1
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Laydevant J, Marković D, Grollier J. Training an Ising machine with equilibrium propagation. Nat Commun 2024; 15:3671. [PMID: 38693108 PMCID: PMC11063034 DOI: 10.1038/s41467-024-46879-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 03/12/2024] [Indexed: 05/03/2024] Open
Abstract
Ising machines, which are hardware implementations of the Ising model of coupled spins, have been influential in the development of unsupervised learning algorithms at the origins of Artificial Intelligence (AI). However, their application to AI has been limited due to the complexities in matching supervised training methods with Ising machine physics, even though these methods are essential for achieving high accuracy. In this study, we demonstrate an efficient approach to train Ising machines in a supervised way through the Equilibrium Propagation algorithm, achieving comparable results to software-based implementations. We employ the quantum annealing procedure of the D-Wave Ising machine to train a fully-connected neural network on the MNIST dataset. Furthermore, we demonstrate that the machine's connectivity supports convolution operations, enabling the training of a compact convolutional network with minimal spins per neuron. Our findings establish Ising machines as a promising trainable hardware platform for AI, with the potential to enhance machine learning applications.
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Affiliation(s)
- Jérémie Laydevant
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767, Palaiseau, France.
| | - Danijela Marković
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767, Palaiseau, France
| | - Julie Grollier
- Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay, 91767, Palaiseau, France.
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2
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Rattacaso D, Passarelli G, Russomanno A, Lucignano P, Santoro GE, Fazio R. Parent Hamiltonian Reconstruction via Inverse Quantum Annealing. PHYSICAL REVIEW LETTERS 2024; 132:160401. [PMID: 38701449 DOI: 10.1103/physrevlett.132.160401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Revised: 03/04/2024] [Accepted: 03/07/2024] [Indexed: 05/05/2024]
Abstract
Finding a local Hamiltonian H[over ^] that has a given many-body wave function |ψ⟩ as its ground state, i.e., a parent Hamiltonian, is a challenge of fundamental importance in quantum technologies. Here we introduce a numerical method, inspired by quantum annealing, that efficiently performs this task through an artificial inverse dynamics: a slow deformation of the states |ψ(λ(t))⟩, starting from a simple state |ψ_{0}⟩ with a known H[over ^]_{0}, generates an adiabatic evolution of the corresponding Hamiltonian. We name this approach inverse quantum annealing. The method, implemented through a projection onto a set of local operators, only requires the knowledge of local expectation values, and, for long annealing times, leads to an approximate parent Hamiltonian whose degree of locality depends on the correlations built up by the states |ψ(λ)⟩. We illustrate the method on two paradigmatic models: the Kitaev fermionic chain and a quantum Ising chain in longitudinal and transverse fields.
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Affiliation(s)
- Davide Rattacaso
- Dipartimento di Fisica "E. Pancini", Università di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy
- Dipartimento di Fisica e Astronomia "G. Galilei," Università di Padova, I-35131 Padova, Italy
| | | | - Angelo Russomanno
- Dipartimento di Fisica "E. Pancini", Università di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy
- Scuola Superiore Meridionale, Università di Napoli Federico II, Largo San Marcellino 10, I-80138 Napoli, Italy
| | - Procolo Lucignano
- Dipartimento di Fisica "E. Pancini", Università di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy
| | - Giuseppe E Santoro
- SISSA, Via Bonomea 265, I-34136 Trieste, Italy
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- CNR-IOM Democritos National Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy
| | - Rosario Fazio
- Dipartimento di Fisica "E. Pancini", Università di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy
- The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
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3
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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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4
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Alcazar J, Ghazi Vakili M, Kalayci CB, Perdomo-Ortiz A. Enhancing combinatorial optimization with classical and quantum generative models. Nat Commun 2024; 15:2761. [PMID: 38553469 PMCID: PMC10980691 DOI: 10.1038/s41467-024-46959-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2021] [Accepted: 03/15/2024] [Indexed: 04/02/2024] Open
Abstract
Devising an efficient exploration of the search space is one of the key challenges in the design of combinatorial optimization algorithms. Here, we introduce the Generator-Enhanced Optimization (GEO) strategy: a framework that leverages any generative model (classical, quantum, or quantum-inspired) to solve optimization problems. We focus on a quantum-inspired version of GEO relying on tensor-network Born machines, and referred to hereafter as TN-GEO. To illustrate our results, we run these benchmarks in the context of the canonical cardinality-constrained portfolio optimization problem by constructing instances from the S&P 500 and several other financial stock indexes, and demonstrate how the generalization capabilities of these quantum-inspired generative models can provide real value in the context of an industrial application. We also comprehensively compare state-of-the-art algorithms and show that TN-GEO is among the best; a remarkable outcome given the solvers used in the comparison have been fine-tuned for decades in this real-world industrial application. Also, a promising step toward a practical advantage with quantum-inspired models and, subsequently, with quantum generative models.
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Affiliation(s)
- Javier Alcazar
- Zapata Computing Canada Inc., 25 Adelaide St E, Suite 1500, Toronto, ON, M5C 3A1, Canada
- Acadian Asset Management LLC, 24 King William St, London, EC4R 9AT, England
| | - Mohammad Ghazi Vakili
- Zapata Computing Canada Inc., 25 Adelaide St E, Suite 1500, Toronto, ON, M5C 3A1, Canada
- Department of Chemistry, University of Toronto, Toronto, ON, M5G 1Z8, Canada
- Department of Computer Science, University of Toronto, Toronto, ON, M5S 2E4, Canada
| | - Can B Kalayci
- Zapata Computing Canada Inc., 25 Adelaide St E, Suite 1500, Toronto, ON, M5C 3A1, Canada
- Department of Industrial Engineering, Pamukkale University, Kinikli Campus, 20160, Denizli, Turkey
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5
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Li X, Chen X, Hu S, Xu J, Liu Z. A parameter-independent algorithm of finding maximum clique with Seidel continuous-time quantum walks. iScience 2024; 27:108953. [PMID: 38333715 PMCID: PMC10850753 DOI: 10.1016/j.isci.2024.108953] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Revised: 01/02/2024] [Accepted: 01/15/2024] [Indexed: 02/10/2024] Open
Abstract
The maximum clique (MC) problem holds significance in network analysis. Quantum-based algorithms have recently emerged as promising approaches for this problem. However, these algorithms heavily depend on parameters of quantum system and vary significantly for different graphs. In order to tackle this issue, we initially demonstrate that continuous-time quantum walks (CTQW) driven by the Seidel matrix offer valuable insights into the clique structure of graphs, outperforming the CTQW driven by adjacency matrix. Specifically, we conduct an in-depth analysis for CTQW of 4 types of graphs, meticulously calculating the amplitudes associated with different vertices. Our findings consistently reveal that vertices belonging to MC exhibit the highest intensity at the largest frequency component of the probability amplitude for these types of graphs. Considering the varying intensities, we propose a parameter-independent algorithm for determining the MC. We compare our algorithm with a typical quantum-based algorithm, the results indicate that our algorithm exhibits greater stability.
