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Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian. Nat Commun 2022; 13:2212. [PMID: 35468917 PMCID: PMC9038765 DOI: 10.1038/s41467-022-29887-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 03/11/2022] [Indexed: 11/20/2022] Open
Abstract
Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, HI. Here, we point to the existence of an analytical solution for such a problem for an arbitrary HI beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotonic power-law suppression of nonadiabatic excitations with time T of QA, without any signature of a transition to a glass phase, which is usually characterized by a logarithmic energy relaxation. This behavior suggests that the energy relaxation can differ in classical and quantum spin glasses strongly, when it is assisted by external time-dependent fields. In specific cases of HI, the solution also shows a considerable quantum speedup in computations. The computational capabilities of quantum annealing in the accessible regimes of operation are still subject to debate. Here, the authors study a model admitting an analytical solution far from the adiabatic regime, and show evidences of better convergence and energy relaxation rates over classical annealing.
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2
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Yuan W, Zhong F. Phases fluctuations, self-similarity breaking and anomalous scalings in driven nonequilibrium critical phenomena. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:385401. [PMID: 34186525 DOI: 10.1088/1361-648x/ac0f9d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 06/29/2021] [Indexed: 06/13/2023]
Abstract
We study in detail the dynamic scaling of the three-dimensional (3D) Ising model driven through its critical point on finite-sized lattices. We show explicitly that while finite-size scaling (FSS) at fixed driving rates and finite-time scaling (FTS) on fixed lattice sizes are satisfied for one set of all four observables we measure in their respective scaling regimes, they can be violated for the other set of the observables even in the same regimes. The different behaviors of the two sets of the observables indicate that the usual critical fluctuations can be divided into the so-called phases fluctuations and magnitude fluctuations. The self-similarity of criticality can also be divided into intrinsic and extrinsic self-similarities. The numerical results show that the phases fluctuations lead to the different behaviors while breaking the extrinsic self-similarity gives rise to the violations of the scalings. The set of the observables that violate the scalings is further divided into a primary observable and a secondary observable. Their different leading behaviors enable us to identify four breaking-of-extrinsic-self-similarity exponents for rectifying the violations of either FSS or FTS in either heating or cooling. Crossovers from the extrinsic-self-similarity-breaking-controlled regimes to the usual FSS or FTS regimes are also discussed. In addition, qualitatively different behaviors of the magnitude fluctuations in cooling and in heating and their origin are revealed. Moreover, both FTS and FSS are good down to quite low temperatures in cooling with the extrinsic self-similarity. This indicates that phase ordering can only have an effect at even lower temperatures. Besides, from the quality of curve collapses, we find that the 3D dynamic critical exponentzin heating and in cooling appears identical but the two-dimensional ones different. Our results demonstrate that new exponents are generally required for scaling in the whole driven process near criticality once the lattice size is taken into account. This opens a new door in critical phenomena and suggest that much is yet to be explored in driven nonequilibrium critical phenomena.
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Affiliation(s)
- Weilun Yuan
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-sen University, Guangzhou 510275, People's Republic of China
| | - Fan Zhong
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-sen University, Guangzhou 510275, People's Republic of China
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Yuan W, Zhong F. Phases fluctuations and anomalous finite-time scaling in an externally applied field on finite-sized lattices. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:375401. [PMID: 34171847 DOI: 10.1088/1361-648x/ac0ea8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2021] [Accepted: 06/24/2021] [Indexed: 06/13/2023]
Abstract
We study in detail the dynamic scaling of the three-dimensional Ising model under cooling on finite-sized lattices subject to an externally applied field whose magnitude fixes a scaled variable pertinent to it. Three different protocols, protocols A, B, and C, in which the field is applied either only below or only above the critical point besides during the whole process, respectively, are investigated. Anomalous finite-time scaling (FTS) are found in protocols B and C on a large lattice only and in protocol A when extrinsic self-similarity is broken. However, these anomalous scalings in cooling can be rectified unexpectedly by the recently found breaking-of-extrinsic-self-similarity exponent of FTS in zero-field heating, except in the case of protocol B in which a reduced zero-field cooling exponent is additionally required. This provides a distinctive source to the breaking-of-extrinsic-self-similarity exponents and thus confirms their validity. The different scaling behaviors of the three different protocols also shows that the so-called phases fluctuations at and above the critical point are more important than those below it. The previously found qualitative difference between zero-field heating and zero-field cooling is essentially the symmetry of the system states, namely whether they are ordered or disordered. We also confirm that there exists a revised FTS regime-the regime in which both the lattice sizes and driving rates are indispensable-in between the two end regimes of FTS and finite-size scaling even in the presence of the field. Its crossover to the end FTS regime is responsible for the anomalous scalings of the large lattice size in protocols B and C. However, our results show that the revised FTS is never needed for the usual order parameter in which no absolute value is taken. In addition, the end FTS regime in cooling is found to exhibit a special feature different from that in heating. Our results demonstrate that new exponents are needed for scaling in the whole driven process even in the case in which an external field is applied.
