Efficiency of quantum vs. classical annealing in nonconvex learning problems

Baldassi, Carlo; Zecchina, Riccardo

doi:10.1073/pnas.1711456115

Cited by 53 publications

(59 citation statements)

References 47 publications

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“…But quite remarkably, as recently shown in Ref. 35, non-convex optimization problems are known in which SQA, with the P → ∞ limit properly taken, is definitely more efficient than its classical SA counterpart.…”

Section: Introductionmentioning

confidence: 94%

Dynamics of simulated quantum annealing in random Ising chains

et al. 2019

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Simulated Quantum Annealing (SQA), that is emulating a Quantum Annealing (QA) dynamics on a classical computer by a Quantum Monte Carlo whose parameters are changed during the simulation, is a well established computational strategy to cope with the exponentially large Hilbert space. It has enjoyed some early successes but has also raised more recent criticisms. Here we investigate, on the paradigmatic case of a one-dimensional transverse field Ising chain, two issues related to SQA in its Path-Integral implementation: the question of Monte Carlo vs physical (Schrödinger) dynamics and the issue of the imaginary-time continuum limit to eliminate the Trotter error. We show that, while a proper time-continuum limit is able to restitute the correct Kibble-Zurek scaling of the residual energy εres(τ ) ∼ τ −1/2 for the ordered case − − − τ being the total annealing time -, the presence of disorder leads to a characteristic sampling crisis for a large number of Trotter time-slices, in the low-temperature ordered phase. Such sampling problem, in turn, leads to SQA results which are apparently unrelated to the coherent Schrödinger QA even at intermediate τ .

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Section: Introductionmentioning

confidence: 94%

Dynamics of simulated quantum annealing in random Ising chains

et al. 2019

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“…The proposed algorithm generates an elastic term between different realizations of DNNs and could find a better solution in terms of generalization performance than that by classical Adam. The point is to control the quantum fluctuation by introducing the adaptive change of the coefficient and inducing the wide-flat local minimum by means of the entropy effect, as discussed in the previous studies 9,26 . In the present study, we directly optimize the M-replicated DNNs while dealing with the non-perturbative effect, which allows the quantum tunneling effect.…”

Section: Discussionmentioning

confidence: 99%

“…In addition, the current version of a quantum annealer, the D-Wave 2000Q, implements two optimization techniques by manipulating a certain value of quantum fluctuation, namely quenching, and reverse annealing. These two techniques will be available for efficiently attaining better generalization performance in real experiments, as discussed in the literature 26 .…”

Section: Discussionmentioning

confidence: 99%

“…In particular, the performance of QA has been discussed through the decrease of the cost function. However, the robustness of the solution can be attained by optimization of the cost function in conjunction with the local entropy as discussed in the literature 9,26 . The optimization with quantum fluctuation automatically and potentially leads to the robustness of the solution as discussed in the present study.…”

Section: Discussionmentioning

confidence: 99%

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Optimization of neural networks via finite-value quantum fluctuations

Ohzeki

Okada

Terabe

et al. 2018

Sci Rep

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We numerically test an optimization method for deep neural networks (DNNs) using quantum fluctuations inspired by quantum annealing. For efficient optimization, our method utilizes the quantum tunneling effect beyond the potential barriers. The path integral formulation of the DNN optimization generates an attracting force to simulate the quantum tunneling effect. In the standard quantum annealing method, the quantum fluctuations will vanish at the last stage of optimization. In this study, we propose a learning protocol that utilizes a finite value for quantum fluctuations strength to obtain higher generalization performance, which is a type of robustness. We demonstrate the performance of our method using two well-known open datasets: the MNIST dataset and the Olivetti face dataset. Although computational costs prevent us from testing our method on large datasets with high-dimensional data, results show that our method can enhance generalization performance by induction of the finite value for quantum fluctuations.

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“…This allows a quantum system to be emulated by a number of classical replicas that are interacting with each other [16] (FIG. 1) and this approach is commonly used in software or high-level hardware simulations [17][18][19][20][21]. By contrast, we show that a compact, embedded MTJ-based coprocessor can speed up the simulation by several orders of magnitude.…”

Section: Scopementioning

confidence: 96%

Scalable Emulation of Sign-Problem–Free Hamiltonians with Room-Temperature p -bits

Çamsarı¹,

Chowdhury²,

Datta³

2019

Phys. Rev. Applied

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The growing field of quantum computing is based on the concept of a q-bit which is a delicate superposition of 0 and 1, requiring cryogenic temperatures for its physical realization along with challenging coherent coupling techniques for entangling them. By contrast, a probabilistic bit or a p-bit is a robust classical entity that fluctuates between 0 and 1, and can be implemented at room temperature using present-day technology. Here, we show that a probabilistic coprocessor built out of room temperature p-bits can be used to accelerate simulations of a special class of quantum many-body systems that are sign-problem−free or "stoquastic", leveraging the well-known Suzuki-Trotter decomposition that maps a d-dimensional quantum many body Hamiltonian to a d+1-dimensional classical Hamiltonian. This mapping allows an efficient emulation of a quantum system by classical computers and is commonly used in software to perform Quantum Monte Carlo (QMC) algorithms. By contrast, we show that a compact, embedded MTJ-based coprocessor can serve as a highly efficient hardware-accelerator for such QMC algorithms providing several orders of magnitude improvement in speed compared to optimized CPU implementations. Using realistic device-level SPICE simulations we demonstrate that the correct quantum correlations can be obtained using a classical p-circuit built with existing technology and operating at room temperature. The proposed coprocessor can serve as a tool to study stoquastic quantum many-body systems, overcoming challenges associated with physical quantum annealers. arXiv:1810.07144v4 [quant-ph]

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Efficiency of quantum vs. classical annealing in nonconvex learning problems

Cited by 53 publications

References 47 publications

Dynamics of simulated quantum annealing in random Ising chains

Dynamics of simulated quantum annealing in random Ising chains

Optimization of neural networks via finite-value quantum fluctuations

Scalable Emulation of Sign-Problem–Free Hamiltonians with Room-Temperature p -bits

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