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Affiliation(s)
- Xi Li
- School of Computer Science and Engineering, Southeast University, No.2, Sipailou District, Nanjing, Jiangsu 210096, China
- Key Laboratory of Computer Network and Information Integration (Southeast University), Ministry of Education, No.2, Southeast University Road, Jiangning District, Nanjing, Jiangsu 211189, China
| | - Xiao Chen
- School of Computer Science and Engineering, Southeast University, No.2, Sipailou District, Nanjing, Jiangsu 210096, China
- Key Laboratory of Computer Network and Information Integration (Southeast University), Ministry of Education, No.2, Southeast University Road, Jiangning District, Nanjing, Jiangsu 211189, China
| | - Shouwei Hu
- School of Computer Science and Engineering, Southeast University, No.2, Sipailou District, Nanjing, Jiangsu 210096, China
- Key Laboratory of Computer Network and Information Integration (Southeast University), Ministry of Education, No.2, Southeast University Road, Jiangning District, Nanjing, Jiangsu 211189, China
| | - Juan Xu
- College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, No.29, Junjun Dadao, Jiangning District, Nanjing, Jiangsu 210016, China
- Collaborative Innovation Center of Novel Software Technology and Industrialization, No.29, Junjun Dadao, Jiangning District, Nanjing, Jiangsu 210023, China
| | - Zhihao Liu
- School of Computer Science and Engineering, Southeast University, No.2, Sipailou District, Nanjing, Jiangsu 210096, China
- Key Laboratory of Computer Network and Information Integration (Southeast University), Ministry of Education, No.2, Southeast University Road, Jiangning District, Nanjing, Jiangsu 211189, China
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6
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Charles C, Gustafson EJ, Hardt E, Herren F, Hogan N, Lamm H, Starecheski S, Van de Water RS, Wagman ML. Simulating Z_{2} lattice gauge theory on a quantum computer. Phys Rev E 2024; 109:015307. [PMID: 38366518 DOI: 10.1103/physreve.109.015307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 12/21/2023] [Indexed: 02/18/2024]
Abstract
The utility of quantum computers for simulating lattice gauge theories is currently limited by the noisiness of the physical hardware. Various quantum error mitigation strategies exist to reduce the statistical and systematic uncertainties in quantum simulations via improved algorithms and analysis strategies. We perform quantum simulations of Z_{2} gauge theory with matter to study the efficacy and interplay of different error mitigation methods: readout error mitigation, randomized compiling, rescaling, and dynamical decoupling. We compute Minkowski correlation functions in this confining gauge theory and extract the mass of the lightest spin-1 state from fits to their time dependence. Quantum error mitigation extends the range of times over which our correlation function calculations are accurate by a factor of 6 and is therefore essential for obtaining reliable masses.
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Affiliation(s)
- Clement Charles
- Department of Physics, The University of the West Indies, St. Augustine Campus, Trinidad and Tobago
- Physics Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Erik J Gustafson
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
- Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, Moffett Field, California 94035, USA
- USRA Research Institute for Advanced Computer Science (RIACS), Mountain View, California 94043, USA
| | - Elizabeth Hardt
- Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA
- Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Florian Herren
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Norman Hogan
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
| | - Henry Lamm
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
| | - Sara Starecheski
- Department of Physics, Sarah Lawrence College, Bronxville, New York 10708, USA
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | | | - Michael L Wagman
- Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
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7
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Kumar A, Asthana A, Abraham V, Crawford TD, Mayhall NJ, Zhang Y, Cincio L, Tretiak S, Dub PA. Quantum Simulation of Molecular Response Properties in the NISQ Era. J Chem Theory Comput 2023; 19:9136-9150. [PMID: 38054645 DOI: 10.1021/acs.jctc.3c00731] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
Accurate modeling of the response of molecular systems to an external electromagnetic field is challenging on classical computers, especially in the regime of strong electronic correlation. In this article, we develop a quantum linear response (qLR) theory to calculate molecular response properties on near-term quantum computers. Inspired by the recently developed variants of the quantum counterpart of equation of motion (qEOM) theory, the qLR formalism employs "killer condition" satisfying excitation operator manifolds that offer a number of theoretical advantages along with reduced quantum resource requirements. We also used the qEOM framework in this work to calculate the state-specific response properties. Further, through noiseless quantum simulations, we show that response properties calculated using the qLR approach are more accurate than the ones obtained from the classical coupled-cluster-based linear response models due to the improved quality of the ground-state wave function obtained using the ADAPT-VQE algorithm.
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Affiliation(s)
- Ashutosh Kumar
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ayush Asthana
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Vibin Abraham
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - T Daniel Crawford
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Nicholas J Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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8
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Sarkar A, Lee D, Meißner UG. Floating Block Method for Quantum Monte Carlo Simulations. PHYSICAL REVIEW LETTERS 2023; 131:242503. [PMID: 38181156 DOI: 10.1103/physrevlett.131.242503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2023] [Revised: 10/27/2023] [Accepted: 11/16/2023] [Indexed: 01/07/2024]
Abstract
Quantum Monte Carlo simulations are powerful and versatile tools for the quantum many-body problem. In addition to the usual calculations of energies and eigenstate observables, quantum Monte Carlo simulations can in principle be used to build fast and accurate many-body emulators using eigenvector continuation or design time-dependent Hamiltonians for adiabatic quantum computing. These new applications require something that is missing from the published literature, an efficient quantum Monte Carlo scheme for computing the inner product of ground state eigenvectors corresponding to different Hamiltonians. In this work, we introduce an algorithm called the floating block method, which solves the problem by performing Euclidean time evolution with two different Hamiltonians and interleaving the corresponding time blocks. We use the floating block method and nuclear lattice simulations to build eigenvector continuation emulators for energies of ^{4}He, ^{8}Be, ^{12}C, and ^{16}O nuclei over a range of local and nonlocal interaction couplings. From the emulator data, we identify the quantum phase transition line from a Bose gas of alpha particles to a nuclear liquid.
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Affiliation(s)
- Avik Sarkar
- Institut für Kernphysik, Institute for Advanced Simulation and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany
- Facility for Rare Isotope Beams and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Dean Lee
- Facility for Rare Isotope Beams and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - Ulf-G Meißner
- Institut für Kernphysik, Institute for Advanced Simulation and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich, Germany
- Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn, Germany
- Tbilisi State University, 0186 Tbilisi, Georgia
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9
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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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10
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Parajuli P, Govindarajan A, Tian L. State preparation in a Jaynes-Cummings lattice with quantum optimal control. Sci Rep 2023; 13:19924. [PMID: 37963930 PMCID: PMC10645998 DOI: 10.1038/s41598-023-47002-1] [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: 06/20/2023] [Accepted: 11/07/2023] [Indexed: 11/16/2023] Open
Abstract
High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation.
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Affiliation(s)
- Prabin Parajuli
- School of Natural Sciences, University of California, Merced, California, 95343, USA
| | - Anuvetha Govindarajan
- School of Natural Sciences, University of California, Merced, California, 95343, USA
| | - Lin Tian
- School of Natural Sciences, University of California, Merced, California, 95343, USA.