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Affiliation(s)
- Weilun Yuan
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-Sen University, Guangzhou 510275, People's Republic of China
| | - Fan Zhong
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-Sen University, Guangzhou 510275, People's Republic of China
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4
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Pilati S, Pieri P. Simulating disordered quantum Ising chains via dense and sparse restricted Boltzmann machines. Phys Rev E 2020; 101:063308. [PMID: 32688495 DOI: 10.1103/physreve.101.063308] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2020] [Accepted: 06/02/2020] [Indexed: 06/11/2023]
Abstract
In recent years, generative artificial neural networks based on restricted Boltzmann machines (RBMs) have been successfully employed as accurate and flexible variational wave functions for clean quantum many-body systems. In this article, we explore their use in simulations of disordered quantum Ising chains. The standard dense RBM with all-to-all interlayer connectivity is not particularly appropriate for large disordered systems, since in such systems one cannot exploit translational invariance to reduce the amount of parameters to be optimized. To circumvent this problem, we implement sparse RBMs, whereby the visible spins are connected only to a subset of local hidden neurons, thus reducing the amount of parameters. We assess the performance of sparse RBMs as a function of the range of the allowed connections, and we compare it with that of dense RBMs. Benchmark results are provided for two sign-problem-free Hamiltonians, namely pure and random quantum Ising chains. The RBM Ansätzes are trained using the unsupervised learning scheme based on projective quantum Monte Carlo (PQMC) algorithms. We find that the sparse connectivity facilitates the training process and allows sparse RBMs to outperform their dense counterparts. Furthermore, the use of sparse RBMs as guiding functions for PQMC simulations allows us to perform PQMC simulations at a reduced computational cost, avoiding possible biases due to finite random-walker populations. We obtain unbiased predictions for the ground-state energies and the magnetization profiles with fixed boundary conditions, at the ferromagnetic quantum critical point. The magnetization profiles agree with the Fisher-de Gennes scaling relation for conformally invariant systems, including the scaling dimension predicted by the renormalization-group analysis.
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Affiliation(s)
- S Pilati
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino (MC), Italy
| | - P Pieri
- School of Science and Technology, Physics Division, Università di Camerino, 62032 Camerino (MC), Italy
- INFN, Sezione di Perugia, 06123 Perugia (PG), Italy
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5
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Weinberg P, Tylutki M, Rönkkö JM, Westerholm J, Åström JA, Manninen P, Törmä P, Sandvik AW. Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device. PHYSICAL REVIEW LETTERS 2020; 124:090502. [PMID: 32202854 DOI: 10.1103/physrevlett.124.090502] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2019] [Accepted: 02/10/2020] [Indexed: 05/02/2023]
Abstract
We discuss quantum annealing of the two-dimensional transverse-field Ising model on a D-Wave device, encoded on L×L lattices with L≤32. Analyzing the residual energy and deviation from maximal magnetization in the final classical state, we find an optimal L dependent annealing rate v for which the two quantities are minimized. The results are well described by a phenomenological model with two powers of v and L-dependent prefactors to describe the competing effects of reduced quantum fluctuations (for which we see evidence of the Kibble-Zurek mechanism) and increasing noise impact when v is lowered. The same scaling form also describes results of numerical solutions of a transverse-field Ising model with the spins coupled to noise sources. We explain why the optimal annealing time is much longer than the coherence time of the individual qubits.
