: 10.1088/1361-6633/ac8c54] [Citation(s) in RCA: 14] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2021] [Accepted: 08/24/2022] [Indexed: 06/15/2023]
Abstract
Quantum annealing (QA) is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale quantum processors that implement the QA algorithm for programmable use. Specifically, QA processors produced by D-Wave systems have been studied and tested extensively in both research and industrial settings across different disciplines. In this paper we provide a literature review of the theoretical motivations for QA as a heuristic quantum optimization algorithm, the software and hardware that is required to use such quantum processors, and the state-of-the-art applications and proofs-of-concepts that have been demonstrated using them. The goal of our review is to provide a centralized and condensed source regarding applications of QA technology. We identify the advantages, limitations, and potential of QA for both researchers and practitioners from various fields.
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13
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Mean field approximation for solving QUBO problems. PLoS One 2022; 17:e0273709. [PMID: 36041120 PMCID: PMC9427122 DOI: 10.1371/journal.pone.0273709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 08/11/2022] [Indexed: 11/19/2022] Open
Abstract
The Quadratic Unconstrained Binary Optimization (QUBO) problem is NP-hard. Some exact methods like the Branch-and-Bound algorithm are suitable for small problems. Some approximations like stochastic simulated annealing for discrete variables or mean-field annealing for continuous variables exist for larger ones, and quantum computers based on the quantum adiabatic annealing principle have also been developed. Here we show that the mean-field approximation of the quantum adiabatic annealing leads to equations similar to those of thermal mean-field annealing. However, a new type of sigmoid function replaces the thermal one. The new mean-field quantum adiabatic annealing can replicate the best-known cut values on some of the popular benchmark Maximum Cut problems.
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14
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Kudo K. Localization Detection Based on Quantum Dynamics. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1085. [PMID: 36010749 PMCID: PMC9407476 DOI: 10.3390/e24081085] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Revised: 08/04/2022] [Accepted: 08/04/2022] [Indexed: 06/15/2023]
Abstract
Detecting many-body localization (MBL) typically requires the calculation of high-energy eigenstates using numerical approaches. This study investigates methods that assume the use of a quantum device to detect disorder-induced localization. Numerical simulations for small systems demonstrate how the magnetization and twist overlap, which can be easily obtained from the measurement of qubits in a quantum device, changing from the thermal phase to the localized phase. The twist overlap evaluated using the wave function at the end of the time evolution behaves similarly to the one evaluated with eigenstates in the middle of the energy spectrum under a specific condition. The twist overlap evaluated using the wave function after time evolution for many disorder realizations is a promising probe for detecting MBL in quantum computing approaches.
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Affiliation(s)
- Kazue Kudo
- Department of Computer Science, Ochanomizu University, Tokyo 112-8610, Japan;
- Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
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15
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Endo K, Matsuda Y, Tanaka S, Muramatsu M. A phase-field model by an Ising machine and its application to the phase-separation structure of a diblock polymer. Sci Rep 2022; 12:10794. [PMID: 35750879 PMCID: PMC9232493 DOI: 10.1038/s41598-022-14735-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2021] [Accepted: 06/13/2022] [Indexed: 11/09/2022] Open
Abstract
A novel model to be applied to next-generation accelerators, Ising machines, is formulated on the basis of the phase-field model of the phase-separation structure of a diblock polymer. Recently, Ising machines including quantum annealing machines, attract overwhelming attention as a technology that opens up future possibilities. On the other hand, the phase-field model has demonstrated its high performance in material development, though it takes a long time to achieve equilibrium. Although the convergence time problem might be solved by the next-generation accelerators, no solution has been proposed. In this study, we show the calculation of the phase-separation structure of a diblock polymer as the equilibrium state using phase-field model by an actual Ising machine. The proposed new model brings remarkable acceleration in obtaining the phase-separation structure. Our model can be solved on a large-scale quantum annealing machine. The significant acceleration of the phase-field simulation by the quantum technique pushes the material development to the next stage.