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11
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Dupont M, Evert B, Hodson MJ, Sundar B, Jeffrey S, Yamaguchi Y, Feng D, Maciejewski FB, Hadfield S, Alam MS, Wang Z, Grabbe S, Lott PA, Rieffel EG, Venturelli D, Reagor MJ. Quantum-enhanced greedy combinatorial optimization solver. SCIENCE ADVANCES 2023; 9:eadi0487. [PMID: 37948523 PMCID: PMC10637743 DOI: 10.1126/sciadv.adi0487] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2023] [Accepted: 10/10/2023] [Indexed: 11/12/2023]
Abstract
Combinatorial optimization is a broadly attractive area for potential quantum advantage, but no quantum algorithm has yet made the leap. Noise in quantum hardware remains a challenge, and more sophisticated quantum-classical algorithms are required to bolster their performance. Here, we introduce an iterative quantum heuristic optimization algorithm to solve combinatorial optimization problems. The quantum algorithm reduces to a classical greedy algorithm in the presence of strong noise. We implement the quantum algorithm on a programmable superconducting quantum system using up to 72 qubits for solving paradigmatic Sherrington-Kirkpatrick Ising spin glass problems. We find the quantum algorithm systematically outperforms its classical greedy counterpart, signaling a quantum enhancement. Moreover, we observe an absolute performance comparable with a state-of-the-art semidefinite programming method. Classical simulations of the algorithm illustrate that a key challenge to reaching quantum advantage remains improving the quantum device characteristics.
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Affiliation(s)
| | - Bram Evert
- Rigetti Computing, Berkeley, CA 94710, USA
| | | | | | | | | | | | - Filip B. Maciejewski
- QuAIL, NASA Ames Research Center, Moffett Field, CA 94035, USA
- USRA Research Institute for Advanced Computer Science, Mountain View, CA 94035, USA
| | - Stuart Hadfield
- QuAIL, NASA Ames Research Center, Moffett Field, CA 94035, USA
- USRA Research Institute for Advanced Computer Science, Mountain View, CA 94035, USA
| | - M. Sohaib Alam
- QuAIL, NASA Ames Research Center, Moffett Field, CA 94035, USA
- USRA Research Institute for Advanced Computer Science, Mountain View, CA 94035, USA
| | - Zhihui Wang
- QuAIL, NASA Ames Research Center, Moffett Field, CA 94035, USA
- USRA Research Institute for Advanced Computer Science, Mountain View, CA 94035, USA
| | - Shon Grabbe
- QuAIL, NASA Ames Research Center, Moffett Field, CA 94035, USA
| | - P. Aaron Lott
- QuAIL, NASA Ames Research Center, Moffett Field, CA 94035, USA
- USRA Research Institute for Advanced Computer Science, Mountain View, CA 94035, USA
| | | | - Davide Venturelli
- QuAIL, NASA Ames Research Center, Moffett Field, CA 94035, USA
- USRA Research Institute for Advanced Computer Science, Mountain View, CA 94035, USA
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12
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Xia W, Zou J, Qiu X, Chen F, Zhu B, Li C, Deng DL, Li X. Configured quantum reservoir computing for multi-task machine learning. Sci Bull (Beijing) 2023; 68:2321-2329. [PMID: 37679257 DOI: 10.1016/j.scib.2023.08.040] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2023] [Revised: 07/22/2023] [Accepted: 08/16/2023] [Indexed: 09/09/2023]
Abstract
Amidst the rapid advancements in experimental technology, noise-intermediate-scale quantum (NISQ) devices have become increasingly programmable, offering versatile opportunities to leverage quantum computational advantage. Here we explore the intricate dynamics of programmable NISQ devices for quantum reservoir computing. Using a genetic algorithm to configure the quantum reservoir dynamics, we systematically enhance the learning performance. Remarkably, a single configured quantum reservoir can simultaneously learn multiple tasks, including a synthetic oscillatory network of transcriptional regulators, chaotic motifs in gene regulatory networks, and the fractional-order Chua's circuit. Our configured quantum reservoir computing yields highly precise predictions for these learning tasks, outperforming classical reservoir computing. We also test the configured quantum reservoir computing in foreign exchange (FX) market applications and demonstrate its capability to capture the stochastic evolution of the exchange rates with significantly greater accuracy than classical reservoir computing approaches. Through comparison with classical reservoir computing, we highlight the unique role of quantum coherence in the quantum reservoir, which underpins its exceptional learning performance. Our findings suggest the exciting potential of configured quantum reservoir computing for exploiting the quantum computation power of NISQ devices in developing artificial general intelligence.
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Affiliation(s)
- Wei Xia
- State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University, Shanghai 200433, China
| | - Jie Zou
- State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University, Shanghai 200433, China
| | - Xingze Qiu
- State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University, Shanghai 200433, China; School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
| | - Feng Chen
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China
| | - Bing Zhu
- Hong Kong and Shang Hai Banking Corporation Laboratory, Hong Kong and Shang Hai Banking Corporation Holdings PLC, Guangzhou 511458, China
| | - Chunhe Li
- Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai 200433, China; Shanghai Center for Mathematical Sciences and School of Mathematical Sciences, Fudan University, Shanghai 200433, China
| | - Dong-Ling Deng
- Center for Quantum Information, IIIS, Tsinghua University, Beijing 100084, China; Shanghai Qi Zhi Institute, AI Tower, Shanghai 200232, China
| | - Xiaopeng Li
- State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University, Shanghai 200433, China; Shanghai Qi Zhi Institute, AI Tower, Shanghai 200232, China; Shanghai Research Center for Quantum Sciences, Shanghai 201315, China.
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13
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Motta M, Sung KJ, Whaley KB, Head-Gordon M, Shee J. Bridging physical intuition and hardware efficiency for correlated electronic states: the local unitary cluster Jastrow ansatz for electronic structure. Chem Sci 2023; 14:11213-11227. [PMID: 37860666 PMCID: PMC10583744 DOI: 10.1039/d3sc02516k] [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: 05/18/2023] [Accepted: 09/20/2023] [Indexed: 10/21/2023] Open
Abstract
A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than a unitary coupled cluster with single and double excitations (qUCCSD), with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. As in the case of qUCCSD, exactly computing the energy scales factorially with system size on classical computers but polynomially on quantum devices. The local unitary cluster Jastrow ansatz removes the need for SWAP gates, can be tailored to arbitrary qubit topologies (e.g., square, hex, and heavy-hex), and is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers. The proposed family of ansatzes demonstrates that hardware efficiency and physical transparency are not mutually exclusive; indeed, chemical and physical intuition regarding electron correlation can illuminate a useful path towards hardware-friendly quantum circuits.
