1
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Honda R, Endo K, Kaji T, Suzuki Y, Matsuda Y, Tanaka S, Muramatsu M. Development of optimization method for truss structure by quantum annealing. Sci Rep 2024; 14:13872. [PMID: 38879604 PMCID: PMC11180109 DOI: 10.1038/s41598-024-64588-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Accepted: 06/11/2024] [Indexed: 06/19/2024] Open
Abstract
In this study, we developed a new method of topology optimization for truss structures by quantum annealing. To perform quantum annealing analysis with real variables, representation of real numbers as a sum of random number combinations is employed. The nodal displacement is expressed with binary variables. The Hamiltonian H is formulated on the basis of the elastic strain energy and position energy of a truss structure. It is confirmed that truss deformation analysis is possible by quantum annealing. For the analysis of the optimization method for the truss structure, the cross-sectional area of the truss is expressed with binary variables. The iterative calculation for the changes in displacement and cross-sectional area leads to the optimal structure under the prescribed boundary conditions.
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Affiliation(s)
- Rio Honda
- Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan
| | - Katsuhiro Endo
- Research Center for Computational Design of Advanced Functional Materials, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan
| | - Taichi Kaji
- Graduate School of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan
| | - Yudai Suzuki
- 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
- Keio Quantum Computing Center, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan
- 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
- Human Biology-Microbiome-Quantum Research Center (WPI-Bio2Q), Keio University, 35 Shinanomachi, Shinjuku-ku, Tokyo, 160-8582, Japan
| | - Mayu Muramatsu
- Keio Quantum Computing Center, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan.
- Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan.
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2
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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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3
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Deng Y, Zhang Y, Zhang X, Jiang Y, Chen X, Yang Y, Tong X, Cai Y, Liu W, Sun C, Shang D, Wang Q, Yu H, Wang Z. MEMS Oscillators-Network-Based Ising Machine with Grouping Method. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2024:e2310096. [PMID: 38696663 DOI: 10.1002/advs.202310096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2023] [Revised: 03/17/2024] [Indexed: 05/04/2024]
Abstract
Combinatorial optimization (CO) has a broad range of applications in various fields, including operations research, computer science, and artificial intelligence. However, many of these problems are classified as nondeterministic polynomial-time (NP)-complete or NP-hard problems, which are known for their computational complexity and cannot be solved in polynomial time on traditional digital computers. To address this challenge, continuous-time Ising machine solvers have been developed, utilizing different physical principles to map CO problems to ground state finding. However, most Ising machine prototypes operate at speeds comparable to digital hardware and rely on binarizing node states, resulting in increased system complexity and further limiting operating speed. To tackle these issues, a novel device-algorithm co-design method is proposed for fast sub-optimal solution finding with low hardware complexity. On the device side, a piezoelectric lithium niobate (LiNbO3) microelectromechanical system (MEMS) oscillator network-based Ising machine without second-harmonic injection locking (SHIL) is devised to solve Max-cut and graph coloring problems. The LiNbO3 oscillator operates at speeds greater than 9 GHz, making it one of the fastest oscillatory Ising machines. System-wise, an innovative grouping method is used that achieves a performance guarantee of 0.878 for Max-cut and 0.658 for graph coloring problems, which is comparable to Ising machines that utilize binarization.
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Affiliation(s)
- Yi Deng
- Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 999077, China
- ACCESS - AI Chip Center for Emerging Smart Systems, InnoHK Centers, Hong Kong Science Park, Hong Kong, 999077, China
| | - Yi Zhang
- Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 999077, China
- ACCESS - AI Chip Center for Emerging Smart Systems, InnoHK Centers, Hong Kong Science Park, Hong Kong, 999077, China
- School of Microelectronics, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Xinyuan Zhang
- Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 999077, China
- ACCESS - AI Chip Center for Emerging Smart Systems, InnoHK Centers, Hong Kong Science Park, Hong Kong, 999077, China
| | - Yang Jiang
- Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 999077, China
- ACCESS - AI Chip Center for Emerging Smart Systems, InnoHK Centers, Hong Kong Science Park, Hong Kong, 999077, China
- School of Microelectronics, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Xi Chen
- Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 999077, China
- ACCESS - AI Chip Center for Emerging Smart Systems, InnoHK Centers, Hong Kong Science Park, Hong Kong, 999077, China
| | - Yansong Yang
- Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Hong Kong, 999077, China
| | - Xin Tong
- Institute of Technological Sciences, Wuhan University, Wuhan, 430072, China
| | - Yao Cai
- Institute of Technological Sciences, Wuhan University, Wuhan, 430072, China
| | - Wenjuan Liu
- Institute of Technological Sciences, Wuhan University, Wuhan, 430072, China
| | - Chengliang Sun
- Institute of Technological Sciences, Wuhan University, Wuhan, 430072, China
| | - Dashan Shang
- Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
| | - Qing Wang
- School of Microelectronics, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Hongyu Yu
- School of Microelectronics, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Zhongrui Wang
- Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 999077, China
- ACCESS - AI Chip Center for Emerging Smart Systems, InnoHK Centers, Hong Kong Science Park, Hong Kong, 999077, China
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Nagy S, Paredes R, Dudek JM, Dueñas-Osorio L, Vardi MY. Ising model partition-function computation as a weighted counting problem. Phys Rev E 2024; 109:055301. [PMID: 38907408 DOI: 10.1103/physreve.109.055301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2024] [Accepted: 03/27/2024] [Indexed: 06/24/2024]
Abstract
While the Ising model is most often used to understand physical phenomena, its natural connection to combinatorial reasoning also makes it one of the best models to probe complex systems in science and engineering. We bring a computational lens to the study of Ising models, where our computer-science perspective is twofold: On the one hand, we show that partition function computation (#Ising) can be reduced to weighted model counting (WMC). This enables us to take off-the-shelf model counters and apply them to #Ising. We show that one model counter (TensorOrder) outperforms state-of-the-art tools for #Ising on midsize and topologically unstructured instances, suggesting the tool would be a useful addition to a portfolio of partition function solvers. On the other hand, we consider the computational complexity of #Ising and relate it to the logic-based counting of constraint-satisfaction problems or #CSP. We show that known dichotomy results for #CSP give an easy proof of the hardness of #Ising and provide intuition on where the difficulty of #Ising comes from.
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Affiliation(s)
- Shaan Nagy
- Department of Computer Science, Rice University, Houston, Texas 77005, USA
- Department of Computer Sciences, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Roger Paredes
- Department of Civil and Environmental Engineering, Rice University, Houston, Texas 77005, USA
| | - Jeffrey M Dudek
- Department of Computer Science, Rice University, Houston, Texas 77005, USA
| | - Leonardo Dueñas-Osorio
- Department of Civil and Environmental Engineering, Rice University, Houston, Texas 77005, USA
| | - Moshe Y Vardi
- Department of Computer Science, Rice University, Houston, Texas 77005, USA
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5
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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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6
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Si J, Yang S, Cen Y, Chen J, Huang Y, Yao Z, Kim DJ, Cai K, Yoo J, Fong X, Yang H. Energy-efficient superparamagnetic Ising machine and its application to traveling salesman problems. Nat Commun 2024; 15:3457. [PMID: 38658582 PMCID: PMC11043373 DOI: 10.1038/s41467-024-47818-z] [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: 06/16/2022] [Accepted: 04/11/2024] [Indexed: 04/26/2024] Open
Abstract
The growth of artificial intelligence leads to a computational burden in solving non-deterministic polynomial-time (NP)-hard problems. The Ising computer, which aims to solve NP-hard problems faces challenges such as high power consumption and limited scalability. Here, we experimentally present an Ising annealing computer based on 80 superparamagnetic tunnel junctions (SMTJs) with all-to-all connections, which solves a 70-city traveling salesman problem (TSP, 4761-node Ising problem). By taking advantage of the intrinsic randomness of SMTJs, implementing global annealing scheme, and using efficient algorithm, our SMTJ-based Ising annealer outperforms other Ising schemes in terms of power consumption and energy efficiency. Additionally, our approach provides a promising way to solve complex problems with limited hardware resources. Moreover, we propose a cross-bar array architecture for scalable integration using conventional magnetic random-access memories. Our results demonstrate that the SMTJ-based Ising computer with high energy efficiency, speed, and scalability is a strong candidate for future unconventional computing schemes.
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Affiliation(s)
- Jia Si
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
- Key Laboratory for the Physics and Chemistry of Nanodevices and Center for Carbon-based Electronics, School of Electronics, Peking University, Beijing, China
| | - Shuhan Yang
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Yunuo Cen
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Jiaer Chen
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Yingna Huang
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Zhaoyang Yao
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Dong-Jun Kim
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Kaiming Cai
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Jerald Yoo
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Xuanyao Fong
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Hyunsoo Yang
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore.