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Affiliation(s)
- Katsuhiro Endo
- Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan.
| | - Yoshiki Matsuda
- Fixstars, 3-1-1 Shibaura, Minato-ku, Tokyo, 108-0023, Japan.,Green Computing System Research Organization, Waseda University, 27 Wasedacho, Shinjuku-ku, Tokyo, 162-0042, Japan
| | - Shu Tanaka
- Green Computing System Research Organization, Waseda University, 27 Wasedacho, Shinjuku-ku, Tokyo, 162-0042, Japan.,Department of Applied Physics and Physico-Informatics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan
| | - Mayu Muramatsu
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan
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16
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Oshiyama H, Suzuki S, Shibata N. Classical Simulation and Theory of Quantum Annealing in a Thermal Environment. PHYSICAL REVIEW LETTERS 2022; 128:170502. [PMID: 35570457 DOI: 10.1103/physrevlett.128.170502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Revised: 02/21/2022] [Accepted: 03/22/2022] [Indexed: 06/15/2023]
Abstract
We study quantum annealing in the quantum Ising model coupled to a thermal environment. When the speed of quantum annealing is sufficiently slow, the system evolves following the instantaneous thermal equilibrium. This quasistatic and isothermal evolution, however, fails near the end of annealing because the relaxation time grows infinitely, therefore yielding excess energy from the thermal equilibrium. We develop a phenomenological theory based on this picture and derive a scaling relation of the excess energy after annealing. The theoretical results are numerically confirmed using a novel non-Markovian method that we recently proposed based on a path-integral representation of the reduced density matrix and the infinite time evolving block decimation. In addition, we discuss crossovers from weak to strong coupling as well as from the adiabatic to quasistatic regime, and propose experiments on the D-Wave quantum annealer.
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Affiliation(s)
- Hiroki Oshiyama
- Department of Physics, Tohoku University, Sendai 980-8578, Japan
| | - Sei Suzuki
- Department of Liberal Arts, Saitama Medical University, Moroyama, Saitama 350-0495, Japan
| | - Naokazu Shibata
- Department of Physics, Tohoku University, Sendai 980-8578, Japan
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17
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Optimizing quantum annealing schedules with Monte Carlo tree search enhanced with neural networks. NAT MACH INTELL 2022. [DOI: 10.1038/s42256-022-00446-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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18
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Relaxation of the Ising spin system coupled to a bosonic bath and the time dependent mean field equation. PLoS One 2022; 17:e0264412. [PMID: 35226670 PMCID: PMC8884623 DOI: 10.1371/journal.pone.0264412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2021] [Accepted: 02/10/2022] [Indexed: 11/30/2022] Open
Abstract
The Ising model does not have strictly defined dynamics, only a spectrum. There are different ways to equip it with time dependence, e.g., the Glauber or the Kawasaki dynamics, which are both stochastic, but it means there is a master equation that can also describe their dynamics. These equations can be derived from the Redfield equation, where the spin system is weakly coupled to a bosonic bath. In this paper, we investigate the temperature dependence of the relaxation time of a Glauber-type master equation, especially in the case of the fully connected, uniform Ising model. The finite-size effects were analyzed with a reduced master equation and the thermodynamic limit with a time-dependent mean field equation.
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19
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King AD, Nisoli C, Dahl ED, Poulin-Lamarre G, Lopez-Bezanilla A. Qubit spin ice. Science 2021; 373:576-580. [PMID: 34326242 DOI: 10.1126/science.abe2824] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 06/17/2021] [Indexed: 11/02/2022]
Abstract
Artificial spin ices are frustrated spin systems that can be engineered, in which fine tuning of geometry and topology has allowed the design and characterization of exotic emergent phenomena at the constituent level. Here, we report a realization of spin ice in a lattice of superconducting qubits. Unlike conventional artificial spin ice, our system is disordered by both quantum and thermal fluctuations. The ground state is classically described by the ice rule, and we achieved control over a fragile degeneracy point, leading to a Coulomb phase. The ability to pin individual spins allows us to demonstrate Gauss's law for emergent effective monopoles in two dimensions. The demonstrated qubit control lays the groundwork for potential future study of topologically protected artificial quantum spin liquids.