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Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research - Almaden San Jose CA 95120 USA
| | - Kevin J Sung
- IBM Quantum, IBM T. J. Watson Research Center Yorktown Heights NY 10598 USA
| | - K Birgitta Whaley
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Berkeley Quantum Information and Computation Center, University of California Berkeley CA 94720 USA
- Challenge Institute for Quantum Computation, University of California Berkeley CA 94720 USA
| | - Martin Head-Gordon
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley CA 94720 USA
| | - James Shee
- Department of Chemistry, University of California Berkeley CA 94720 USA
- Department of Chemistry, Rice University Houston TX 77005 USA
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14
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Nau MA, Vija AH, Gohn W, Reymann MP, Maier AK. Exploring the Limitations of Hybrid Adiabatic Quantum Computing for Emission Tomography Reconstruction. J Imaging 2023; 9:221. [PMID: 37888328 PMCID: PMC10607451 DOI: 10.3390/jimaging9100221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2023] [Revised: 10/07/2023] [Accepted: 10/08/2023] [Indexed: 10/28/2023] Open
Abstract
Our study explores the feasibility of quantum computing in emission tomography reconstruction, addressing a noisy ill-conditioned inverse problem. In current clinical practice, this is typically solved by iterative methods minimizing a L2 norm. After reviewing quantum computing principles, we propose the use of a commercially available quantum annealer and employ corresponding hybrid solvers, which combine quantum and classical computing to handle more significant problems. We demonstrate how to frame image reconstruction as a combinatorial optimization problem suited for these quantum annealers and hybrid systems. Using a toy problem, we analyze reconstructions of binary and integer-valued images with respect to their image size and compare them to conventional methods. Additionally, we test our method's performance under noise and data underdetermination. In summary, our method demonstrates competitive performance with traditional algorithms for binary images up to an image size of 32×32 on the toy problem, even under noisy and underdetermined conditions. However, scalability challenges emerge as image size and pixel bit range increase, restricting hybrid quantum computing as a practical tool for emission tomography reconstruction until significant advancements are made to address this issue.
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Affiliation(s)
- Merlin A. Nau
- Pattern Recognition Lab, Department of Computer Science, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), Martensstrasse 3, 91058 Erlangen, Germany
- Siemens Healthineers GmbH, Siemensstrasse 1, 91301 Forchheim, Germany
| | - A. Hans Vija
- Siemens Medical Solutions USA, Inc., 2501 Barrington Rd, Hoffman Estates, IL 60192, USA
| | - Wesley Gohn
- Siemens Medical Solutions USA, Inc., 2501 Barrington Rd, Hoffman Estates, IL 60192, USA
| | - Maximilian P. Reymann
- Pattern Recognition Lab, Department of Computer Science, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), Martensstrasse 3, 91058 Erlangen, Germany
- Siemens Healthineers GmbH, Siemensstrasse 1, 91301 Forchheim, Germany
| | - Andreas K. Maier
- Pattern Recognition Lab, Department of Computer Science, Friedrich-Alexander Universität Erlangen-Nürnberg (FAU), Martensstrasse 3, 91058 Erlangen, Germany
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15
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Pal S, Bhattacharya M, Dash S, Lee SS, Chakraborty C. Future Potential of Quantum Computing and Simulations in Biological Science. Mol Biotechnol 2023:10.1007/s12033-023-00863-3. [PMID: 37717248 DOI: 10.1007/s12033-023-00863-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 08/16/2023] [Indexed: 09/19/2023]
Abstract
The review article presents the recent progress in quantum computing and simulation within the field of biological sciences. The article is designed mainly into two portions: quantum computing and quantum simulation. In the first part, significant aspects of quantum computing was illustrated, such as quantum hardware, quantum RAM and big data, modern quantum processors, qubit, superposition effect in quantum computation, quantum interference, quantum entanglement, and quantum logic gates. Simultaneously, in the second part, vital features of the quantum simulation was illustrated, such as the quantum simulator, algorithms used in quantum simulations, and the use of quantum simulation in biological science. Finally, the review provides exceptional views to future researchers about different aspects of quantum simulation in biological science.
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Affiliation(s)
- Soumen Pal
- School of Mechanical Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India
| | - Manojit Bhattacharya
- Department of Zoology, Fakir Mohan University, Vyasa Vihar, Balasore, Odisha, 756020, India
| | - Snehasish Dash
- School of Mechanical Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India
| | - Sang-Soo Lee
- Institute for Skeletal Aging & Orthopedic Surgery, Hallym University-Chuncheon Sacred Heart Hospital, Chuncheon, Gangwon-Do, 24252, Republic of Korea
| | - Chiranjib Chakraborty
- Department of Biotechnology, School of Life Science and Biotechnology, Adamas University, Kolkata, West Bengal, 700126, India.
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16
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Ye M, Tian Y, Lin J, Luo Y, You J, Hu J, Zhang W, Chen W, Li X. Universal Quantum Optimization with Cold Atoms in an Optical Cavity. PHYSICAL REVIEW LETTERS 2023; 131:103601. [PMID: 37739373 DOI: 10.1103/physrevlett.131.103601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Accepted: 08/15/2023] [Indexed: 09/24/2023]
Abstract
Cold atoms in an optical cavity have been widely used for quantum simulations of many-body physics, where the quantum control capability has been advancing rapidly in recent years. Here, we show the atom cavity system is universal for quantum optimization with arbitrary connectivity. We consider a single-mode cavity and develop a Raman coupling scheme by which the engineered quantum Hamiltonian for atoms directly encodes number partition problems. The programmability is introduced by placing the atoms at different positions in the cavity with optical tweezers. The number partition problem solution is encoded in the ground state of atomic qubits coupled through a photonic cavity mode, which can be reached by adiabatic quantum computing. We construct an explicit mapping for the 3-SAT and vertex cover problems to be efficiently encoded by the cavity system, which costs linear overhead in the number of atomic qubits. The atom cavity encoding is further extended to quadratic unconstrained binary optimization problems. The encoding protocol is optimal in the cost of atom number scaling with the number of binary degrees of freedom of the computation problem. Our theory implies the atom cavity system is a promising quantum optimization platform searching for practical quantum advantage.
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Affiliation(s)
- Meng Ye
- State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University, Shanghai 200433, China
- Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai 200232, China
| | - Ye Tian
- Department of Physics and State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Jian Lin
- State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University, Shanghai 200433, China
| | - Yuchen Luo
- State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University, Shanghai 200433, China
- Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai 200232, China
| | - Jiaqi You
- Department of Physics and State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Jiazhong Hu
- Department of Physics and State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Wenjun Zhang
- Department of Physics and State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Wenlan Chen
- Department of Physics and State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing 100084, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100084, China
| | - Xiaopeng Li
- State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University, Shanghai 200433, China
- Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai 200232, China
- Institute of Nanoelectronics and Quantum Computing, Fudan University, Shanghai 200433, China
- Shanghai Artificial Intelligence Laboratory, Shanghai 200232, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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17
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Yin XF, Yao XC, Wu B, Fei YY, Mao Y, Zhang R, Liu LZ, Wang Z, Li L, Liu NL, Wilczek F, Chen YA, Pan JW. Solving independent set problems with photonic quantum circuits. Proc Natl Acad Sci U S A 2023; 120:e2212323120. [PMID: 37216545 PMCID: PMC10235971 DOI: 10.1073/pnas.2212323120] [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: 08/08/2022] [Accepted: 03/01/2023] [Indexed: 05/24/2023] Open
Abstract
An independent set (IS) is a set of vertices in a graph such that no edge connects any two vertices. In adiabatic quantum computation [E. Farhi, et al., Science 292, 472-475 (2001); A. Das, B. K. Chakrabarti, Rev. Mod. Phys. 80, 1061-1081 (2008)], a given graph G(V, E) can be naturally mapped onto a many-body Hamiltonian [Formula: see text], with edges [Formula: see text] being the two-body interactions between adjacent vertices [Formula: see text]. Thus, solving the IS problem is equivalent to finding all the computational basis ground states of [Formula: see text]. Very recently, non-Abelian adiabatic mixing (NAAM) has been proposed to address this task, exploiting an emergent non-Abelian gauge symmetry of [Formula: see text] [B. Wu, H. Yu, F. Wilczek, Phys. Rev. A 101, 012318 (2020)]. Here, we solve a representative IS problem [Formula: see text] by simulating the NAAM digitally using a linear optical quantum network, consisting of three C-Phase gates, four deterministic two-qubit gate arrays (DGA), and ten single rotation gates. The maximum IS has been successfully identified with sufficient Trotterization steps and a carefully chosen evolution path. Remarkably, we find IS with a total probability of 0.875(16), among which the nontrivial ones have a considerable weight of about 31.4%. Our experiment demonstrates the potential advantage of NAAM for solving IS-equivalent problems.