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7
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Karimov T, Ostrovskii V, Rybin V, Druzhina O, Kolev G, Butusov D. Magnetic Flux Sensor Based on Spiking Neurons with Josephson Junctions. SENSORS (BASEL, SWITZERLAND) 2024; 24:2367. [PMID: 38610577 PMCID: PMC11014145 DOI: 10.3390/s24072367] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Revised: 04/05/2024] [Accepted: 04/06/2024] [Indexed: 04/14/2024]
Abstract
Josephson junctions (JJs) are superconductor-based devices used to build highly sensitive magnetic flux sensors called superconducting quantum interference devices (SQUIDs). These sensors may vary in design, being the radio frequency (RF) SQUID, direct current (DC) SQUID, and hybrid, such as D-SQUID. In addition, recently many of JJ's applications were found in spiking models of neurons exhibiting nearly biological behavior. In this study, we propose and investigate a new circuit model of a sensory neuron based on DC SQUID as part of the circuit. The dependence of the dynamics of the designed model on the external magnetic flux is demonstrated. The design of the circuit and derivation of the corresponding differential equations that describe the dynamics of the system are given. Numerical simulation is used for experimental evaluation. The experimental results confirm the applicability and good performance of the proposed magnetic-flux-sensitive neuron concept: the considered device can encode the magnetic flux in the form of neuronal dynamics with the linear section. Furthermore, some complex behavior was discovered in the model, namely the intermittent chaotic spiking and plateau bursting. The proposed design can be efficiently applied to developing the interfaces between circuitry and spiking neural networks. However, it should be noted that the proposed neuron design shares the main limitation of all the superconductor-based technologies, i.e., the need for a cryogenic and shielding system.
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Affiliation(s)
- Timur Karimov
- Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197022 Saint Petersburg, Russia; (T.K.); (V.O.)
| | - Valerii Ostrovskii
- Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197022 Saint Petersburg, Russia; (T.K.); (V.O.)
| | - Vyacheslav Rybin
- Computer-Aided Design Department, Saint Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia; (V.R.); (O.D.); (G.K.)
| | - Olga Druzhina
- Computer-Aided Design Department, Saint Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia; (V.R.); (O.D.); (G.K.)
| | - Georgii Kolev
- Computer-Aided Design Department, Saint Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia; (V.R.); (O.D.); (G.K.)
| | - Denis Butusov
- Computer-Aided Design Department, Saint Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197022 Saint Petersburg, Russia; (V.R.); (O.D.); (G.K.)
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8
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Casilli N, Kaisar T, Colombo L, Ghosh S, Feng PXL, Cassella C. Parametric Frequency Divider Based Ising Machines. PHYSICAL REVIEW LETTERS 2024; 132:147301. [PMID: 38640363 DOI: 10.1103/physrevlett.132.147301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Accepted: 02/20/2024] [Indexed: 04/21/2024]
Abstract
We report on a new class of Ising machines (IMs) that rely on coupled parametric frequency dividers (PFDs) as macroscopic artificial spins. Unlike the IM counterparts based on subharmonic-injection locking (SHIL), PFD IMs do not require strong injected continuous-wave signals or applied dc voltages. Therefore, they show a significantly lower power consumption per spin compared to SHIL-based IMs, making it feasible to accurately solve large-scale combinatorial optimization problems that are hard or even impossible to solve by using the current von Neumann computing architectures. Furthermore, using high quality factor resonators in the PFD design makes PFD IMs able to exhibit a nanowatt-level power per spin. Also, it remarkably allows a speedup of the phase synchronization among the PFDs, resulting in shorter time to solution and lower energy to solution despite the resonators' longer relaxation time. As a proof of concept, a 4-node PFD IM has been demonstrated. This IM correctly solves a set of Max-Cut problems while consuming just 600 nanowatts per spin. This power consumption is 2 orders of magnitude lower than the power per spin of state-of-the-art SHIL-based IMs operating at the same frequency.
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Affiliation(s)
- Nicolas Casilli
- Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Tahmid Kaisar
- Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida 32611, USA
| | - Luca Colombo
- Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Siddhartha Ghosh
- Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Philip X-L Feng
- Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida 32611, USA
| | - Cristian Cassella
- Department of Electrical and Computer Engineering, Northeastern University, Boston, Massachusetts 02115, USA
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9
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Dote A, Hukushima K. Effect of constraint relaxation on the minimum vertex cover problem in random graphs. Phys Rev E 2024; 109:044304. [PMID: 38755898 DOI: 10.1103/physreve.109.044304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2023] [Accepted: 03/05/2024] [Indexed: 05/18/2024]
Abstract
A statistical-mechanical study of the effect of constraint relaxation on the minimum vertex cover problem in Erdős-Rényi random graphs is presented. Using a penalty-method formulation for constraint relaxation, typical properties of solutions, including infeasible solutions that violate the constraints, are analyzed by means of the replica method and cavity method. The problem involves a competition between reducing the number of vertices to be covered and satisfying the edge constraints. The analysis under the replica-symmetric (RS) ansatz clarifies that the competition leads to degeneracies in the vertex and edge states, which determine the quantitative properties of the system, such as the cover and penalty ratios. A precise analysis of these effects improves the accuracy of RS approximation for the minimum cover ratio in the replica symmetry-breaking (RSB) region. Furthermore, the analysis based on the RS cavity method indicates that the RS/RSB boundary of the ground states with respect to the mean degree of the graphs is expanded, and the critical temperature is lowered by constraint relaxation.
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Affiliation(s)
- Aki Dote
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan
- Fujitsu Limited. 4-1-1 Kamikodanaka, Nakahara-ku, Kawasaki, 211-8588, Japan
| | - Koji Hukushima
- Graduate School of Arts and Sciences, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan
- Komaba Institute for Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan
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10
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Jones JA. Controlling NMR spin systems for quantum computation. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2024; 140-141:49-85. [PMID: 38705636 DOI: 10.1016/j.pnmrs.2024.02.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Accepted: 02/05/2024] [Indexed: 05/07/2024]
Abstract
Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.
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Affiliation(s)
- Jonathan A Jones
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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11
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Śmierzchalski T, Mzaouali Z, Deffner S, Gardas B. Efficiency optimization in quantum computing: balancing thermodynamics and computational performance. Sci Rep 2024; 14:4555. [PMID: 38402296 PMCID: PMC10894240 DOI: 10.1038/s41598-024-55314-z] [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: 10/27/2023] [Accepted: 02/22/2024] [Indexed: 02/26/2024] Open
Abstract
We investigate the computational efficiency and thermodynamic cost of the D-Wave quantum annealer under reverse-annealing with and without pausing. Our demonstration on the D-Wave 2000Q annealer shows that the combination of reverse-annealing and pausing leads to improved computational efficiency while minimizing the thermodynamic cost compared to reverse-annealing alone. Moreover, we find that the magnetic field has a positive impact on the performance of the quantum annealer during reverse-annealing but becomes detrimental when pausing is involved. Our results, which are reproducible, provide strategies for optimizing the performance and energy consumption of quantum annealing systems employing reverse-annealing protocols.
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Affiliation(s)
- Tomasz Śmierzchalski
- Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100, Gliwice, Poland
| | - Zakaria Mzaouali
- Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100, Gliwice, Poland.
| | - Sebastian Deffner
- Department of Physics, University of Maryland, Baltimore County, Baltimore, MD, 21250, USA
- National Quantum Laboratory, College Park, MD, 20740, USA
| | - Bartłomiej Gardas
- Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100, Gliwice, Poland
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12
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Ma X, Zhang G, Wu F, Bao F, Chang X, Chen J, Deng H, Gao R, Gao X, Hu L, Ji H, Ku HS, Lu K, Ma L, Mao L, Song Z, Sun H, Tang C, Wang F, Wang H, Wang T, Xia T, Ying M, Zhan H, Zhou T, Zhu M, Zhu Q, Shi Y, Zhao HH, Deng C. Native Approach to Controlled-Z Gates in Inductively Coupled Fluxonium Qubits. PHYSICAL REVIEW LETTERS 2024; 132:060602. [PMID: 38394561 DOI: 10.1103/physrevlett.132.060602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Accepted: 01/08/2024] [Indexed: 02/25/2024]
Abstract
The fluxonium qubits have emerged as a promising platform for gate-based quantum information processing. However, their extraordinary protection against charge fluctuations comes at a cost: when coupled capacitively, the qubit-qubit interactions are restricted to XX interactions. Consequently, effective ZZ or XZ interactions are only constructed either by temporarily populating higher-energy states, or by exploiting perturbative effects under microwave driving. Instead, we propose and demonstrate an inductive coupling scheme, which offers a wide selection of native qubit-qubit interactions for fluxonium. In particular, we leverage a built-in, flux-controlled ZZ interaction to perform qubit entanglement. To combat the increased flux-noise-induced dephasing away from the flux-insensitive position, we use a continuous version of the dynamical decoupling scheme to perform noise filtering. Combining these, we demonstrate a 20 ns controlled-z gate with a mean fidelity of 99.53%. More than confirming the efficacy of our gate scheme, this high-fidelity result also reveals a promising but rarely explored parameter space uniquely suitable for gate operations between fluxonium qubits.
