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arXiv:1706.01283 · Quantum Science and Technology

Performance evaluation of coherent Ising machines against classical neural networks

Yoshitaka Haribara, Hitoshi Ishikawa, Shoko Utsunomiya, Kazuyuki Aihara, Y. Yamamoto

Published Aug 14, 2017• 46 citations
arXivHTMLPDF

Abstract

Abstract The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators and a field programmable gate array circuit. The similar mathematical models were proposed three decades ago by Hopfield et al in the context of classical neural networks. In this article, we compare the computational performance of both models.

DOI
10.1088/2058-9565/aa8190

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Abstract The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators and a field programmable gate array circuit. The similar mathematical models were proposed three decades ago by Hopfield et al in the context of classical neural networks. In this article, we compare the computational performance of both models.
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Abstract Coherent Ising machines (CIM) have shown promising potential as hardware solvers for tackling combinatorial optimization problems, where discrete variables are encoded onto physical states to form an Ising Hamiltonian. Various platforms, starting from optical parametric oscillators, have been proposed and demonstrated to implement an actual physical CIM. In this review article, we briefly introduce the basic operation principle of CIMs and review physical schemes focusing on MEMS-based nanophotonics.
Coherent Ising machines (CIMs) are increasingly anticipated as a new computer that can solve combinatorial optimization problems. CIMs use degenerate optical parametric oscillator pulses as artificial spins. We constructed a 100,512-spin coherent Ising machine, the world's largest. Our CIM can find good solutions to maximum cut problems of 100,000-node graphs ~1000 times faster than simulated annealing. Furthermore, it provides both very good scores and a broad distribution when we operate it near the phase transition point.
Coherent Ising Machine (CIM) is a network of optical parametric oscillators that solve combinatorial optimization problems by finding the ground state of an Ising Hamiltonian. In CIMs, a problem arises when attempting to realize the Zeeman term because of the mismatch in size between interaction and Zeeman terms due to the variable amplitude of the optical parametric oscillator pulses corresponding to spins. There have been three approaches proposed so far to address this problem for CIM, including the absolute mean amplitude method, the auxiliary spin method, and the chaotic amplitude control (CAC) method. This paper focuses on the efficient implementation of Zeeman terms within the mean-field CIM model, which is a physics-inspired heuristic solver without quantum noise. With the mean-field model, computation is easier than with more physically accurate models, which makes it suitable for implementation in field programmable gate arrays and large-scale simulations. First, we examined the performance of the mean-field CIM model for realizing the Zeeman term with the CAC method, as well as their performance when compared to a more physically accurate model. Next, we compared the CAC method to other Zeeman term realization techniques on the mean-field model and a more physically accurate model. In both models, the CAC method outperformed the other methods while retaining similar performance.
Recently, new optimization machines based on non-silicon physical systems, such as quantum annealing machines, have been developed, and their commercialization has been started. These machines solve the problems by searching the state of the Ising spins, which minimizes the Ising Hamiltonian. Such a property of minimization of the Ising Hamiltonian can be applied to various combinatorial optimization problems. In this paper, we introduce the coherent Ising machine (CIM), which can solve the problems in a milli-second order, and has higher performance than the quantum annealing machines especially on the problems with dense mutual connections in the corresponding Ising model. We explain how a target problem can be implemented on the CIM, based on the optimization scheme using the mutually connected neural networks. We apply the CIM to traveling salesman problems as an example benchmark, and show experimental results of the real machine of the CIM. We also apply the CIM to several combinatorial optimization problems in wireless communication systems, such as channel assignment problems. The CIM's ultra-fast optimization may enable a real-time optimization of various communication systems even in a dynamic communication environment.