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Affiliation(s)
- Xu-Fei Yin
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Xing-Can Yao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Biao Wu
- International Center for Quantum Materials, School of Physics, Peking University, Beijing100871, China
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai200240, China
| | - Yue-Yang Fei
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Yingqiu Mao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Rui Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Li-Zheng Liu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Zhenduo Wang
- International Center for Quantum Materials, School of Physics, Peking University, Beijing100871, China
| | - Li Li
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Nai-Le Liu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Frank Wilczek
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai200240, China
- Center for Theoretical Physics, MIT, Cambridge, MA02139
- T. D. Lee Institute, Shanghai Jiao Tong University, Shanghai200240, China
- Department of Physics, Stockholm University, StockholmSE-106 91, Sweden
- Department of Physics and Origins Project, Arizona State University, Tempe, AZ25287
| | - Yu-Ao Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei230088, China
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18
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John M, Schuhmacher J, Barkoutsos P, Tavernelli I, Tacchino F. Optimizing Quantum Classification Algorithms on Classical Benchmark Datasets. ENTROPY (BASEL, SWITZERLAND) 2023; 25:860. [PMID: 37372204 DOI: 10.3390/e25060860] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2023] [Revised: 05/24/2023] [Accepted: 05/24/2023] [Indexed: 06/29/2023]
Abstract
The discovery of quantum algorithms offering provable advantages over the best known classical alternatives, together with the parallel ongoing revolution brought about by classical artificial intelligence, motivates a search for applications of quantum information processing methods to machine learning. Among several proposals in this domain, quantum kernel methods have emerged as particularly promising candidates. However, while some rigorous speedups on certain highly specific problems have been formally proven, only empirical proof-of-principle results have been reported so far for real-world datasets. Moreover, no systematic procedure is known, in general, to fine tune and optimize the performances of kernel-based quantum classification algorithms. At the same time, certain limitations such as kernel concentration effects-hindering the trainability of quantum classifiers-have also been recently pointed out. In this work, we propose several general-purpose optimization methods and best practices designed to enhance the practical usefulness of fidelity-based quantum classification algorithms. Specifically, we first describe a data pre-processing strategy that, by preserving the relevant relationships between data points when processed through quantum feature maps, substantially alleviates the effect of kernel concentration on structured datasets. We also introduce a classical post-processing method that, based on standard fidelity measures estimated on a quantum processor, yields non-linear decision boundaries in the feature Hilbert space, thus achieving the quantum counterpart of the radial basis functions technique that is widely employed in classical kernel methods. Finally, we apply the so-called quantum metric learning protocol to engineer and adjust trainable quantum embeddings, demonstrating substantial performance improvements on several paradigmatic real-world classification tasks.
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Affiliation(s)
- Manuel John
- IBM Quantum, IBM Research Europe-Zurich, 8803 Rüschlikon, Switzerland
- Institute for Theoretical Physics, ETH Zürich, 8093 Zurich, Switzerland
| | | | | | - Ivano Tavernelli
- IBM Quantum, IBM Research Europe-Zurich, 8803 Rüschlikon, Switzerland
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19
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Yan Z, Wang YC, Samajdar R, Sachdev S, Meng ZY. Emergent Glassy Behavior in a Kagome Rydberg Atom Array. PHYSICAL REVIEW LETTERS 2023; 130:206501. [PMID: 37267547 DOI: 10.1103/physrevlett.130.206501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Revised: 03/12/2023] [Accepted: 03/16/2023] [Indexed: 06/04/2023]
Abstract
We present large-scale quantum Monte Carlo simulation results on a realistic Hamiltonian of kagome-lattice Rydberg atom arrays. Although the system has no intrinsic disorder, intriguingly, our analyses of static and dynamic properties on large system sizes reveal emergent glassy behavior in a region of parameter space located between two valence bond solid phases. The extent of this glassy region is demarcated using the Edwards-Anderson order parameter, and its phase transitions to the two proximate valence bond solids-as well as the crossover towards a trivial paramagnetic phase-are identified. We demonstrate the intrinsically slow (imaginary) time dynamics deep inside the glassy phase and discuss experimental considerations for detecting such a quantum disordered phase with numerous nearly degenerate local minima. Our proposal paves a new route to the study of real-time glassy phenomena and highlights the potential for quantum simulation of a distinct phase of quantum matter beyond solids and liquids in current-generation Rydberg platforms.
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Affiliation(s)
- Zheng Yan
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
| | - Yan-Cheng Wang
- Beihang Hangzhou Innovation Institute Yuhang, Hangzhou 310023, China
- Zhongfa Aviation Institute of Beihang University, Hangzhou 310023, China
| | - Rhine Samajdar
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - Subir Sachdev
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Zi Yang Meng
- Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
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20
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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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21
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Sampei H, Saegusa K, Chishima K, Higo T, Tanaka S, Yayama Y, Nakamura M, Kimura K, Sekine Y. Quantum Annealing Boosts Prediction of Multimolecular Adsorption on Solid Surfaces Avoiding Combinatorial Explosion. JACS AU 2023; 3:991-996. [PMID: 37124301 PMCID: PMC10131206 DOI: 10.1021/jacsau.3c00018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/09/2023] [Revised: 03/11/2023] [Accepted: 03/17/2023] [Indexed: 05/03/2023]
Abstract
Quantum annealing has been used to predict molecular adsorption on solid surfaces. Evaluation of adsorption, which takes place in all solid surface reactions, is a crucially important subject for study in various fields. However, predicting the most stable coordination by theoretical calculations is challenging for multimolecular adsorption because there are numerous candidates. This report presents a novel method for quick adsorption coordination searches using the quantum annealing principle without combinatorial explosion. This method exhibited much faster search and more stable molecular arrangement findings than conventional methods did, particularly in a high coverage region. We were able to complete a configurational prediction of the adsorption of 16 molecules in 2286 s (including 2154 s for preparation, only required once), whereas previously it has taken 38 601 s. This approach accelerates the tuning of adsorption behavior, especially in composite materials and large-scale modeling, which possess more combinations of molecular configurations.