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Affiliation(s)
- Phillip Weinberg
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Marek Tylutki
- Department of Applied Physics, Aalto University School of Science, FI-00076 Aalto, Finland
- Faculty of Physics, Warsaw University of Technology, Ulica Koszykowa 75, PL-00662 Warsaw, Poland
| | - Jami M Rönkkö
- CSC-IT Center for Science, P.O. Box 405, FIN-02101 Espoo, Finland
| | - Jan Westerholm
- Faculty of Science and Engineering, Åbo Akademi University, Vattenborgsvägen 3, FI 20500 Åbo, Finland
| | - Jan A Åström
- CSC-IT Center for Science, P.O. Box 405, FIN-02101 Espoo, Finland
| | - Pekka Manninen
- CSC-IT Center for Science, P.O. Box 405, FIN-02101 Espoo, Finland
| | - Päivi Törmä
- Department of Applied Physics, Aalto University School of Science, FI-00076 Aalto, Finland
| | - Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
- Beijing National Laboratory of Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
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6
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Li Y, Zeng Z, Zhong F. Driving driven lattice gases to identify their universality classes. Phys Rev E 2019; 100:020105. [PMID: 31574700 DOI: 10.1103/physreve.100.020105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2019] [Indexed: 06/10/2023]
Abstract
The critical behaviors of driven lattice gas models have been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in their universality classes. This is of paramount importance as it implies the question of whether or not a microscopic model and its mesoscopic field theory may possess different symmetries in nonequilibrium critical phenomena in contrast to their equilibrium counterparts. Here, we heat with finite rates two generic models of driven lattice gases across their respective nonequilibrium critical points into further nonequilibrium situations. Employing the theory of finite-time scaling, we are able to unambiguously discriminate the universality classes between the two models. In particular, the infinitely driven lattice gas and the randomly driven lattice gas models belong to different universality classes. These results show that finite-time scaling is effective even in nonequilibrium phase transitions.
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Affiliation(s)
- Yahui Li
- School of Physics, Sun Yat-Sen University, Guangzhou, 510275, People's Republic of China
| | - Zhongda Zeng
- School of Physics, Sun Yat-Sen University, Guangzhou, 510275, People's Republic of China
| | - Fan Zhong
- School of Physics, Sun Yat-Sen University, Guangzhou, 510275, People's Republic of China
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7
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Albash T, Wagenbreth G, Hen I. Off-diagonal expansion quantum Monte Carlo. Phys Rev E 2017; 96:063309. [PMID: 29347413 DOI: 10.1103/physreve.96.063309] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2017] [Indexed: 11/07/2022]
Abstract
We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a decomposition of the quantum partition function that can be viewed as a series expansion about its classical part. We argue that the algorithm not only provides a theoretical advancement in the field of quantum Monte Carlo simulations, but is optimally suited to tackle quantum many-body systems that exhibit a range of behaviors from "fully quantum" to "fully classical," in contrast to many existing methods. We demonstrate the advantages, sometimes by orders of magnitude, of the technique by comparing it against existing state-of-the-art schemes such as path integral quantum Monte Carlo and stochastic series expansion. We also illustrate how our method allows for the unification of quantum and classical thermal parallel tempering techniques into a single algorithm and discuss its practical significance.