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Affiliation(s)
- Andrew D King
- D-Wave Systems, Burnaby, British Columbia V5G 4M9, Canada.
| | - Cristiano Nisoli
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA.
| | - Edward D Dahl
- D-Wave Systems, Burnaby, British Columbia V5G 4M9, Canada
- Associate Laboratory Directorate for Simulation and Computation, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
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20
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Quantum phases of matter on a 256-atom programmable quantum simulator. Nature 2021; 595:227-232. [PMID: 34234334 DOI: 10.1038/s41586-021-03582-4] [Citation(s) in RCA: 127] [Impact Index Per Article: 42.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 04/26/2021] [Indexed: 11/09/2022]
Abstract
Motivated by far-reaching applications ranging from quantum simulations of complex processes in physics and chemistry to quantum information processing1, a broad effort is currently underway to build large-scale programmable quantum systems. Such systems provide insights into strongly correlated quantum matter2-6, while at the same time enabling new methods for computation7-10 and metrology11. Here we demonstrate a programmable quantum simulator based on deterministically prepared two-dimensional arrays of neutral atoms, featuring strong interactions controlled by coherent atomic excitation into Rydberg states12. Using this approach, we realize a quantum spin model with tunable interactions for system sizes ranging from 64 to 256 qubits. We benchmark the system by characterizing high-fidelity antiferromagnetically ordered states and demonstrating quantum critical dynamics consistent with an Ising quantum phase transition in (2 + 1) dimensions13. We then create and study several new quantum phases that arise from the interplay between interactions and coherent laser excitation14, experimentally map the phase diagram and investigate the role of quantum fluctuations. Offering a new lens into the study of complex quantum matter, these observations pave the way for investigations of exotic quantum phases, non-equilibrium entanglement dynamics and hardware-efficient realization of quantum algorithms.
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21
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King AD, Raymond J, Lanting T, Isakov SV, Mohseni M, Poulin-Lamarre G, Ejtemaee S, Bernoudy W, Ozfidan I, Smirnov AY, Reis M, Altomare F, Babcock M, Baron C, Berkley AJ, Boothby K, Bunyk PI, Christiani H, Enderud C, Evert B, Harris R, Hoskinson E, Huang S, Jooya K, Khodabandelou A, Ladizinsky N, Li R, Lott PA, MacDonald AJR, Marsden D, Marsden G, Medina T, Molavi R, Neufeld R, Norouzpour M, Oh T, Pavlov I, Perminov I, Prescott T, Rich C, Sato Y, Sheldan B, Sterling G, Swenson LJ, Tsai N, Volkmann MH, Whittaker JD, Wilkinson W, Yao J, Neven H, Hilton JP, Ladizinsky E, Johnson MW, Amin MH. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nat Commun 2021; 12:1113. [PMID: 33602927 PMCID: PMC7892843 DOI: 10.1038/s41467-021-20901-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2020] [Accepted: 12/22/2020] [Indexed: 11/09/2022] Open
Abstract
The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of geometrically frustrated magnets in which topological phenomena can emerge from competition between quantum and thermal fluctuations. Here we report on experimental observations of equilibration in such simulations, measured on up to 1440 qubits with microsecond resolution. By initializing the system in a state with topological obstruction, we observe quantum annealing (QA) equilibration timescales in excess of one microsecond. Measurements indicate a dynamical advantage in the quantum simulation compared with spatially local update dynamics of path-integral Monte Carlo (PIMC). The advantage increases with both system size and inverse temperature, exceeding a million-fold speedup over an efficient CPU implementation. PIMC is a leading classical method for such simulations, and a scaling advantage of this type was recently shown to be impossible in certain restricted settings. This is therefore an important piece of experimental evidence that PIMC does not simulate QA dynamics even for sign-problem-free Hamiltonians, and that near-term quantum devices can be used to accelerate computational tasks of practical relevance.
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Affiliation(s)
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Ryan Li
- D-Wave Systems, Burnaby, BC, Canada
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | - Mohammad H Amin
- D-Wave Systems, Burnaby, BC, Canada.,Department of Physics, Simon Fraser University, Burnaby, BC, Canada
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22
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Carcy C, Hercé G, Tenart A, Roscilde T, Clément D. Certifying the Adiabatic Preparation of Ultracold Lattice Bosons in the Vicinity of the Mott Transition. PHYSICAL REVIEW LETTERS 2021; 126:045301. [PMID: 33576669 DOI: 10.1103/physrevlett.126.045301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2020] [Accepted: 01/08/2021] [Indexed: 06/12/2023]
Abstract
We present a joint experimental and theoretical analysis to assess the adiabatic experimental preparation of ultracold bosons in optical lattices aimed at simulating the three-dimensional Bose-Hubbard model. Thermometry of lattice gases is realized from the superfluid to the Mott regime by combining the measurement of three-dimensional momentum-space densities with ab initio quantum Monte Carlo (QMC) calculations of the same quantity. The measured temperatures are in agreement with isentropic lines reconstructed via QMC for the experimental parameters of interest, with a conserved entropy per particle of S/N=0.8(1)k_{B}. In addition, the Fisher information associated with this thermometry method shows that the latter is most accurate in the critical regime close to the Mott transition, as confirmed in the experiment. These results prove that equilibrium states of the Bose-Hubbard model-including those in the quantum-critical regime above the Mott transition-can be adiabatically prepared in cold-atom apparatus.