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Affiliation(s)
- Hiroshi Sampei
- Department
of Applied Chemistry, Waseda University, Tokyo 169-8555, Japan
| | - Koki Saegusa
- Department
of Applied Chemistry, Waseda University, Tokyo 169-8555, Japan
| | - Kenshin Chishima
- Department
of Applied Chemistry, Waseda University, Tokyo 169-8555, Japan
| | - Takuma Higo
- Department
of Applied Chemistry, Waseda University, Tokyo 169-8555, Japan
| | - Shu Tanaka
- Department
of Applied Physics and Physico-Informatics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
- Green
Computing System Research Organization, Waseda University, Wasedamachi-27,
Shinjuku-ku, Tokyo 162-0042, Japan
| | - Yoshihiro Yayama
- Central
Technical Research Laboratory, ENEOS Corporation, 231-0815, 8 Chidoricho, Naka-ku, Yokohama, Kanagawa 100-8162, Japan
| | - Makoto Nakamura
- Quantum
Research Center, Fujitsu Ltd., 4-1-1 Kamiodanaka, Kawasaki, Kanagawa 211-8588, Japan
| | - Koichi Kimura
- Quantum
Research Center, Fujitsu Ltd., 4-1-1 Kamiodanaka, Kawasaki, Kanagawa 211-8588, Japan
| | - Yasushi Sekine
- Department
of Applied Chemistry, Waseda University, Tokyo 169-8555, Japan
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22
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Mwamsojo N, Lehmann F, Merghem K, Benkelfat BE, Frignac Y. Optoelectronic coherent Ising machine for combinatorial optimization problems. OPTICS LETTERS 2023; 48:2150-2153. [PMID: 37058664 DOI: 10.1364/ol.485215] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2023] [Accepted: 03/20/2023] [Indexed: 06/19/2023]
Abstract
Hopfield networks are iterative procedures able to solve combinatorial optimization problems. New studies regarding algorithm-architecture adequacy are fostered by the re-emergence of hardware implementations of such methods in the form of Ising machines. In this work, we propose an optoelectronic architecture suitable for fast processing and low energy consumption. We show that our approach allows effective optimization relevant to statistical image denoising.
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23
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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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24
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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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25
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Suppressing quantum errors by scaling a surface code logical qubit. Nature 2023; 614:676-681. [PMID: 36813892 PMCID: PMC9946823 DOI: 10.1038/s41586-022-05434-1] [Citation(s) in RCA: 40] [Impact Index Per Article: 40.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Accepted: 10/10/2022] [Indexed: 02/24/2023]
Abstract
Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10-6 logical error per cycle floor set by a single high-energy event (1.6 × 10-7 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.
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26
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Lu B, Fan CR, Liu L, Wen K, Wang C. Speed-up coherent Ising machine with a spiking neural network. OPTICS EXPRESS 2023; 31:3676-3684. [PMID: 36785354 DOI: 10.1364/oe.479903] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Coherent Ising machine (CIM) is a hardware solver that simulates the Ising model and finds optimal solutions to combinatorial optimization problems. However, for practical tasks, the computational process may be trapped in local minima, which is a key challenge for CIM. In this work, we design a CIM structure with a spiking neural network by adding dissipative pulses, which are anti-symmetrically coupled to the degenerate optical parametric oscillator pulses in CIM with a measurement feedback system. We find that the unstable oscillatory region of the spiking neural network could assist the CIM to escape from the trapped local minima. Moreover, we show that the machine has a different search mechanism than CIM, which can achieve a higher solution success probability and speed-up effect.
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27
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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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28
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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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29
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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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30
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Kadowaki T, Nishimori H. Greedy parameter optimization for diabatic quantum annealing. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20210416. [PMID: 36463922 PMCID: PMC9719795 DOI: 10.1098/rsta.2021.0416] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
A shorter processing time is desirable for quantum computation to minimize the effects of noise. We propose a simple procedure to variationally determine a set of parameters in the transverse-field Ising model for quantum annealing (QA) appended with a field along the [Formula: see text]-axis. The method consists of greedy optimization of the signs of coefficients of the [Formula: see text]-field term based on the outputs of short annealing processes. We test the idea in the ferromagnetic system with all-to-all couplings and spin-glass problems, and find that the method outperforms the traditional form of QA and simulated annealing in terms of the success probability and the time to solution, in particular, in the case of shorter annealing times, achieving the goal of improved performance while avoiding noise. The non-stoquastic [Formula: see text] term can be eliminated by a rotation in the spin space, resulting in a non-trivial diabatic control of the coefficients in the stoquastic transverse-field Ising model, which may be feasible for experimental realization. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
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Affiliation(s)
| | - Hidetoshi Nishimori
- Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Kanagawa 226-8503, Japan
- Graduate School of Information Sciences, Tohoku University, Sendai, Miyagi 980-8579, Japan
- RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), Wako, Saitama 351-0198, Japan
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31
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Ruan Y, Yuan Z, Xue X, Liu Z. Quantum approximate optimization for combinatorial problems with constraints. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.11.020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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32
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Many-body localization enables iterative quantum optimization. Nat Commun 2022; 13:5503. [PMID: 36127344 PMCID: PMC9489738 DOI: 10.1038/s41467-022-33179-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Accepted: 09/07/2022] [Indexed: 11/08/2022] Open
Abstract
Many discrete optimization problems are exponentially hard due to the underlying glassy landscape. This means that the optimization cost exhibits multiple local minima separated by an extensive number of switched discrete variables. Quantum computation was coined to overcome this predicament, but so far had only a limited progress. Here we suggest a quantum approximate optimization algorithm which is based on a repetitive cycling around the tricritical point of the many-body localization (MBL) transition. Each cycle includes quantum melting of the glassy state through a first order transition with a subsequent reentrance through the second order MBL transition. Keeping the reentrance path sufficiently close to the tricritical point separating the first and second order transitions, allows one to systematically improve optimization outcomes. The running time of this algorithm scales algebraically with the system size and the required precision. The corresponding exponents are related to critical indexes of the continuous MBL transition. There are several proposals for quantum algorithms solving optimisation problems, but so far none of them has provided a clear speedup. Here, the authors propose an iterative protocol featuring periodic cycling around the tricritical point of a many-body localization transition.
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33
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Veis L. A further step towards the practical application of quantum computing in chemistry. Commun Chem 2022; 5:108. [PMID: 36697898 PMCID: PMC9814620 DOI: 10.1038/s42004-022-00727-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2022] [Accepted: 08/24/2022] [Indexed: 01/28/2023] Open
Affiliation(s)
- Libor Veis
- grid.418095.10000 0001 1015 3316J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Prague, Czech Republic
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34
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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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35
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Kumar A, Asthana A, Masteran C, Valeev EF, Zhang Y, Cincio L, Tretiak S, Dub PA. Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits. J Chem Theory Comput 2022; 18:5312-5324. [PMID: 35984716 DOI: 10.1021/acs.jctc.2c00520] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.
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Affiliation(s)
- Ashutosh Kumar
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ayush Asthana
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Conner Masteran
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Yu Zhang
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Lukasz Cincio
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States.,Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Pavel A Dub
- Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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36
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Schleier-Smith M. Solving a puzzle with atomic qubits. Science 2022; 376:1155-1156. [PMID: 35679424 DOI: 10.1126/science.abq3754] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
A quantum com puter makes light work of the maximum independent set problem.