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Affiliation(s)
- Xizheng Ma
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Gengyan Zhang
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Feng Wu
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Feng Bao
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Xu Chang
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Jianjun Chen
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Hao Deng
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Ran Gao
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Xun Gao
- DAMO Quantum Laboratory, Alibaba Group USA, Bellevue, Washington 98004, USA
| | - Lijuan Hu
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Honghong Ji
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Hsiang-Sheng Ku
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Kannan Lu
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Lu Ma
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Liyong Mao
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Zhijun Song
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Hantao Sun
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Chengchun Tang
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Fei Wang
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Hongcheng Wang
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Tenghui Wang
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Tian Xia
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Make Ying
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Huijuan Zhan
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Tao Zhou
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Mengyu Zhu
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Qingbin Zhu
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
| | - Yaoyun Shi
- DAMO Quantum Laboratory, Alibaba Group USA, Bellevue, Washington 98004, USA
| | - Hui-Hai Zhao
- DAMO Quantum Laboratory, Alibaba Group, Beijing 100102, China
| | - Chunqing Deng
- DAMO Quantum Laboratory, Alibaba Group, Hangzhou, Zhejiang 311121, China
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13
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Mazzola G. Quantum computing for chemistry and physics applications from a Monte Carlo perspective. J Chem Phys 2024; 160:010901. [PMID: 38165101 DOI: 10.1063/5.0173591] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2023] [Accepted: 10/18/2023] [Indexed: 01/03/2024] Open
Abstract
This Perspective focuses on the several overlaps between quantum algorithms and Monte Carlo methods in the domains of physics and chemistry. We will analyze the challenges and possibilities of integrating established quantum Monte Carlo solutions into quantum algorithms. These include refined energy estimators, parameter optimization, real and imaginary-time dynamics, and variational circuits. Conversely, we will review new ideas for utilizing quantum hardware to accelerate the sampling in statistical classical models, with applications in physics, chemistry, optimization, and machine learning. This review aims to be accessible to both communities and intends to foster further algorithmic developments at the intersection of quantum computing and Monte Carlo methods. Most of the works discussed in this Perspective have emerged within the last two years, indicating a rapidly growing interest in this promising area of research.
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Affiliation(s)
- Guglielmo Mazzola
- Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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14
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Tučs A, Ito T, Kurumida Y, Kawada S, Nakazawa H, Saito Y, Umetsu M, Tsuda K. Extensive antibody search with whole spectrum black-box optimization. Sci Rep 2024; 14:552. [PMID: 38177656 PMCID: PMC10767033 DOI: 10.1038/s41598-023-51095-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Accepted: 12/30/2023] [Indexed: 01/06/2024] Open
Abstract
In designing functional biological sequences with machine learning, the activity predictor tends to be inaccurate due to shortage of data. Top ranked sequences are thus unlikely to contain effective ones. This paper proposes to take prediction stability into account to provide domain experts with a reasonable list of sequences to choose from. In our approach, multiple prediction models are trained by subsampling the training set and the multi-objective optimization problem, where one objective is the average activity and the other is the standard deviation, is solved. The Pareto front represents a list of sequences with the whole spectrum of activity and stability. Using this method, we designed VHH (Variable domain of Heavy chain of Heavy chain) antibodies based on the dataset obtained from deep mutational screening. To solve multi-objective optimization, we employed our sequence design software MOQA that uses quantum annealing. By applying several selection criteria to 19,778 designed sequences, five sequences were selected for wet-lab validation. One sequence, 16 mutations away from the closest training sequence, was successfully expressed and found to possess desired binding specificity. Our whole spectrum approach provides a balanced way of dealing with the prediction uncertainty, and can possibly be applied to extensive search of functional sequences.
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Affiliation(s)
- Andrejs Tučs
- Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Japan
| | - Tomoyuki Ito
- Department of Biomolecular Engineering, Graduate School of Engineering, Tohoku University, Sendai, Japan
| | - Yoichi Kurumida
- Artificial Intelligence Research Center, National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan
- Department of Data Science, School of Frontier Engineering, Kitasato University, Sagamihara, Japan
| | - Sakiya Kawada
- Department of Biomolecular Engineering, Graduate School of Engineering, Tohoku University, Sendai, Japan
| | - Hikaru Nakazawa
- Department of Biomolecular Engineering, Graduate School of Engineering, Tohoku University, Sendai, Japan
| | - Yutaka Saito
- Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Japan
- Artificial Intelligence Research Center, National Institute of Advanced Industrial Science and Technology (AIST), Tokyo, Japan
- RIKEN Center for Advanced Intelligence Project, RIKEN, Tokyo, 103-0027, Japan
- AIST-Waseda University Computational Bio Big-Data Open Innovation Laboratory (CBBD-OIL), Tokyo, Japan
- Department of Data Science, School of Frontier Engineering, Kitasato University, Sagamihara, Japan
| | - Mitsuo Umetsu
- Department of Biomolecular Engineering, Graduate School of Engineering, Tohoku University, Sendai, Japan.
- RIKEN Center for Advanced Intelligence Project, RIKEN, Tokyo, 103-0027, Japan.
| | - Koji Tsuda
- Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Japan.
- RIKEN Center for Advanced Intelligence Project, RIKEN, Tokyo, 103-0027, Japan.
- Center for Basic Research on Materials, National Institute for Materials Science (NIMS), Tsukuba, Japan.
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15
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Sakabe T, Shimomura S, Ogura Y, Okubo KI, Yamashita H, Suzuki H, Tanida J. Spatial-photonic Ising machine by space-division multiplexing with physically tunable coefficients of a multi-component model. OPTICS EXPRESS 2023; 31:44127-44138. [PMID: 38178491 DOI: 10.1364/oe.508069] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Accepted: 12/04/2023] [Indexed: 01/06/2024]
Abstract
This paper proposes a space-division multiplexed spatial-photonic Ising machine (SDM-SPIM) that physically calculates the weighted sum of the Ising Hamiltonians for individual components in a multi-component model. Space-division multiplexing enables tuning a set of weight coefficients as an optical parameter and obtaining the desired Ising Hamiltonian at a time. We solved knapsack problems to verify the system's validity, demonstrating that optical parameters impact the search property. We also investigated a new dynamic coefficient search algorithm to enhance search performance. The SDM-SPIM would physically calculate the Hamiltonian and a part of the optimization with an electronics process.
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16
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Luo L, Mi Z, Huang J, Ruan Z. Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields. SCIENCE ADVANCES 2023; 9:eadg6238. [PMID: 38039362 PMCID: PMC10691765 DOI: 10.1126/sciadv.adg6238] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Accepted: 11/02/2023] [Indexed: 12/03/2023]
Abstract
Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in unconventional Ising machines. Here, we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. With this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: ±J models, Sherrington-Kirkpatrick models, and only locally connected J1-J2 models and observe the phase transitions. We also demonstrate the ground-state search for solving Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high-power efficiency Boltzmann sampling to a generalized large-scale Ising model.
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Affiliation(s)
- Li Luo
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Zhiyi Mi
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Junyi Huang
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
| | - Zhichao Ruan
- School of Physics, State Key Laboratory of Extreme Photonics and Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Zhejiang University, Hangzhou 310027, China
- College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China
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17
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Ahn D. Non-Markovian cost function for quantum error mitigation with Dirac Gamma matrices representation. Sci Rep 2023; 13:20069. [PMID: 37973833 PMCID: PMC10654775 DOI: 10.1038/s41598-023-45053-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: 06/17/2023] [Accepted: 10/15/2023] [Indexed: 11/19/2023] Open
Abstract
This paper investigates the non-Markovian cost function in quantum error mitigation (QEM) and employs Dirac Gamma matrices to illustrate two-qubit operators, significant in relativistic quantum mechanics. Amid the focus on error reduction in noisy intermediate-scale quantum (NISQ) devices, understanding non-Markovian noise, commonly found in solid-state quantum computers, is crucial. We propose a non-Markovian model for quantum state evolution and a corresponding QEM cost function, using simple harmonic oscillators as a proxy for environmental noise. Owing to their shared algebraic structure with two-qubit gate operators, Gamma matrices allow for enhanced analysis and manipulation of these operators. We evaluate the fluctuations of the output quantum state across various input states for identity and SWAP gate operations, and by comparing our findings with ion-trap and superconducting quantum computing systems' experimental data, we derive essential QEM cost function parameters. Our findings indicate a direct relationship between the quantum system's coupling strength with its environment and the QEM cost function. The research highlights non-Markovian models' importance in understanding quantum state evolution and assessing experimental outcomes from NISQ devices.