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Affiliation(s)
- Cécile Carcy
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Gaétan Hercé
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Antoine Tenart
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Tommaso Roscilde
- Université de Lyon, Ens de Lyon, Université Claude Bernard and CNRS, Laboratoire de Physique, F-69342 Lyon, France
| | - David Clément
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
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23
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Winci W, Buffoni L, Sadeghi H, Khoshaman A, Andriyash E, Amin MH. A path towards quantum advantage in training deep generative models with quantum annealers. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2020. [DOI: 10.1088/2632-2153/aba220] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
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24
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Schmidt M, Kellermann N, Zimmer FM. Transverse field effects on the competition between antiferromagnetic and cluster spin-glass phases. Phys Rev E 2020; 102:032139. [PMID: 33075931 DOI: 10.1103/physreve.102.032139] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Accepted: 09/07/2020] [Indexed: 11/07/2022]
Abstract
We investigate a disordered cluster Ising antiferromagnet in the presence of a transverse field. By adopting a replica cluster mean-field framework, we analyze the role of quantum fluctuations in a model with competing short-range antiferromagnetic and intercluster disordered interactions. The model exhibits paramagnetic (PM), antiferromagnetic (AF), and cluster spin-glass (CSG) phases, which are separated by thermal and quantum phase transitions. A scenario of strong competition between AF and CSG unveils a number of interesting phenomena induced by quantum fluctuations, including a quantum PM state and quantum driven criticality. The latter occurs when the thermally driven PM-AF discontinuous phase transition becomes continuous at strong transverse fields. Analogous phenomena have been reported in a number of systems, but a description of underlying mechanisms is still required. Our results indicate that quantum driven criticality can be found in a highly competitive regime of disordered antiferromagnets, which is in consonance with recent findings in spin models with competing interactions.
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Affiliation(s)
- M Schmidt
- Departamento de Física, Universidade Federal de Santa Maria, 97105-900 Santa Maria, RS, Brazil
| | - N Kellermann
- Departamento de Física, Universidade Federal de Santa Maria, 97105-900 Santa Maria, RS, Brazil
| | - F M Zimmer
- Instituto de Física, Universidade Federal de Mato Grosso do Sul, 79070-900 Campo Grande, MS, Brazil
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25
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Jałowiecki K, Więckowski A, Gawron P, Gardas B. Parallel in time dynamics with quantum annealers. Sci Rep 2020; 10:13534. [PMID: 32782306 PMCID: PMC7421488 DOI: 10.1038/s41598-020-70017-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2020] [Accepted: 06/24/2020] [Indexed: 11/27/2022] Open
Abstract
Recent years have witnessed an unprecedented increase in experiments and hybrid simulations involving quantum computers. In particular, quantum annealers. There exist a plethora of algorithms promising to outperform classical computers in the near-term future. Here, we propose a parallel in time approach to simulate dynamical systems designed to be executed already on present-day quantum annealers. In essence, purely classical methods for solving dynamics systems are serial. Therefore, their parallelization is substantially limited. In the presented approach, however, the time evolution is rephrased as a ground-state search of a classical Ising model. Such a problem is solved intrinsically in parallel by quantum computers. The main idea is exemplified by simulating the Rabi oscillations generated by a two-level quantum system (i.e. qubit) experimentally.
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Affiliation(s)
- Konrad Jałowiecki
- Institute of Physics, University of Silesia, 75 Pułku Piechoty 1, 41-500, Chorzów, Poland.