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37
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Mosca M, Verschoor SR. Factoring semi-primes with (quantum) SAT-solvers. Sci Rep 2022; 12:7982. [PMID: 35568707 PMCID: PMC9107490 DOI: 10.1038/s41598-022-11687-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Accepted: 04/25/2022] [Indexed: 11/09/2022] Open
Abstract
The computational difficulty of factoring large integers forms the basis of security for RSA public-key cryptography. The best-known factoring algorithms for classical computers run in sub-exponential time. The integer factorization problem can be reduced to the Boolean Satisfiability problem (SAT). While this reduction has proved to be useful for studying SAT solvers, large integers have not been factored via such a reduction. Shor's quantum factoring algorithm factors integers in expected polynomial time. Large-scale fault-tolerant quantum computers capable of implementing Shor's algorithm are not yet available, preventing relevant benchmarking experiments. Recently, several authors have attempted quantum factorizations via reductions to SAT or similar NP-hard problems. While this approach may shed light on algorithmic approaches for quantum solutions to NP-hard problems, in this paper we study and question its practicality. We find no evidence that this is a viable path toward factoring large numbers, even for scalable fault-tolerant quantum computers, as well as for various quantum annealing or other special purpose quantum hardware.
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Affiliation(s)
- Michele Mosca
- Institute for Quantum Computing, University of Waterloo, Waterloo, Canada.,Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada.,Perimeter Institute for Theoretical Physics, Waterloo, Canada.,Canadian Institute for Advanced Research, Toronto, Canada.,evolutionQ Inc., Waterloo, Canada
| | - Sebastian R Verschoor
- Institute for Quantum Computing, University of Waterloo, Waterloo, Canada. .,David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada.
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38
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Ebadi S, Keesling A, Cain M, Wang TT, Levine H, Bluvstein D, Semeghini G, Omran A, Liu JG, Samajdar R, Luo XZ, Nash B, Gao X, Barak B, Farhi E, Sachdev S, Gemelke N, Zhou L, Choi S, Pichler H, Wang ST, Greiner M, Vuletic V, Lukin MD. Quantum optimization of maximum independent set using Rydberg atom arrays. Science 2022; 376:1209-1215. [PMID: 35511943 DOI: 10.1126/science.abo6587] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally investigate quantum algorithms for solving the Maximum Independent Set problem. We use a hardware-efficient encoding associated with Rydberg blockade, realize closed-loop optimization to test several variational algorithms, and subsequently apply them to systematically explore a class of graphs with programmable connectivity. We find the problem hardness is controlled by the solution degeneracy and number of local minima, and experimentally benchmark the quantum algorithm's performance against classical simulated annealing. On the hardest graphs, we observe a superlinear quantum speedup in finding exact solutions in the deep circuit regime and analyze its origins.
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Affiliation(s)
- S Ebadi
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Keesling
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - M Cain
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - T T Wang
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - H Levine
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - D Bluvstein
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - G Semeghini
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - A Omran
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - J-G Liu
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,QuEra Computing Inc., Boston, MA 02135, USA
| | - R Samajdar
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - X-Z Luo
- QuEra Computing Inc., Boston, MA 02135, USA.,Department of Physics and Astronomy, University of Waterloo, Waterloo N2L 3G1, Canada.,Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
| | - B Nash
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - X Gao
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - B Barak
- School of Engineering and Applied Science, Harvard University, Cambridge, MA 02138, USA
| | - E Farhi
- Google Quantum AI, Venice, CA 90291, USA.,Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - S Sachdev
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,School of Natural Sciences, Institute for Advanced Study, Princeton, NJ 08540, USA
| | - N Gemelke
- QuEra Computing Inc., Boston, MA 02135, USA
| | - L Zhou
- Department of Physics, Harvard University, Cambridge, MA 02138, USA.,Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - S Choi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - H Pichler
- Institute for Theoretical Physics, University of Innsbruck, Innsbruck A-6020, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - S-T Wang
- QuEra Computing Inc., Boston, MA 02135, USA
| | - M Greiner
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | | | - M D Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
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39
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Motta M, Rice JE. Emerging quantum computing algorithms for quantum chemistry. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1580] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Mario Motta
- IBM Quantum, IBM Research‐Almaden San Jose California USA
| | - Julia E. Rice
- IBM Quantum, IBM Research‐Almaden San Jose California USA
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40
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Oshiyama H, Suzuki S, Shibata N. Classical Simulation and Theory of Quantum Annealing in a Thermal Environment. PHYSICAL REVIEW LETTERS 2022; 128:170502. [PMID: 35570457 DOI: 10.1103/physrevlett.128.170502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Revised: 02/21/2022] [Accepted: 03/22/2022] [Indexed: 06/15/2023]
Abstract
We study quantum annealing in the quantum Ising model coupled to a thermal environment. When the speed of quantum annealing is sufficiently slow, the system evolves following the instantaneous thermal equilibrium. This quasistatic and isothermal evolution, however, fails near the end of annealing because the relaxation time grows infinitely, therefore yielding excess energy from the thermal equilibrium. We develop a phenomenological theory based on this picture and derive a scaling relation of the excess energy after annealing. The theoretical results are numerically confirmed using a novel non-Markovian method that we recently proposed based on a path-integral representation of the reduced density matrix and the infinite time evolving block decimation. In addition, we discuss crossovers from weak to strong coupling as well as from the adiabatic to quasistatic regime, and propose experiments on the D-Wave quantum annealer.
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Affiliation(s)
- Hiroki Oshiyama
- Department of Physics, Tohoku University, Sendai 980-8578, Japan
| | - Sei Suzuki
- Department of Liberal Arts, Saitama Medical University, Moroyama, Saitama 350-0495, Japan
| | - Naokazu Shibata
- Department of Physics, Tohoku University, Sendai 980-8578, Japan
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41
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Schuetz MJA, Brubaker JK, Katzgraber HG. Combinatorial optimization with physics-inspired graph neural networks. NAT MACH INTELL 2022. [DOI: 10.1038/s42256-022-00468-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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42
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Abstract
Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute high quality solutions of NP-hard problems. This is done by mapping a problem onto the physical qubits of the quantum chip, from which a solution is obtained after quantum annealing. However, since the connectivity of the physical qubits on the chip is limited, a minor embedding of the problem structure onto the chip is required. In this process, and especially for smaller problems, many qubits will stay unused. We propose a novel method, called parallel quantum annealing, to make better use of available qubits, wherein either the same or several independent problems are solved in the same annealing cycle of a quantum annealer, assuming enough physical qubits are available to embed more than one problem. Although the individual solution quality may be slightly decreased when solving several problems in parallel (as opposed to solving each problem separately), we demonstrate that our method may give dramatic speed-ups in terms of the Time-To-Solution (TTS) metric for solving instances of the Maximum Clique problem when compared to solving each problem sequentially on the quantum annealer. Additionally, we show that solving a single Maximum Clique problem using parallel quantum annealing reduces the TTS significantly.