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Affiliation(s)
- Doyeol Ahn
- Department of Electrical and Computer Engineering, University of Seoul, 163 Seoulsiripdae-Ro, Tongdaimoon-Gu, Seoul, 02504, Republic of Korea.
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18
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Slongo F, Hauke P, Faccioli P, Micheletti C. Quantum-inspired encoding enhances stochastic sampling of soft matter systems. SCIENCE ADVANCES 2023; 9:eadi0204. [PMID: 37878707 PMCID: PMC10599611 DOI: 10.1126/sciadv.adi0204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 09/21/2023] [Indexed: 10/27/2023]
Abstract
Quantum advantage in solving physical problems is still hard to assess due to hardware limitations. However, algorithms designed for quantum computers may engender transformative frameworks for modeling and simulating paradigmatically hard systems. Here, we show that the quadratic unconstrained binary optimization encoding enables tackling classical many-body systems that are challenging for conventional Monte Carlo. Specifically, in self-assembled melts of rigid lattice ring polymers, the combination of high density, chain stiffness, and topological constraints results in divergent autocorrelation times for real-space Monte Carlo. Our quantum-inspired encoding overcomes this problem and enables sampling melts of lattice rings with fixed curvature and compactness, unveiling counterintuitive topological effects. Tackling the same problems with the D-Wave quantum annealer leads to substantial performance improvements and advantageous scaling of sampling computational cost with the size of the self-assembled ring melts.
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Affiliation(s)
- Francesco Slongo
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, I-34136 Trieste, Italy
| | - Philipp Hauke
- Pitaevskii BEC Center, Department of Physics, University of Trento, Via Sommarive 14, I-38123 Povo, Trento, Italy
- INFN-TIFPA, Via Sommarive 14, I-38123 Povo, Trento, Italy
| | - Pietro Faccioli
- Department of Physics and BiQuTe Center, University of Milano-Bicocca, Piazza della Scienza 3, I-20126 Milan, Italy
- Department of Physics, University of Trento, Via Sommarive 14, I-38123 Povo, Trento, Italy
| | - Cristian Micheletti
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, I-34136 Trieste, Italy
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19
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Asaoka H, Kudo K. Nonnegative/Binary matrix factorization for image classification using quantum annealing. Sci Rep 2023; 13:16527. [PMID: 37783730 PMCID: PMC10545830 DOI: 10.1038/s41598-023-43729-z] [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: 05/20/2023] [Accepted: 09/27/2023] [Indexed: 10/04/2023] Open
Abstract
Classical computing has borne witness to the development of machine learning. The integration of quantum technology into this mix will lead to unimaginable benefits and be regarded as a giant leap forward in mankind's ability to compute. Demonstrating the benefits of this integration now becomes essential. With the advance of quantum computing, several machine-learning techniques have been proposed that use quantum annealing. In this study, we implement a matrix factorization method using quantum annealing for image classification and compare the performance with traditional machine-learning methods. Nonnegative/binary matrix factorization (NBMF) was originally introduced as a generative model, and we propose a multiclass classification model as an application. We extract the features of handwritten digit images using NBMF and apply them to solve the classification problem. Our findings show that when the amount of data, features, and epochs is small, the accuracy of models trained by NBMF is superior to classical machine-learning methods, such as neural networks. Moreover, we found that training models using a quantum annealing solver significantly reduces computation time. Under certain conditions, there is a benefit to using quantum annealing technology with machine learning.
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Affiliation(s)
- Hinako Asaoka
- Department of Computer Science, Ochanomizu University, Tokyo, 112-8610, Japan.
| | - 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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20
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Jung H, Kim H, Lee W, Jeon J, Choi Y, Park T, Kim C. A quantum-inspired probabilistic prime factorization based on virtually connected Boltzmann machine and probabilistic annealing. Sci Rep 2023; 13:16186. [PMID: 37758803 PMCID: PMC10533543 DOI: 10.1038/s41598-023-43054-5] [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: 04/21/2023] [Accepted: 09/19/2023] [Indexed: 09/29/2023] Open
Abstract
Probabilistic computing has been introduced to operate functional networks using a probabilistic bit (p-bit), broadening the computational abilities in non-deterministic polynomial searching operations. However, previous developments have focused on emulating the operation of quantum computers similarly, implementing every p-bit with large weight-sum matrix multiplication blocks and requiring tens of times more p-bits than semiprime bits. In addition, operations based on a conventional simulated annealing scheme required a large number of sampling operations, which deteriorated the performance of the Ising machines. Here we introduce a prime factorization machine with a virtually connected Boltzmann machine and probabilistic annealing method, which are designed to reduce the hardware complexity and number of sampling operations. From 10-bit to 64-bit prime factorizations were performed, and the machine offers up to 1.2 × 108 times improvement in the number of sampling operations compared with previous factorization machines, with a 22-fold smaller hardware resource.
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21
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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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22
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Yamashita H, Okubo KI, Shimomura S, Ogura Y, Tanida J, Suzuki H. Low-Rank Combinatorial Optimization and Statistical Learning by Spatial Photonic Ising Machine. PHYSICAL REVIEW LETTERS 2023; 131:063801. [PMID: 37625069 DOI: 10.1103/physrevlett.131.063801] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2023] [Revised: 06/09/2023] [Accepted: 07/10/2023] [Indexed: 08/27/2023]
Abstract
The spatial photonic Ising machine (SPIM) [13D. Pierangeli et al., Large-Scale Photonic Ising Machine by Spatial Light Modulation, Phys. Rev. Lett. 122, 213902 (2019).PRLTAO0031-900710.1103/PhysRevLett.122.213902] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems efficiently. The primitive version of the SPIM, however, can accommodate Ising problems with only rank-one interaction matrices. In this Letter, we propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. Moreover, it acquires the learning ability of Boltzmann machines. We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using the model with low-rank interactions. Thus, the proposed model exhibits higher practical applicability to various problems of combinatorial optimization and statistical learning, without losing the scalability inherent in the SPIM architecture.
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Affiliation(s)
- Hiroshi Yamashita
- Graduate School of Information Science and Technology, Osaka University, Osaka 565-0871, Japan
| | - Ken-Ichi Okubo
- Graduate School of Information Science and Technology, Osaka University, Osaka 565-0871, Japan
| | - Suguru Shimomura
- Graduate School of Information Science and Technology, Osaka University, Osaka 565-0871, Japan
| | - Yusuke Ogura
- Graduate School of Information Science and Technology, Osaka University, Osaka 565-0871, Japan
| | - Jun Tanida
- Graduate School of Information Science and Technology, Osaka University, Osaka 565-0871, Japan
| | - Hideyuki Suzuki
- Graduate School of Information Science and Technology, Osaka University, Osaka 565-0871, Japan
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23
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Chen CH, Lai YT, Chen CF, Wu PT, Su KJ, Hsu SY, Dai GJ, Huang ZY, Hsu CL, Lee SY, Shen CH, Chen HY, Lee CC, Hsieh DR, Lin YF, Chao TS, Lo ST. Single-Gate In-Transistor Readout of Current Superposition and Collapse Utilizing Quantum Tunneling and Ferroelectric Switching. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2301206. [PMID: 37282350 DOI: 10.1002/adma.202301206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Revised: 06/01/2023] [Indexed: 06/08/2023]
Abstract
In nanostructure assemblies, the superposition of current paths forms microscopic electric circuits, and different circuit networks produce varying results, particularly when utilized as transistor channels for computing applications. However, the intricate nature of assembly networks and the winding paths of commensurate currents hinder standard circuit modeling. Inspired by the quantum collapse of superposition states for information decoding in quantum circuits, the implementation of analogous current path collapse to facilitate the detection of microscopic circuits by modifying their network topology is explored. Here, the superposition and collapse of current paths in gate-all-around polysilicon nanosheet arrays are demonstrated to enrich the computational resources within transistors by engineering the channel length and quantity. Switching the ferroelectric polarization of Hf0.5 Zr0.5 O2 gate dielectric, which drives these transistors out-of-equilibrium, decodes the output polymorphism through circuit topological modifications. Furthermore, a protocol for the single-electron readout of ferroelectric polarization is presented with tailoring the channel coherence. The introduction of lateral path superposition results into intriguing metal-to-insulator transitions due to transient behavior of ferroelectric switching. This ability to adjust the current networks within transistors and their interaction with ferroelectric polarization in polycrystalline nanostructures lays the groundwork for generating diverse current characteristics as potential physical databases for optimization-based computing.