| | - Andrzej Więckowski
- Department of Theoretical Physics, Faculty of Fundamental Problems of Technology, Wrocław University of Science and Technology, 50-370, Wrocław, Poland
| | - Piotr Gawron
- Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100, Gliwice, Poland
- AstroCeNT, Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Rektorska 4, 00-614, Warsaw, Poland
| | - Bartłomiej Gardas
- Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100, Gliwice, Poland
- Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348, Kraków, Poland
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26
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Lysne NK, Kuper KW, Poggi PM, Deutsch IH, Jessen PS. Small, Highly Accurate Quantum Processor for Intermediate-Depth Quantum Simulations. PHYSICAL REVIEW LETTERS 2020; 124:230501. [PMID: 32603170 DOI: 10.1103/physrevlett.124.230501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Revised: 05/01/2020] [Accepted: 05/11/2020] [Indexed: 06/11/2023]
Abstract
Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. With current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when simulating complex systems likely to exhibit quantum chaos. Here we describe a quantum simulator based on the combined electron-nuclear spins of individual Cs atoms, and its use to run high fidelity simulations of three different model Hamiltonians for >100 time steps. While not scalable to exponentially large Hilbert spaces, it provides the accuracy and programmability required to explore the interplay between dynamics, imperfections, and accuracy in quantum simulation.
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Affiliation(s)
- Nathan K Lysne
- Center for Quantum Information and Control, Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | - Kevin W Kuper
- Center for Quantum Information and Control, Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | - Pablo M Poggi
- Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Ivan H Deutsch
- Center for Quantum Information and Control, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Poul S Jessen
- Center for Quantum Information and Control, Wyant College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
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27
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Weinberg P, Tylutki M, Rönkkö JM, Westerholm J, Åström JA, Manninen P, Törmä P, Sandvik AW. Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device. PHYSICAL REVIEW LETTERS 2020; 124:090502. [PMID: 32202854 DOI: 10.1103/physrevlett.124.090502] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Accepted: 02/10/2020] [Indexed: 05/02/2023]
Abstract
We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on L×L lattices with L≤32. Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal L dependent annealing rate v for which the two quantities are minimized. The results are well described by a phenomenological model with two powers of v and L-dependent prefactors to describe the competing effects of reduced quantum fluctuations (for which we see evidence of the Kibble-Zurek mechanism) and increasing noise impact when v is lowered. The same scaling form also describes results of numerical solutions of a transverse-field Ising model with the spins coupled to noise sources. We explain why the optimal annealing time is much longer than the coherence time of the individual qubits.
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Affiliation(s)
- Phillip Weinberg
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Marek Tylutki
- Department of Applied Physics, Aalto University School of Science, FI-00076 Aalto, Finland
- Faculty of Physics, Warsaw University of Technology, Ulica Koszykowa 75, PL-00662 Warsaw, Poland
| | - Jami M Rönkkö
- CSC-IT Center for Science, P.O. Box 405, FIN-02101 Espoo, Finland
| | - Jan Westerholm
- Faculty of Science and Engineering, Åbo Akademi University, Vattenborgsvägen 3, FI 20500 Åbo, Finland
| | - Jan A Åström
- CSC-IT Center for Science, P.O. Box 405, FIN-02101 Espoo, Finland
| | - Pekka Manninen
- CSC-IT Center for Science, P.O. Box 405, FIN-02101 Espoo, Finland
| | - Päivi Törmä
- Department of Applied Physics, Aalto University School of Science, FI-00076 Aalto, Finland
| | - Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Beijing National Laboratory of Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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28
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Urbina F. Equilibrium and nonequilibrium in the three-dimensional Q2R cellular automata. Phys Rev E 2020; 101:012111. [PMID: 32069625 DOI: 10.1103/physreve.101.012111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Indexed: 06/10/2023]
Abstract
I study the equilibrium and nonequilibrium dynamics of a conservative and reversible Q2R cellular automata. This system exhibits a configuration space with 2^{2N} states, which grows with the size of the system. In this context, for small size, the phase space has fixed points and cycles. Through numerical studies and using a statistical approach, I can observe stable and unstable behaviors as well as a phase transition around a critical energy E_{c}. I introduce a coupling constant as a perturbation to the classic Q2R model and show through the phase diagram how this modified model exhibits three different phases.