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Affiliation(s)
- Tameem Albash
- Information Sciences Institute, University of Southern California, Marina del Rey, California 90292, USA.,Department of Physics and Astronomy and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
| | | | - Itay Hen
- Information Sciences Institute, University of Southern California, Marina del Rey, California 90292, USA.,Department of Physics and Astronomy and Center for Quantum Information Science & Technology, University of Southern California, Los Angeles, California 90089, USA
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8
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Xu N, Wu KH, Rubin SJ, Kao YJ, Sandvik AW. Dynamic scaling in the two-dimensional Ising spin glass with normal-distributed couplings. Phys Rev E 2017; 96:052102. [PMID: 29347699 DOI: 10.1103/physreve.96.052102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2017] [Indexed: 06/07/2023]
Abstract
We carry out simulated annealing and employ a generalized Kibble-Zurek scaling hypothesis to study the two-dimensional Ising spin glass with normal-distributed couplings. The system has an equilibrium glass transition at temperature T=0. From a scaling analysis when T→0 at different annealing velocities v, we find power-law scaling in the system size for the velocity required in order to relax toward the ground state, v∼L^{-(z+1/ν)}, the Kibble-Zurek ansatz where z is the dynamic critical exponent and ν the previously known correlation-length exponent, ν≈3.6. We find z≈13.6 for both the Edwards-Anderson spin-glass order parameter and the excess energy. This is different from a previous study of the system with bimodal couplings [Rubin et al., Phys. Rev. E 95, 052133 (2017)2470-004510.1103/PhysRevE.95.052133] where the dynamics is faster (z is smaller) and the above two quantities relax with different dynamic exponents (with that of the energy being larger). We argue that the different behaviors arise as a consequence of the different low-energy landscapes: for normal-distributed couplings the ground state is unique (up to a spin reflection), while the system with bimodal couplings is massively degenerate. Our results reinforce the conclusion of anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the case of a continuous coupling distribution, our results presented here also indicate that, although Kibble-Zurek scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasidegenerate states, and the scaling function takes a different form.
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Affiliation(s)
- Na Xu
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Kai-Hsin Wu
- Department of Physics and Center of Theoretical Sciences, National Taiwan University, Taipei 10607, Taiwan
| | - Shanon J Rubin
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Ying-Jer Kao
- Department of Physics and Center of Theoretical Sciences, National Taiwan University, Taipei 10607, Taiwan
- National Center of Theoretical Sciences, National Tsinghua University, Hsinchu, Taiwan
| | - Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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9
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Rubin SJ, Xu N, Sandvik AW. Dual time scales in simulated annealing of a two-dimensional Ising spin glass. Phys Rev E 2017; 95:052133. [PMID: 28618601 DOI: 10.1103/physreve.95.052133] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2016] [Indexed: 11/07/2022]
Abstract
We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature T=0 of the two-dimensional Ising model with random J=±1 couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, τ∼L^{z}, are z=8.28±0.03 for the relaxation of the order parameter and z=10.31±0.04 for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for T→0 simulated annealing are different from the temperature-dependent equilibrium dynamic exponent z_{eq}(T), for which previous studies have found a divergent behavior: z_{eq}(T→0)→∞. Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.
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Affiliation(s)
- Shanon J Rubin
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Na Xu
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
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10
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Yin S, Huang GY, Lo CY, Chen P. Kibble-Zurek Scaling in the Yang-Lee Edge Singularity. PHYSICAL REVIEW LETTERS 2017; 118:065701. [PMID: 28234541 DOI: 10.1103/physrevlett.118.065701] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2016] [Indexed: 06/06/2023]
Abstract
We study the driven dynamics across the critical points of the Yang-Lee edge singularities (YLESs) in a finite-size quantum Ising chain with an imaginary symmetry-breaking field. In contrast to the conventional classical or quantum phase transitions, these phase transitions are induced by tuning the strength of the dissipation in a non-Hermitian system and can occur even at finite size. For conventional phase transitions, universal behaviors in driven dynamics across critical points are usually described by the Kibble-Zurek mechanism, which states that the scaling in dynamics is dictated by the critical exponents associated with one critical point and topological defects will emerge after the quench. While the mechanism leading to topological defects breaks down in the YLES, we find that for small lattice size, the driven dynamics can still be described by the Kibble-Zurek scaling with the exponents determined by the (0+1)-dimensional YLES. For medium finite size, however, the driven dynamics can be described by the Kibble-Zurek scaling with two sets of critical exponents determined by both the (0+1)-dimensional and the (1+1)-dimensional YLESs.