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Affiliation(s)
- Ching-Hung Chen
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Yu-Ting Lai
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Ciao-Fen Chen
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
- Department of Physics, National Chung Hsing University, Taichung, 40227, Taiwan
| | - Pei-Tzu Wu
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Kuan-Jung Su
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Sheng-Yang Hsu
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Guo-Jin Dai
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Zan-Yi Huang
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Chien-Lung Hsu
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Shen-Yang Lee
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Chuan-Hui Shen
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Hsin-Yu Chen
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Chia-Chin Lee
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Dong-Ru Hsieh
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Yen-Fu Lin
- Department of Physics, National Chung Hsing University, Taichung, 40227, Taiwan
| | - Tien-Sheng Chao
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
| | - Shun-Tsung Lo
- Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
- Center for Emergent Functional Matter Science, National Yang Ming Chiao Tung University, Hsinchu, 30010, Taiwan
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24
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Gusev VV, Adamson D, Deligkas A, Antypov D, Collins CM, Krysta P, Potapov I, Darling GR, Dyer MS, Spirakis P, Rosseinsky MJ. Optimality guarantees for crystal structure prediction. Nature 2023; 619:68-72. [PMID: 37407679 DOI: 10.1038/s41586-023-06071-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Accepted: 04/04/2023] [Indexed: 07/07/2023]
Abstract
Crystalline materials enable essential technologies, and their properties are determined by their structures. Crystal structure prediction can thus play a central part in the design of new functional materials1,2. Researchers have developed efficient heuristics to identify structural minima on the potential energy surface3-5. Although these methods can often access all configurations in principle, there is no guarantee that the lowest energy structure has been found. Here we show that the structure of a crystalline material can be predicted with energy guarantees by an algorithm that finds all the unknown atomic positions within a unit cell by combining combinatorial and continuous optimization. We encode the combinatorial task of finding the lowest energy periodic allocation of all atoms on a lattice as a mathematical optimization problem of integer programming6,7, enabling guaranteed identification of the global optimum using well-developed algorithms. A single subsequent local minimization of the resulting atom allocations then reaches the correct structures of key inorganic materials directly, proving their energetic optimality under clear assumptions. This formulation of crystal structure prediction establishes a connection to the theory of algorithms and provides the absolute energetic status of observed or predicted materials. It provides the ground truth for heuristic or data-driven structure prediction methods and is uniquely suitable for quantum annealers8-10, opening a path to overcome the combinatorial explosion of atomic configurations.
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Affiliation(s)
- Vladimir V Gusev
- Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory, University of Liverpool, Liverpool, UK
- Department of Computer Science, University of Liverpool, Liverpool, UK
| | - Duncan Adamson
- Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory, University of Liverpool, Liverpool, UK
| | - Argyrios Deligkas
- Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory, University of Liverpool, Liverpool, UK
- Department of Computer Science, Royal Holloway, University of London, London, UK
| | - Dmytro Antypov
- Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory, University of Liverpool, Liverpool, UK
| | | | - Piotr Krysta
- Department of Computer Science, University of Liverpool, Liverpool, UK
| | - Igor Potapov
- Department of Computer Science, University of Liverpool, Liverpool, UK
| | | | - Matthew S Dyer
- Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory, University of Liverpool, Liverpool, UK
- Department of Chemistry, University of Liverpool, Liverpool, UK
| | - Paul Spirakis
- Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory, University of Liverpool, Liverpool, UK.
- Department of Computer Science, University of Liverpool, Liverpool, UK.
| | - Matthew J Rosseinsky
- Leverhulme Research Centre for Functional Materials Design, Materials Innovation Factory, University of Liverpool, Liverpool, UK.
- Department of Chemistry, University of Liverpool, Liverpool, UK.
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25
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Gircha AI, Boev AS, Avchaciov K, Fedichev PO, Fedorov AK. Hybrid quantum-classical machine learning for generative chemistry and drug design. Sci Rep 2023; 13:8250. [PMID: 37217521 DOI: 10.1038/s41598-023-32703-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Accepted: 03/31/2023] [Indexed: 05/24/2023] Open
Abstract
Deep generative chemistry models emerge as powerful tools to expedite drug discovery. However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome with hybrid architectures combining quantum computers with deep classical networks. As the first step toward this goal, we built a compact discrete variational autoencoder (DVAE) with a Restricted Boltzmann Machine (RBM) of reduced size in its latent layer. The size of the proposed model was small enough to fit on a state-of-the-art D-Wave quantum annealer and allowed training on a subset of the ChEMBL dataset of biologically active compounds. Finally, we generated 2331 novel chemical structures with medicinal chemistry and synthetic accessibility properties in the ranges typical for molecules from ChEMBL. The presented results demonstrate the feasibility of using already existing or soon-to-be-available quantum computing devices as testbeds for future drug discovery applications.
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Affiliation(s)
- A I Gircha
- Russian Quantum Center, Skolkovo, Moscow, 121205, Russia
| | - A S Boev
- Russian Quantum Center, Skolkovo, Moscow, 121205, Russia
| | - K Avchaciov
- Gero PTE. LTD., 133 Cecil Street #14-01 Keck Seng Tower, Singapore, 069535, Singapore
| | - P O Fedichev
- Gero PTE. LTD., 133 Cecil Street #14-01 Keck Seng Tower, Singapore, 069535, Singapore.
| | - A K Fedorov
- Russian Quantum Center, Skolkovo, Moscow, 121205, Russia.
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26
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Tučs A, Berenger F, Yumoto A, Tamura R, Uzawa T, Tsuda K. Quantum Annealing Designs Nonhemolytic Antimicrobial Peptides in a Discrete Latent Space. ACS Med Chem Lett 2023; 14:577-582. [PMID: 37197452 PMCID: PMC10184305 DOI: 10.1021/acsmedchemlett.2c00487] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Accepted: 04/10/2023] [Indexed: 05/19/2023] Open
Abstract
Increasing the variety of antimicrobial peptides is crucial in meeting the global challenge of multi-drug-resistant bacterial pathogens. While several deep-learning-based peptide design pipelines are reported, they may not be optimal in data efficiency. High efficiency requires a well-compressed latent space, where optimization is likely to fail due to numerous local minima. We present a multi-objective peptide design pipeline based on a discrete latent space and D-Wave quantum annealer with the aim of solving the local minima problem. To achieve multi-objective optimization, multiple peptide properties are encoded into a score using non-dominated sorting. Our pipeline is applied to design therapeutic peptides that are antimicrobial and non-hemolytic at the same time. From 200 000 peptides designed by our pipeline, four peptides proceeded to wet-lab validation. Three of them showed high anti-microbial activity, and two are non-hemolytic. Our results demonstrate how quantum-based optimizers can be taken advantage of in real-world medical studies.
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Affiliation(s)
- Andrejs Tučs
- Graduate
School of Frontier Sciences, The University
of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8561, Japan
| | - Francois Berenger
- Graduate
School of Frontier Sciences, The University
of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8561, Japan
| | - Akiko Yumoto
- Emergent
Bioengineering Materials Research Team, RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Ryo Tamura
- Graduate
School of Frontier Sciences, The University
of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8561, Japan
- International
Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), Tsukuba 305−0044, Japan
- Research
and Services Division of Materials Data and Integrated System, National Institute for Materials Science (NIMS), Tsukuba 305-0044, Japan
- RIKEN
Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihombashi, Chuo-ku, Tokyo 103-0027, Japan
| | - Takanori Uzawa
- Emergent
Bioengineering Materials Research Team, RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- Nano Medical
Engineering Laboratory, RIKEN Cluster for
Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
- E-mail:
| | - Koji Tsuda
- Graduate
School of Frontier Sciences, The University
of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8561, Japan
- Research
and Services Division of Materials Data and Integrated System, National Institute for Materials Science (NIMS), Tsukuba 305-0044, Japan
- RIKEN
Center for Advanced Intelligence Project, RIKEN, 1-4-1 Nihombashi, Chuo-ku, Tokyo 103-0027, Japan
- E-mail:
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27
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Hatakeyama-Sato K, Uchima Y, Kashikawa T, Kimura K, Oyaizu K. Extracting higher-conductivity designs for solid polymer electrolytes by quantum-inspired annealing. RSC Adv 2023; 13:14651-14659. [PMID: 37197684 PMCID: PMC10183718 DOI: 10.1039/d3ra01982a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2023] [Accepted: 05/04/2023] [Indexed: 05/19/2023] Open
Abstract
Data-driven optimal structure exploration has become a hot topic in materials for energy-related devices. However, this method is still challenging due to the insufficient prediction accuracy of material properties and large exploration space for candidate structures. We propose a data trend analysis system for materials using quantum-inspired annealing. Structure-property relationships are learned by a hybrid decision tree and quadratic regression algorithm. Then, ideal solutions to maximize the property are explored by a Fujitsu Digital Annealer, which is unique hardware that can quickly extract promising solutions from the ample search space. The system's validity is investigated with an experimental study examining solid polymer electrolytes as potential components for solid-state lithium-ion batteries. A new trithiocarbonate polymer electrolyte offers a conductivity of 10-6 S cm-1 at room temperature, even though it is in a glassy state. Molecular design through data science will enable accelerated exploration of functional materials for energy-related devices.