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Affiliation(s)
- Felipe Urbina
- Centro de Investigación DAiTA Lab, Facultad de Estudios Interdisciplinarios, Universidad Mayor, Santiago 7560913, Chile
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29
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Embedding Algorithms for Quantum Annealers with Chimera and Pegasus Connection Topologies. LECTURE NOTES IN COMPUTER SCIENCE 2020. [PMCID: PMC7295343 DOI: 10.1007/978-3-030-50743-5_10] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We propose two new algorithms – Spring-Based MinorMiner (SPMM) and Clique-Based MinorMiner (CLMM) – which take as input the connectivity graph of a Quadratic Unconstrained Binary Optimization (QUBO) problem and produce as output an embedding of the input graph on a host graph that models the topology of a quantum computing device. As host graphs, we take the Chimera graph and the Pegasus graph, which are the topology graphs of D-Wave’s 2000 qubit (first introduced in 2017) and 5000 qubit (expected 2020) quantum annealer devices, respectively. We evaluate our algorithms on a large set of random graph QUBO inputs (Erdős-Rényi \documentclass[12pt]{minimal}
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\begin{document}$$G_{n,p}$$\end{document}, Barabási-Albert and d-regular graphs) on both host topologies against other embedding algorithms. For the Pegasus topology, we find that CLMM outperforms all other algorithms at edge densities larger than 0.08, while SPMM wins at edge densities smaller than 0.08 for Erdős-Rényi graphs, with very similar transition densities for the other graph classes. Surprisingly, the standard D-Wave MinorMiner embedding algorithm – while also getting slightly outperformed by SPMM for sparse and very dense graphs on Chimera – does not manage to extend its overall good performance on Chimera to Pegasus as it fails to embed even medium-density graphs on 175–180 nodes which are known to have clique embeddings on Pegasus.
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30
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Aurell E, Domínguez E, Machado D, Mulet R. Theory of Nonequilibrium Local Search on Random Satisfaction Problems. PHYSICAL REVIEW LETTERS 2019; 123:230602. [PMID: 31868433 DOI: 10.1103/physrevlett.123.230602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/08/2019] [Revised: 10/08/2019] [Indexed: 06/10/2023]
Abstract
We study local search algorithms to solve instances of the random k-satisfiability problem, equivalent to finding (if they exist) zero-energy ground states of statistical models with disorder on random hypergraphs. It is well known that the best such algorithms are akin to nonequilibrium processes in a high-dimensional space. In particular, algorithms known as focused, and which do not obey detailed balance, outperform simulated annealing and related methods in the task of finding the solution to a complex satisfiability problem, that is to find (exactly or approximately) the minimum in a complex energy landscape. A physical question of interest is if the dynamics of these processes can be well predicted by the well-developed theory of equilibrium Gibbs states. While it has been known empirically for some time that this is not the case, an alternative systematic theory that does so has been lacking. In this Letter we introduce such a theory based on the recently developed technique of cavity master equations and test it on the paradigmatic random 3-satisfiability problem. Our theory predicts the qualitative form of the phase boundary between the satisfiable (SAT) and unsatisfiable (UNSAT) region of the phase diagram where the numerics of a focused Metropolis search and cavity master equation cannot be distinguished.
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Affiliation(s)
- Erik Aurell
- Department of Computational Science and Technology, AlbaNova University Center, SE-106 91 Stockholm, Sweden
| | - Eduardo Domínguez
- Group of Complex Systems and Statistical Physics. Department of Theoretical Physics, Physics Faculty, University of Havana, CP 10400 La Habana. Cuba
| | - David Machado
- Group of Complex Systems and Statistical Physics. Department of Theoretical Physics, Physics Faculty, University of Havana, CP 10400 La Habana. Cuba
| | - Roberto Mulet
- Group of Complex Systems and Statistical Physics. Department of Theoretical Physics, Physics Faculty, University of Havana, CP 10400 La Habana. Cuba
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31
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Graß T. Quantum Annealing with Longitudinal Bias Fields. PHYSICAL REVIEW LETTERS 2019; 123:120501. [PMID: 31633984 DOI: 10.1103/physrevlett.123.120501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2019] [Indexed: 06/10/2023]
Abstract
Quantum annealing aims at solving hard computational problems through adiabatic state preparation. Here, I propose to use inhomogeneous longitudinal magnetic fields to enhance the efficiency of the annealing. Such fields are able to bias the annealing dynamics into the desired solution, and in many cases, suitable field configurations can be found iteratively. Alternatively, the longitudinal fields can also be applied as an antibias which filters out unwanted contributions from the final state. This strategy is particularly well suited for instances which are difficult to solve within the standard quantum annealing approach. By numerically simulating the dynamics for small instances of the exact cover problem, the performance of these different strategies is investigated.