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Affiliation(s)
- Shuai Yin
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
- Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China
| | - Guang-Yao Huang
- Department of Electronics and Key Laboratory for the Physics and Chemistry of Nanodevices, Peking University, Beijing 100871, People's Republic of China
| | - Chung-Yu Lo
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
| | - Pochung Chen
- Department of Physics, National Tsing Hua University, Hsinchu 30013, Taiwan
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11
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Effects Induced by the Initial Condition in the Quantum Kibble–Zurek Scaling for Changing the Symmetry-Breaking Field. ENTROPY 2016. [DOI: 10.3390/e18120446] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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12
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Isakov SV, Mazzola G, Smelyanskiy VN, Jiang Z, Boixo S, Neven H, Troyer M. Understanding Quantum Tunneling through Quantum Monte Carlo Simulations. PHYSICAL REVIEW LETTERS 2016; 117:180402. [PMID: 27835027 DOI: 10.1103/physrevlett.117.180402] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2015] [Indexed: 05/02/2023]
Abstract
The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling with system size, as the rate of incoherent tunneling. The scaling in both cases is O(Δ^{2}), where Δ is the tunneling splitting (or equivalently the minimum spectral gap). An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, we obtain a quadratic speedup for QMC simulations, and achieve linear scaling in Δ. We provide a physical understanding of these results and their range of applicability based on an instanton picture.
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Affiliation(s)
| | | | | | - Zhang Jiang
- QuAIL, NASA Ames Research Center, Moffett Field, California 94035, USA
- Stinger Ghaffarian Technologies Inc., 7701 Greenbelt Rd., Suite 400, Greenbelt, Maryland 20770, USA
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13
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Inack EM, Pilati S. Simulated quantum annealing of double-well and multiwell potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:053304. [PMID: 26651813 DOI: 10.1103/physreve.92.053304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2015] [Indexed: 06/05/2023]
Abstract
We analyze the performance of quantum annealing as a heuristic optimization method to find the absolute minimum of various continuous models, including landscapes with only two wells and also models with many competing minima and with disorder. The simulations performed using a projective quantum Monte Carlo (QMC) algorithm are compared with those based on the finite-temperature path-integral QMC technique and with classical annealing. We show that the projective QMC algorithm is more efficient than the finite-temperature QMC technique, and that both are inferior to classical annealing if this is performed with appropriate long-range moves. However, as the difficulty of the optimization problem increases, classical annealing loses efficiency, while the projective QMC algorithm keeps stable performance and is finally the most effective optimization tool. We discuss the implications of our results for the outstanding problem of testing the efficiency of adiabatic quantum computers using stochastic simulations performed on classical computers.
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Affiliation(s)
- E M Inack
- The Abdus Salam International Centre for Theoretical Physics, I-34151 Trieste, Italy
- SISSA, International School for Advanced Studies and INFN, Sezione di Trieste, I-34136 Trieste, Italy
| | - S Pilati
- The Abdus Salam International Centre for Theoretical Physics, I-34151 Trieste, Italy
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14
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Liu CW, Polkovnikov A, Sandvik AW, Young AP. Universal dynamic scaling in three-dimensional Ising spin glasses. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022128. [PMID: 26382365 DOI: 10.1103/physreve.92.022128] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2014] [Indexed: 06/05/2023]
Abstract
We use a nonequilibrium Monte Carlo simulation method and dynamical scaling to study the phase transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity v (temperature change versus time) in Monte Carlo simulations starting at a high temperature. This approach has the advantage that the equilibrium limit does not have to be strictly reached for a scaling analysis to yield critical exponents. For the dynamic exponent we obtain z=5.85(9) for bimodal couplings distribution and z=6.00(10) for the Gaussian case. Assuming universal dynamic scaling, we combine the two results and obtain z=5.93±0.07 for generic 3D Ising spin glasses.
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Affiliation(s)
- Cheng-Wei Liu
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Anatoli Polkovnikov
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Anders W Sandvik
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - A P Young
- Department of Physics, University of California, Santa Cruz, California 95064, USA
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