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Affiliation(s)
| | - Yasuei Uchima
- Department of Applied Chemistry, Waseda University Tokyo 169-8555 Japan
| | | | | | - Kenichi Oyaizu
- Department of Applied Chemistry, Waseda University Tokyo 169-8555 Japan
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28
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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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29
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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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30
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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] [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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31
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Ceselli A, Premoli M. On good encodings for quantum annealer and digital optimization solvers. Sci Rep 2023; 13:5628. [PMID: 37024525 PMCID: PMC10079660 DOI: 10.1038/s41598-023-32232-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2022] [Accepted: 03/24/2023] [Indexed: 04/08/2023] Open
Abstract
Several optimization solvers inspired by quantum annealing have been recently developed, either running on actual quantum hardware or simulating it on traditional digital computers. Industry and academics look at their potential in solving hard combinatorial optimization problems. Formally, they provide heuristic solutions for Ising models, which are equivalent to quadratic unconstrained binary optimization (QUBO). Constraints on solutions feasibility need to be properly encoded. We experiment on different ways of performing such an encoding. As benchmark we consider the cardinality constrained quadratic knapsack problem (CQKP), a minimal extension of QUBO with one inequality and one equality constraint. We consider different strategies of constraints penalization and variables encoding. We compare three QUBO solvers: quantum annealing on quantum hardware (D-Wave Advantage), probabilistic algorithms on digital hardware and mathematical programming solvers. We analyze their QUBO resolution quality and time, and the persistence values extracted in the quantum annealing sampling process. Our results show that a linear penalization of CQKP inequality improves current best practice. Furthermore, using such a linear penalization, persistence values produced by quantum hardware in a generic way allow to match a specific CQKP metric from literature. They are therefore suitable for general purpose variable fixing in core algorithms for combinatorial optimization.
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Affiliation(s)
- Alberto Ceselli
- Department of Computer Science, Università degli Studi di Milano, 18, via Celoria, 20133, Milano, Italy
| | - Marco Premoli
- Department of Computer Science, Università degli Studi di Milano, 18, via Celoria, 20133, Milano, Italy.
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32
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Weinberg SJ, Sanches F, Ide T, Kamiya K, Correll R. Supply chain logistics with quantum and classical annealing algorithms. Sci Rep 2023; 13:4770. [PMID: 36959248 PMCID: PMC10036469 DOI: 10.1038/s41598-023-31765-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Accepted: 03/16/2023] [Indexed: 03/25/2023] Open
Abstract
Noisy intermediate-scale quantum (NISQ) hardware is almost universally incompatible with full-scale optimization problems of practical importance which can have many variables and unwieldy objective functions. As a consequence, there is a growing body of literature that tests quantum algorithms on miniaturized versions of problems that arise in an operations research setting. Rather than taking this approach, we investigate a problem of substantial commercial value, multi-truck vehicle routing for supply chain logistics, at the scale used by a corporation in their operations. Such a problem is too complex to be fully embedded on any near-term quantum hardware or simulator; we avoid confronting this challenge by taking a hybrid workflow approach: we iteratively assign routes for trucks by generating a new binary optimization problem instance one truck at a time. Each instance has [Formula: see text] quadratic binary variables, putting it in a range that is feasible for NISQ quantum computing, especially quantum annealing hardware. We test our methods using simulated annealing and the D-Wave Hybrid solver as a place-holder in wait of quantum hardware developments. After feeding the vehicle routes suggested by these runs into a highly realistic classical supply chain simulation, we find excellent performance for the full supply chain. Our work gives a set of techniques that can be adopted in contexts beyond vehicle routing to apply NISQ devices in a hybrid fashion to large-scale problems of commercial interest.
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Affiliation(s)
| | | | - Takanori Ide
- Aisin Corporation, Tokyo Research Center, Chiyoda-ku, Tokyo, Japan
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33
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Albertsson DI, Rusu A. Highly reconfigurable oscillator-based Ising Machine through quasiperiodic modulation of coupling strength. Sci Rep 2023; 13:4005. [PMID: 36899045 PMCID: PMC10006240 DOI: 10.1038/s41598-023-31155-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2022] [Accepted: 03/06/2023] [Indexed: 03/12/2023] Open
Abstract
Ising Machines (IMs) have the potential to outperform conventional Von-Neuman architectures in notoriously difficult optimization problems. Various IM implementations have been proposed based on quantum, optical, digital and analog CMOS, as well as emerging technologies. Networks of coupled electronic oscillators have recently been shown to exhibit characteristics required for implementing IMs. However, for this approach to successfully solve complex optimization problems, a highly reconfigurable implementation is needed. In this work, the possibility of implementing highly reconfigurable oscillator-based IMs is explored. An implementation based on quasiperiodically modulated coupling strength through a common medium is proposed and its potential is demonstrated through numerical simulations. Moreover, a proof-of-concept implementation based on CMOS coupled ring oscillators is proposed and its functionality is demonstrated. Simulation results show that our proposed architecture can consistently find the Max-Cut solution and demonstrate the potential to greatly simplify the physical implementation of highly reconfigurable oscillator-based IMs.
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Affiliation(s)
- Dagur I Albertsson
- Division of Electronics and Embedded Systems, KTH Royal Institute of Technology, Electrum 229, 164 40, Kista, Sweden.
| | - Ana Rusu
- Division of Electronics and Embedded Systems, KTH Royal Institute of Technology, Electrum 229, 164 40, Kista, Sweden
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34
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Wierzbiński M, Falcó-Roget J, Crimi A. Community detection in brain connectomes with hybrid quantum computing. Sci Rep 2023; 13:3446. [PMID: 36859591 PMCID: PMC9977923 DOI: 10.1038/s41598-023-30579-y] [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: 12/21/2022] [Accepted: 02/27/2023] [Indexed: 03/03/2023] Open
Abstract
Recent advancements in network neuroscience are pointing in the direction of considering the brain as a small-world system with an efficient integration-segregation balance that facilitates different cognitive tasks and functions. In this context, community detection is a pivotal issue in computational neuroscience. In this paper we explored community detection within brain connectomes using the power of quantum annealers, and in particular the Leap's Hybrid Solver in D-Wave. By reframing the modularity optimization problem into a Discrete Quadratic Model, we show that quantum annealers achieved higher modularity indices compared to the Louvain Community Detection Algorithm without the need to overcomplicate the mathematical formulation. We also found that the number of communities detected in brain connectomes slightly differed while still being biologically interpretable. These promising preliminary results, together with recent findings, strengthen the claim that quantum optimization methods might be a suitable alternative against classical approaches when dealing with community assignment in networks.
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Affiliation(s)
- Marcin Wierzbiński
- grid.425010.20000 0001 2286 5863University of Warsaw, Institute of Mathematics, Warsaw, 02-097 Poland ,Sano Center for Compuational Personalised Medicine, Computer Vision Group, Krakow, 30-054 Poland
| | - Joan Falcó-Roget
- Sano Center for Compuational Personalised Medicine, Computer Vision Group, Krakow, 30-054 Poland
| | - Alessandro Crimi
- Sano Center for Compuational Personalised Medicine, Computer Vision Group, Krakow, 30-054, Poland.
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35
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Hybrid quantum-classical multi-cut benders approach with a power system application. Comput Chem Eng 2023. [DOI: 10.1016/j.compchemeng.2023.108161] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023]
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36
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CMOS-compatible ising machines built using bistable latches coupled through ferroelectric transistor arrays. Sci Rep 2023; 13:1515. [PMID: 36707539 PMCID: PMC9883258 DOI: 10.1038/s41598-023-28217-8] [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: 08/12/2022] [Accepted: 01/16/2023] [Indexed: 01/28/2023] Open
Abstract
Realizing compact and scalable Ising machines that are compatible with CMOS-process technology is crucial to the effectiveness and practicality of using such hardware platforms for accelerating computationally intractable problems. Besides the need for realizing compact Ising spins, the implementation of the coupling network, which describes the spin interaction, is also a potential bottleneck in the scalability of such platforms. Therefore, in this work, we propose an Ising machine platform that exploits the novel behavior of compact bi-stable CMOS-latches (cross-coupled inverters) as classical Ising spins interacting through highly scalable and CMOS-process compatible ferroelectric-HfO2-based Ferroelectric FETs (FeFETs) which act as coupling elements. We experimentally demonstrate the prototype building blocks of this system, and evaluate the scaling behavior of the system using simulations. Our work not only provides a pathway to realizing CMOS-compatible designs but also to overcoming their scaling challenges.