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Affiliation(s)
- Tobias Graß
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland, 20742, USA and ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
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32
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Okada S, Ohzeki M, Taguchi S. Efficient partition of integer optimization problems with one-hot encoding. Sci Rep 2019; 9:13036. [PMID: 31506502 PMCID: PMC6737027 DOI: 10.1038/s41598-019-49539-6] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2019] [Accepted: 08/27/2019] [Indexed: 12/03/2022] Open
Abstract
Quantum annealing is a heuristic algorithm for solving combinatorial optimization problems, and hardware for implementing this algorithm has been developed by D-Wave Systems Inc. The current version of the D-Wave quantum annealer can solve unconstrained binary optimization problems with a limited number of binary variables. However, the cost functions of several practical problems are defined by a large number of integer variables. To solve these problems using the quantum annealer, integer variables are generally binarized with one-hot encoding, and the binarized problem is partitioned into small subproblems. However, the entire search space of the binarized problem is considerably larger than that of the original integer problem and is dominated by infeasible solutions. Therefore, to efficiently solve large optimization problems with one-hot encoding, partitioning methods that extract subproblems with as many feasible solutions as possible are required. In this study, we propose two partitioning methods and demonstrate that they result in improved solutions.
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Affiliation(s)
- Shuntaro Okada
- Electronics R & I Division, DENSO CORPORATION, Tokyo, 108-0075, Japan.
- Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan.
| | - Masayuki Ohzeki
- Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan
- Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, 226-8503, Japan
- Sigma-i Co. Ltd., Tokyo, 108-0075, Japan
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33
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Silevitch DM, Tang C, Aeppli G, Rosenbaum TF. Tuning high-Q nonlinear dynamics in a disordered quantum magnet. Nat Commun 2019; 10:4001. [PMID: 31488819 PMCID: PMC6728381 DOI: 10.1038/s41467-019-11985-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2018] [Accepted: 08/13/2019] [Indexed: 11/09/2022] Open
Abstract
Quantum states cohere and interfere. Atoms arranged imperfectly in a solid rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent spin clusters by driving the system nonlinearly and measuring the resulting hole in the linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the Ising magnet LiHo0.045Y0.955F4, the quality factor Q for spectral holes can be as high as 100,000. We tune the dynamics by sweeping the Fano mixing parameter q through zero via the ac pump amplitude as well as a dc transverse field. The zero crossing of q is associated with a dissipationless response at the drive frequency. Identifying localized two-level systems in a dense and disordered magnet advances the search for qubit platforms emerging from strongly interacting, many-body systems.
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Affiliation(s)
- D M Silevitch
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California, 91125, USA
| | - C Tang
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California, 91125, USA
| | - G Aeppli
- Department of Physics, ETH Zurich, Zurich, CH-8093, Switzerland
- Department de Physique, EPF Lausanne, Lausanne, CH-1015, Switzerland
- Paul Scherrer Institut, Villigen, PSI, CH-5232, Switzerland
| | - T F Rosenbaum
- Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California, 91125, USA.
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34
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Yang LP, Jacob Z. Quantum critical detector: amplifying weak signals using discontinuous quantum phase transitions. OPTICS EXPRESS 2019; 27:10482-10494. [PMID: 31052907 DOI: 10.1364/oe.27.010482] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Accepted: 03/19/2019] [Indexed: 06/09/2023]
Abstract
We propose a quantum critical detector (QCD) to amplify weak input signals. Our detector exploits a first-order discontinuous quantum-phase-transition and exhibits giant sensitivity (χ ∝ N2) when biased at the critical point. We propose a model consisting of spins with long-range interactions coupled to a bosonic mode to describe the time-dynamics in the QCD. We numerically demonstrate dynamical features of the first order (discontinuous) quantum phase transition such as time-dependent quantum gain in a system with 80 interacting spins. We also show the linear scaling with the spin number N in both the quantum gain and the corresponding signal-to-quantum noise ratio during the time evolution of the device. Our work shows that engineering first order discontinuous quantum phase transitions can lead to a device application for metrology, weak signal amplification, and single photon detection.
