Comparison between a quantum annealer and a classical approximation algorithm for computing the ground state of an Ising spin glass

Yaacoby, Ran; Schaar, Nathan; Kellerhals, Leon; Raz, Oren; Hermelin, Danny; Pugatch, Rami

doi:10.1103/physreve.105.035305

Cited by 9 publications

(10 citation statements)

References 31 publications

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“…Yaacoby et al. [41] indicate that one can reach the ground state of the spin glass through the QA only if the system can regain its ergodicity in the presence of quantum fluctuations. However, it is not the sufficient condition to ensure the quantum speed up over the classical algorithm.…”

Section: Discussionmentioning

confidence: 99%

“…This is because the ergodicity in the spin glass phase through the phenomenon of quantum tunnelling across the free energy barriers, is the potential reason behind the success of the QA in such ergodic spin glass region. Yaacoby et al [41] indicate that one can reach the ground state of the spin glass through the QA only if the system can regain its ergodicity in the presence of quantum fluctuations. However, it is not the sufficient condition to ensure the quantum speed up over the classical algorithm.…”

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confidence: 99%

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Role of quantum fluctuation in inducing ergodicity in the spin glass phase and its effect in quantum annealing

Mukherjee¹

2022

Phil. Trans. R. Soc. A.

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We review the numerical studies on the critical behaviour of the quantum Sherrington–Kirkpatrick (SK) spin glass model, which indicate that a quantum critical behaviour is observed up to a low but non-zero value of temperature. We revisit the numerical investigations on the spin glass order parameter distributions, which identify a low temperature along with high transverse field spin glass phase where the order parameter distribution becomes a delta function in the thermodynamic limit indicating the restoration of replica symmetry and ergodic nature of the system. In the remaining spin glass phase associated with high temperature and low transverse field, the observed distribution is broad akin to the Parisi order parameter distribution. This essentially indicates the non-ergodic behaviour of the system. We further discuss the annealing dynamics studies on the quantum SK model. Such investigations reveal the system size independence of annealing time when the annealing paths go through the ergodic spin glass region. Interestingly, when such dynamics are performed in the non-ergodic spin glass phase the annealing time becomes an increasing function of the system size. Spin autocorrelation shows faster relaxation in the ergodic spin glass region compared with that found in the non-ergodic spin glass region. This article is part of the theme issue ‘Quantum annealing and computation: challenges and perspectives’.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Role of quantum fluctuation in inducing ergodicity in the spin glass phase and its effect in quantum annealing

Mukherjee¹

2022

Phil. Trans. R. Soc. A.

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“…The data fits to np∼exp⁡[(t−t0)/τ] with τ≃9.7 years. We have marked some of the notable events: BKC denotes Chakrabarti [101]; GL denotes Goldschmidt and Lai [38]; WER denotes Wu et al [4]; CDS denotes Chakrabarti et al [102]; KGL denotes Kao et al [103]; ASA denotes Ancona-Torres et al [48]; SIC denotes Suzuki et al [104]; MRC denotes Mukherjee et al [105]; LMR denotes Leschke et al [106]; YSK denotes Yaacoby et al [107]; SGS denotes Schindler et al [108]. The inset shows direct functional relationship between np and t for category A from 1980 to 2021.…”

Section: Research Network and Study Of Its Growthmentioning

confidence: 99%

Development of research network on Quantum Annealing Computation and Information using Google Scholar data

Sinha¹

2022

Phil. Trans. R. Soc. A.

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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 ( n p ) in each of these four categories, A–D, to the form n p ∼ exp ⁡ ( t / τ ) , where t denotes the time in years. We found the scaling time τ to be of the order of about 10 years for categories A and C, whereas τ 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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“…This role of quantum tunneling was first discussed by Ray et al, in 1989 [16] (see discussions in [17]) in this regard) in the context of the restoration of the replica symmetry or ergodicity due to quantum fluctuation in the quantum version of the Sherrington-Kirkpatrick model [18], which is detailed in the next section. Although the existence of an energy landscape with thin and high barriers in specific models is still an issue of debate, it must be a foundation for the speedup of QA over SA [17,19]. In addition, several numerical and experimental studies have provided evidences for such an advantage of QA over SA in some specific models as shown in Secs.…”

Section: Introductionmentioning

confidence: 99%

Quantum Annealing: An Overview

Rajak¹,

Suzuki²,

Dutta³

et al. 2022

Preprint

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Comparison between a quantum annealer and a classical approximation algorithm for computing the ground state of an Ising spin glass

Cited by 9 publications

References 31 publications

Role of quantum fluctuation in inducing ergodicity in the spin glass phase and its effect in quantum annealing

Role of quantum fluctuation in inducing ergodicity in the spin glass phase and its effect in quantum annealing

Development of research network on Quantum Annealing Computation and Information using Google Scholar data

Quantum Annealing: An Overview

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