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37
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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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38
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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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Chakrabarti BK, Leschke H, Ray P, Shirai T, Tanaka S. Quantum annealing and computation: challenges and perspectives. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210419. [PMID: 36463926 PMCID: PMC9719792 DOI: 10.1098/rsta.2021.0419] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 10/11/2022] [Indexed: 06/17/2023]
Abstract
In the introductory article of this theme issue, we provide an overview of quantum annealing and computation with a very brief summary of the individual contributions to this issue made by experts as well as a few young researchers. We hope the readers will get the touch of the excitement as well as the perspectives in this unusually active field and important developments there. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Bikas K. Chakrabarti
- Saha Institute of Nuclear Physics, Kolkata 700064, India
- Indian Statistical Institute, Kolkata 700108, India
| | - Hajo Leschke
- Institut für Theoretische Physik, Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Purusattam Ray
- The Institute of Mathematical Sciences, Taramani, Chennai 600113, India
| | - Tatsuhiko Shirai
- Department of Computer Science and Communications Engineering, Waseda University, Tokyo 169-8555, Japan
| | - Shu Tanaka
- Department of Applied Physics and Physico-Informatics, Keio University, Yokohama 223-8522, Japan
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40
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Okuyama M, Ohki K, Ohzeki M. Threshold theorem in isolated quantum dynamics with stochastic control errors. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210412. [PMID: 36463918 PMCID: PMC9719793 DOI: 10.1098/rsta.2021.0412] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 10/06/2022] [Indexed: 06/17/2023]
Abstract
We investigate the effect of stochastic control errors in the time-dependent Hamiltonian on isolated quantum dynamics. The control errors are formulated as time-dependent stochastic noise in the Schrödinger equation. For a class of stochastic control errors, we establish a threshold theorem that provides a sufficient condition to obtain the target state, which should be determined in noiseless isolated quantum dynamics, as a relation between the number of measurements and noise strength. The theorem guarantees that if the sum of the noise strengths is less than the inverse of computational time, the target state can be obtained through a constant-order number of measurements. If the opposite is true, the number of measurements to guarantee obtaining the target state increases exponentially with computational time. Our threshold theorem can be applied to any isolated quantum dynamics such as quantum annealing and adiabatic quantum computation. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Manaka Okuyama
- Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
| | - Kentaro Ohki
- Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
| | - Masayuki Ohzeki
- Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan
- Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
- Sigma-i Co., Ltd., Tokyo 108-0075, Japan
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41
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Mozgunov E, Lidar DA. Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210407. [PMID: 36463925 PMCID: PMC9719797 DOI: 10.1098/rsta.2021.0407] [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: 05/01/2022] [Accepted: 07/18/2022] [Indexed: 06/17/2023]
Abstract
We present a new quantum adiabatic theorem that allows one to rigorously bound the adiabatic timescale for a variety of systems, including those described by originally unbounded Hamiltonians that are made finite-dimensional by a cutoff. Our bound is geared towards the qubit approximation of superconducting circuits and presents a sufficient condition for remaining within the [Formula: see text]-dimensional qubit subspace of a circuit model of [Formula: see text] qubits. The novelty of this adiabatic theorem is that, unlike previous rigorous results, it does not contain [Formula: see text] as a factor in the adiabatic timescale, and it allows one to obtain an expression for the adiabatic timescale independent of the cutoff of the infinite-dimensional Hilbert space of the circuit Hamiltonian. As an application, we present an explicit dependence of this timescale on circuit parameters for a superconducting flux qubit and demonstrate that leakage out of the qubit subspace is inevitable as the tunnelling barrier is raised towards the end of a quantum anneal. We also discuss a method of obtaining a [Formula: see text] effective Hamiltonian that best approximates the true dynamics induced by slowly changing circuit control parameters. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
- Evgeny Mozgunov
- Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA 90089, USA
| | - Daniel A. Lidar
- Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, CA 90089, USA
- Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA 90089, USA
- Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089, USA
- Department of Chemistry, University of Southern California, Los Angeles, CA 90089, USA
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42
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Kurita T, Morita M, Oshima H, Sato S. Pauli String Partitioning Algorithm with the Ising Model for Simultaneous Measurements. J Phys Chem A 2023; 127:1068-1080. [PMID: 36653017 PMCID: PMC9900592 DOI: 10.1021/acs.jpca.2c06453] [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] [Indexed: 01/20/2023]
Abstract
We propose an efficient algorithm for partitioning Pauli strings into subgroups, which can be simultaneously measured in a single quantum circuit. Our partitioning algorithm drastically reduces the total number of measurements in a variational quantum eigensolver for a quantum chemistry, one of the most promising applications of quantum computing. The algorithm is based on the Ising model optimization problem, which can be quickly solved using an Ising machine. We develop an algorithm that is applicable to problems with sizes larger than the maximum number of variables that an Ising machine can handle (nbit) through its iterative use. The algorithm has much better time complexity and solution optimality than other existing algorithms. We investigate the performance of the algorithm using the second-generation Digital Annealer, a high-performance Ising hardware, for up to 65535 Pauli strings using Hamiltonians of molecules and the full tomography of quantum states. We demonstrate a time complexity of O(N) for N ≤ nbit and O(N2) for N > nbit for the worst case, where N denotes the number of candidate Pauli strings and nbit = 8,192 in this study. The reduction factor, which is the number of Pauli strings divided by the number of obtained partitions, can be 200 at maximum.
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Affiliation(s)
- Tomochika Kurita
- Quantum
Laboratory, Fujitsu Research, Fujitsu Limited, 10-1 Morinosato-wakamiya, Atsugi, Kanagawa243-0197, Japan,E-mail:
| | - Mikio Morita
- Quantum
Laboratory, Fujitsu Research, Fujitsu Limited, 4-1-1 Kami-odanaka, Nakahara-ku, Kawasaki, Kanagawa211-8588, Japan
| | - Hirotaka Oshima
- Quantum
Laboratory, Fujitsu Research, Fujitsu Limited, 10-1 Morinosato-wakamiya, Atsugi, Kanagawa243-0197, Japan
| | - Shintaro Sato
- Quantum
Laboratory, Fujitsu Research, Fujitsu Limited, 10-1 Morinosato-wakamiya, Atsugi, Kanagawa243-0197, Japan
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43
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Calvanese Strinati M, Conti C. Multidimensional hyperspin machine. Nat Commun 2022; 13:7248. [PMID: 36433964 PMCID: PMC9700766 DOI: 10.1038/s41467-022-34847-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 11/08/2022] [Indexed: 11/26/2022] Open
Abstract
From condensed matter to quantum chromodynamics, multidimensional spins are a fundamental paradigm, with a pivotal role in combinatorial optimization and machine learning. Machines formed by coupled parametric oscillators can simulate spin models, but only for Ising or low-dimensional spins. Currently, machines implementing arbitrary dimensions remain a challenge. Here, we introduce and validate a hyperspin machine to simulate multidimensional continuous spin models. We realize high-dimensional spins by pumping groups of parametric oscillators, and show that the hyperspin machine finds to a very good approximation the ground state of complex graphs. The hyperspin machine can interpolate between different dimensions by tuning the coupling topology, a strategy that we call "dimensional annealing". When interpolating between the XY and the Ising model, the dimensional annealing substantially increases the success probability compared to conventional Ising simulators. Hyperspin machines are a new computational model for combinatorial optimization. They can be realized by off-the-shelf hardware for ultrafast, large-scale applications in classical and quantum computing, condensed-matter physics, and fundamental studies.
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Affiliation(s)
- Marcello Calvanese Strinati
- grid.449962.4Centro Ricerche Enrico Fermi (CREF), Via Panisperna 89a, 00184 Rome, Italy ,grid.472642.1Institute for Complex Systems, National Research Council (ISC-CNR), 00185 Rome, Italy
| | - Claudio Conti
- grid.449962.4Centro Ricerche Enrico Fermi (CREF), Via Panisperna 89a, 00184 Rome, Italy ,grid.472642.1Institute for Complex Systems, National Research Council (ISC-CNR), 00185 Rome, Italy ,grid.7841.aPhysics Department, Sapienza University of Rome, 00185 Rome, Italy
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Cen Q, Ding H, Hao T, Guan S, Qin Z, Lyu J, Li W, Zhu N, Xu K, Dai Y, Li M. Large-scale coherent Ising machine based on optoelectronic parametric oscillator. LIGHT, SCIENCE & APPLICATIONS 2022; 11:333. [PMID: 36433949 PMCID: PMC9700853 DOI: 10.1038/s41377-022-01013-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/07/2022] [Revised: 10/08/2022] [Accepted: 10/11/2022] [Indexed: 06/16/2023]
Abstract
Ising machines based on analog systems have the potential to accelerate the solution of ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machines have been reported, e.g., superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin stability is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement a large-scale Ising machine with high stability. The proposed machine supports 25,600 spins and can operate continuously and stably for hours. Moreover, the proposed Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward solving real-world optimization problems.