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Gong M, Chen MC, Zheng Y, Wang S, Zha C, Deng H, Yan Z, Rong H, Wu Y, Li S, Chen F, Zhao Y, Liang F, Lin J, Xu Y, Guo C, Sun L, Castellano AD, Wang H, Peng C, Lu CY, Zhu X, Pan JW. Genuine 12-Qubit Entanglement on a Superconducting Quantum Processor. PHYSICAL REVIEW LETTERS 2019; 122:110501. [PMID: 30951346 DOI: 10.1103/physrevlett.122.110501] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2018] [Indexed: 06/09/2023]
Abstract
We report the preparation and verification of a genuine 12-qubit entanglement in a superconducting processor. The processor that we designed and fabricated has qubits lying on a 1D chain with relaxation times ranging from 29.6 to 54.6 μs. The fidelity of the 12-qubit entanglement was measured to be above 0.5544±0.0025, exceeding the genuine multipartite entanglement threshold by 21 statistical standard deviations. After thermal cycling, the 12-qubit state fidelity was further improved to be above 0.707±0.008. Our entangling circuit to generate linear cluster states is depth invariant in the number of qubits and uses single- and double-qubit gates instead of collective interactions. Our results are a substantial step towards large-scale random circuit sampling and scalable measurement-based quantum computing.
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Affiliation(s)
- Ming Gong
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Ming-Cheng Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Yarui Zheng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Shiyu Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Chen Zha
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Hui Deng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Zhiguang Yan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Hao Rong
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Yulin Wu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Shaowei Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Fusheng Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Youwei Zhao
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Futian Liang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Jin Lin
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Yu Xu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Cheng Guo
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Lihua Sun
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Anthony D Castellano
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Haohua Wang
- Department of Physics, Zhejiang University, Hangzhou, Zhejiang 310027, China
| | - Chengzhi Peng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Xiaobo Zhu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- Shanghai Branch, CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, 10 University of Science and Technology of China, Shanghai 201315, China
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Okada S, Ohzeki M, Terabe M, Taguchi S. Improving solutions by embedding larger subproblems in a D-Wave quantum annealer. Sci Rep 2019; 9:2098. [PMID: 30765767 PMCID: PMC6376019 DOI: 10.1038/s41598-018-38388-4] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Accepted: 12/27/2018] [Indexed: 11/18/2022] Open
Abstract
Quantum annealing is a heuristic algorithm that solves combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware implementation of this algorithm. However, in general, we cannot embed all the logical variables of a large-scale problem, since the number of available qubits is limited. In order to handle a large problem, qbsolv has been proposed as a method for partitioning the original large problem into subproblems that are embeddable in the D-Wave quantum annealer, and it then iteratively optimizes the subproblems using the quantum annealer. Multiple logical variables in the subproblem are simultaneously updated in this iterative solver, and using this approach we expect to obtain better solutions than can be obtained by conventional local search algorithms. Although embedding of large subproblems is essential for improving the accuracy of solutions in this scheme, the size of the subproblems are small in qbsolv since the subproblems are basically embedded by using an embedding of a complete graph even for sparse problem graphs. This means that the resource of the D-Wave quantum annealer is not exploited efficiently. In this paper, we propose a fast algorithm for embedding larger subproblems, and we show that better solutions are obtained efficiently by embedding larger subproblems.
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Affiliation(s)
- Shuntaro Okada
- Electronics R & I Division, DENSO Corporation, Tokyo, 103-6015, Japan. .,Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan.
| | - Masayuki Ohzeki
- Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan.,Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, 226-8503, Japan
| | - Masayoshi Terabe
- Electronics R & I Division, DENSO Corporation, Tokyo, 103-6015, Japan
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37
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Wang P, Huang K, Sun J, Hu J, Fu H, Lin X. Piezo-driven sample rotation system with ultra-low electron temperature. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2019; 90:023905. [PMID: 30831686 DOI: 10.1063/1.5083994] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2018] [Accepted: 01/19/2019] [Indexed: 06/09/2023]
Abstract
Piezo-driven rotator is convenient for tilted magnetic field experiments due to its precise angle control. However, the rotator itself and the sample mounted on it are difficult to be cooled down because of extra heat leaks and presumably bad thermal contacts from the piezo. Here, we report a piezo-driven sample rotation system designed for ultra-low temperature environment. The sample, as well as the rotating sample holder, can be cooled to as low as 25 mK by customized thermal links and thermal contacts. More importantly, the electron temperature in the electrical transport measurements can also be cooled down to 25 mK with the help of home-made filters. To demonstrate the application of our rotation system at ultra-low electron temperature, a measurement revealing tilt-induced localization and delocalization in the second Landau level of two-dimensional electron gas is provided.
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Affiliation(s)
- Pengjie Wang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Ke Huang
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jian Sun
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Jingjin Hu
- International Center for Quantum Materials, Peking University, Beijing 100871, China
| | - Hailong Fu
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Xi Lin
- International Center for Quantum Materials, Peking University, Beijing 100871, China
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