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43
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Optimizing quantum annealing schedules with Monte Carlo tree search enhanced with neural networks. NAT MACH INTELL 2022. [DOI: 10.1038/s42256-022-00446-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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44
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Yoon B, Nguyen NTT, Chang CC, Rrapaj E. Lossy compression of statistical data using quantum annealer. Sci Rep 2022; 12:3814. [PMID: 35264581 PMCID: PMC8907274 DOI: 10.1038/s41598-022-07539-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Accepted: 02/10/2022] [Indexed: 11/17/2022] Open
Abstract
We present a new lossy compression algorithm for statistical floating-point data through a representation learning with binary variables. The algorithm finds a set of basis vectors and their binary coefficients that precisely reconstruct the original data. The optimization for the basis vectors is performed classically, while binary coefficients are retrieved through both simulated and quantum annealing for comparison. A bias correction procedure is also presented to estimate and eliminate the error and bias introduced from the inexact reconstruction of the lossy compression for statistical data analyses. The compression algorithm is demonstrated on two different datasets of lattice quantum chromodynamics simulations. The results obtained using simulated annealing show 3–3.5 times better compression performance than the algorithm based on neural-network autoencoder. Calculations using quantum annealing also show promising results, but performance is limited by the integrated control error of the quantum processing unit, which yields large uncertainties in the biases and coupling parameters. Hardware comparison is further studied between the previous generation D-Wave 2000Q and the current D-Wave Advantage system. Our study shows that the Advantage system is more likely to obtain low-energy solutions for the problems than the 2000Q.
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Affiliation(s)
- Boram Yoon
- CCS-7, Computer, Computational and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
| | - Nga T T Nguyen
- CCS-3, Computer, Computational and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA
| | - Chia Cheng Chang
- RIKEN iTHEMS, Wako, Saitama, 351-0198, Japan.,Department of Physics, University of California, Berkeley, CA, 94720, USA.,Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA.,LinkedIn Corporation, Sunnyvale, CA, 94085, USA
| | - Ermal Rrapaj
- Department of Physics, University of California, Berkeley, CA, 94720, USA
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45
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Benchmark of quantum-inspired heuristic solvers for quadratic unconstrained binary optimization. Sci Rep 2022; 12:2146. [PMID: 35140264 PMCID: PMC8828756 DOI: 10.1038/s41598-022-06070-5] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Accepted: 01/14/2022] [Indexed: 11/08/2022] Open
Abstract
Recently, inspired by quantum annealing, many solvers specialized for unconstrained binary quadratic programming problems have been developed. For further improvement and application of these solvers, it is important to clarify the differences in their performance for various types of problems. In this study, the performance of four quadratic unconstrained binary optimization problem solvers, namely D-Wave Hybrid Solver Service (HSS), Toshiba Simulated Bifurcation Machine (SBM), Fujitsu Digital Annealer (DA), and simulated annealing on a personal computer, was benchmarked. The problems used for benchmarking were instances of real problems in MQLib, instances of the SAT-UNSAT phase transition point of random not-all-equal 3-SAT (NAE 3-SAT), and the Ising spin glass Sherrington-Kirkpatrick (SK) model. Concerning MQLib instances, the HSS performance ranked first; for NAE 3-SAT, DA performance ranked first; and regarding the SK model, SBM performance ranked first. These results may help understand the strengths and weaknesses of these solvers.
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46
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Zhang Y, Mu X, Liu X, Wang X, Zhang X, Li K, Wu T, Zhao D, Dong C. Applying the quantum approximate optimization algorithm to the minimum vertex cover problem. Appl Soft Comput 2022. [DOI: 10.1016/j.asoc.2022.108554] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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47
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Yin Z, Li C, Allcock J, Zheng Y, Gu X, Dai M, Zhang S, An S. Shortcuts to adiabaticity for open systems in circuit quantum electrodynamics. Nat Commun 2022; 13:188. [PMID: 35013301 PMCID: PMC8748912 DOI: 10.1038/s41467-021-27900-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2021] [Accepted: 12/16/2021] [Indexed: 11/09/2022] Open
Abstract
Shortcuts to adiabaticity are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various shortcuts to adiabaticity protocols have been demonstrated in closed systems. However, realizing shortcuts to adiabaticity for open quantum systems has presented a challenge due to the complex controls in existing proposals. Here, we present the experimental demonstration of shortcuts to adiabaticity for open quantum systems, using a superconducting circuit quantum electrodynamics system. By applying a counterdiabatic driving pulse, we reduce the adiabatic evolution time of a single lossy mode from 800 ns to 100 ns. In addition, we propose and implement an optimal control protocol to achieve fast and qubit-unconditional equilibrium of multiple lossy modes. Our results pave the way for precise time-domain control of open quantum systems and have potential applications in designing fast open-system protocols of physical and interdisciplinary interest, such as accelerating bioengineering and chemical reaction dynamics.
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Affiliation(s)
- Zelong Yin
- Tencent Quantum Laboratory, Tencent, 518057, Shenzhen, Guangdong, China
| | - Chunzhen Li
- Tencent Quantum Laboratory, Tencent, 518057, Shenzhen, Guangdong, China
| | - Jonathan Allcock
- Tencent Quantum Laboratory, Tencent, 518057, Shenzhen, Guangdong, China
| | - Yicong Zheng
- Tencent Quantum Laboratory, Tencent, 518057, Shenzhen, Guangdong, China
| | - Xiu Gu
- Tencent Quantum Laboratory, Tencent, 518057, Shenzhen, Guangdong, China
| | - Maochun Dai
- Tencent Quantum Laboratory, Tencent, 518057, Shenzhen, Guangdong, China
| | - Shengyu Zhang
- Tencent Quantum Laboratory, Tencent, 518057, Shenzhen, Guangdong, China
| | - Shuoming An
- Tencent Quantum Laboratory, Tencent, 518057, Shenzhen, Guangdong, China.
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48
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Artificial Intelligence in Medicine Using Quantum Computing in the Future of Healthcare. Artif Intell Med 2022. [DOI: 10.1007/978-3-030-64573-1_338] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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49
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Yu LP, Chen CY, Lai CS, Sheu B, Kao SK, Chang CR. Annealing in the Noisy Intermediate-Scale Quantum Era: Key concepts and approaches. IEEE NANOTECHNOLOGY MAGAZINE 2021. [DOI: 10.1109/mnano.2021.3113217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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50
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Sun J, Mao T, Wang Y. Solution of Simultaneous Higher Order Equations Based on DNA Strand Displacement Circuit. IEEE Trans Nanobioscience 2021; 21:511-519. [PMID: 34784281 DOI: 10.1109/tnb.2021.3128393] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
Currently, DNA strand displacement is often used to build neural networks or solve logical problems. While there are few studies on the use of DNA strand displacement to solve the higher order equations. In this paper, the catalysis, degradation, annihilation and adjusted reaction modules are built through DNA strand displacement. The chemical reaction networks of the corresponding higher order equations and simultaneous equations are established through these modules, and these chemical reaction networks can be used to build analog circuits to solve binary primary simultaneous equations and binary quadratic simultaneous equations. Finally, through Visual DSD software verification, this design can realize the solution of binary primary simultaneous equations and binary quadratic simultaneous equations, which provides a reference for DNA computation in the future.
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