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Affiliation(s)
- Qizhuang Cen
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China
| | - Hao Ding
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China
| | - Tengfei Hao
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China
| | - Shanhong Guan
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China
| | - Zhiqiang Qin
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China
| | - Jiaming Lyu
- School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, China
| | - Wei Li
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China
| | - Ninghua Zhu
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China
| | - Kun Xu
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China
| | - Yitang Dai
- State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China.
- Peng Cheng Laboratory, Shenzhen, China.
| | - Ming Li
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China.
- School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing, China.
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing, China.
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45
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Inoue T, Seki Y, Tanaka S, Togawa N, Ishizaki K, Noda S. Towards optimization of photonic-crystal surface-emitting lasers via quantum annealing. OPTICS EXPRESS 2022; 30:43503-43512. [PMID: 36523046 DOI: 10.1364/oe.476839] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 11/02/2022] [Indexed: 06/17/2023]
Abstract
Photonic-crystal surface-emitting lasers (PCSELs), which utilize a two-dimensional (2D) optical resonance inside a photonic crystal for lasing, feature various outstanding functionalities such as single-mode high-power operation and arbitrary control of beam polarizations. Although most of the previous designs of PCSELs employ spatially uniform photonic crystals, it is expected that lasing performance can be further improved if it becomes possible to optimize the spatial distribution of photonic crystals. In this paper, we investigate the structural optimization of PCSELs via quantum annealing towards high-power, narrow-beam-divergence operation with linear polarization. The optimization of PCSELs is performed by the iteration of the following three steps: (1) time-dependent 3D coupled-wave analysis of lasing performance, (2) formulation of the lasing performance via a factorization machine, and (3) selection of optimal solution(s) via quantum annealing. By using this approach, we discover an advanced PCSEL with a non-uniform spatial distribution of the band-edge frequency and injection current, which simultaneously enables higher output power, a narrower divergence angle, and a higher linear polarization ratio than conventional uniform PCSELs. Our results potentially indicate the universal applicability of quantum annealing, which has been mainly applied to specific types of discrete optimization problems so far, for various physics and engineering problems in the field of smart manufacturing.
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46
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Travel time optimization on multi-AGV routing by reverse annealing. Sci Rep 2022; 12:17753. [PMID: 36273242 PMCID: PMC9588084 DOI: 10.1038/s41598-022-22704-0] [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: 05/02/2022] [Accepted: 10/18/2022] [Indexed: 12/04/2022] Open
Abstract
Quantum annealing has been actively researched since D-Wave Systems produced the first commercial machine in 2011. Controlling a large fleet of automated guided vehicles is one of the real-world applications utilizing quantum annealing. In this study, we propose a formulation to control the traveling routes to minimize the travel time. We validate our formulation through simulation in a virtual plant and authenticate the effectiveness for faster distribution compared to a greedy algorithm that does not consider the overall detour distance. Furthermore, we utilize reverse annealing to maximize the advantage of the D-Wave’s quantum annealer. Starting from relatively good solutions obtained by a fast greedy algorithm, reverse annealing searches for better solutions around them. Our reverse annealing method improves the performance compared to standard quantum annealing alone and performs up to 10 times faster than a commercial classical solver, Gurobi. This study extends a use of optimization with general problem solvers in the application of multi-AGV systems and reveals the potential of reverse annealing as an optimizer.
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47
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Böhm F, Alonso-Urquijo D, Verschaffelt G, Van der Sande G. Noise-injected analog Ising machines enable ultrafast statistical sampling and machine learning. Nat Commun 2022; 13:5847. [PMID: 36195589 PMCID: PMC9532389 DOI: 10.1038/s41467-022-33441-3] [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: 12/06/2021] [Accepted: 09/19/2022] [Indexed: 11/09/2022] Open
Abstract
Ising machines are a promising non-von-Neumann computational concept for neural network training and combinatorial optimization. However, while various neural networks can be implemented with Ising machines, their inability to perform fast statistical sampling makes them inefficient for training neural networks compared to digital computers. Here, we introduce a universal concept to achieve ultrafast statistical sampling with analog Ising machines by injecting noise. With an opto-electronic Ising machine, we experimentally demonstrate that this can be used for accurate sampling of Boltzmann distributions and for unsupervised training of neural networks, with equal accuracy as software-based training. Through simulations, we find that Ising machines can perform statistical sampling orders-of-magnitudes faster than software-based methods. This enables the use of Ising machines beyond combinatorial optimization and makes them into efficient tools for machine learning and other applications.
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Affiliation(s)
- Fabian Böhm
- Applied Physics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium.
| | - Diego Alonso-Urquijo
- Applied Physics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium
| | - Guy Verschaffelt
- Applied Physics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium
| | - Guy Van der Sande
- Applied Physics Research Group, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium.
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48
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Saida D, Hidaka M, Miyake K, Imafuku K, Yamanashi Y. Superconducting quantum circuit of NOR in quantum annealing. Sci Rep 2022; 12:15894. [PMID: 36151127 PMCID: PMC9508137 DOI: 10.1038/s41598-022-20172-0] [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: 01/18/2022] [Accepted: 09/09/2022] [Indexed: 11/25/2022] Open
Abstract
The applicability of quantum annealing to various problems can be improved by expressing the Hamiltonian using a circuit satisfiability problem. We investigate the detailed characteristics of the NOR/NAND functions of a superconducting quantum circuit, which are the basic building blocks to implementing various types of problem Hamiltonians. The circuit is composed of superconducting flux qubits with all-to-all connectivity, where direct magnetic couplers are utilized instead of the variable couplers in the conventional superconducting quantum circuit. This configuration provides efficient scalability because the problem Hamiltonian is implemented using fewer qubits. We present an experiment with a complete logic operation of NOR/NAND, in which the circuit produces results with a high probability of success for arbitrary combinations of inputs. The features of the quantum circuit agree qualitatively with the theory, especially the mechanism for an operation under external flux modulation. Moreover, by calibrating the bias conditions to compensate for the offset flux from the surrounding circuit, the quantum circuit quantitatively agrees with the theory. To achieve true quantum annealing, we discuss the effects of the reduction in electric noise in quantum annealing.
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Affiliation(s)
- Daisuke Saida
- Device Technology Research Institute, National Institute of Advanced Industrial Science and Technology, Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan. .,Quantum laboratory, Fujitsu research, 1-1 Kamikodanaka, 4-chome, Nakahara-ku, Kawasaki, Kanagawa, 211-8588, Japan.
| | - Mutsuo Hidaka
- Device Technology Research Institute, National Institute of Advanced Industrial Science and Technology, Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan
| | - Kouhei Miyake
- School of Engineering Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama, Kanagawa, 240-8501, Japan
| | - Kentaro Imafuku
- Device Technology Research Institute, National Institute of Advanced Industrial Science and Technology, Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan
| | - Yuki Yamanashi
- School of Engineering Science, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama, Kanagawa, 240-8501, Japan
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49
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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: 13] [Impact Index Per Article: 6.5] [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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50
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Matsuzaki Y, Imoto T, Susa Y. Generation of multipartite entanglement between spin-1 particles with bifurcation-based quantum annealing. Sci Rep 2022; 12:14964. [PMID: 36056092 PMCID: PMC9440094 DOI: 10.1038/s41598-022-17621-1] [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: 02/22/2022] [Accepted: 07/28/2022] [Indexed: 11/09/2022] Open
Abstract
Quantum annealing is a way to solve a combinational optimization problem where quantum fluctuation is induced by transverse fields. Recently, a bifurcation-based quantum annealing with spin-1 particles was suggested as another mechanism to implement the quantum annealing. In the bifurcation-based quantum annealing, each spin is initially prepared in [Formula: see text], let this state evolve by a time-dependent Hamiltonian in an adiabatic way, and we find a state spanned by [Formula: see text] at the end of the evolution. Here, we propose a scheme to generate multipartite entanglement, namely GHZ states, between spin-1 particles by using the bifurcation-based quantum annealing. We gradually decrease the detuning of the spin-1 particles while we adiabatically change the amplitude of the external driving fields. Due to the dipole-dipole interactions between the spin-1 particles, we can prepare the GHZ state after performing this protocol. We discuss possible implementations of our scheme by using nitrogen vacancy centers in diamond.
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Affiliation(s)
- Yuichiro Matsuzaki
- Research Center for Emerging Computing Technologies, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan. .,NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8568, Japan.
| | - Takashi Imoto
- Research Center for Emerging Computing Technologies, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan
| | - Yuki Susa
- NEC-AIST Quantum Technology Cooperative Research Laboratory, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8568, Japan.,System Platform Research Laboratories, NEC Corporation, Kawasaki, Kanagawa, 211-8666, Japan
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