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Japanese Journal of Applied Physics

Physical coherent Ising machines for solving combinatorial optimization problems

Yoonhyuk Rah, Kyoungsik Yu

Published Feb 27, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.35848/1347-4065/ae4034

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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.
Today, world-wide efforts are being undertaken to explore non-von Neumann computation methods to overcome "the end of Moore's law". A promising approach is the coherent Ising machine (CIM), which utilizes a network of degenerate optical parametric oscillators for solving ground-state-search problems of the Ising model. Since its proposal in 2013 and the first proof-of-principle experiment in 2014, research on experimental CIMs has made rapid progress and now reached the level where we can find solutions to large-scale combinatorial optimization problems using a CIM system. In this paper, we review recent progress on CIMs, mainly focusing on the experimental side.
Abstract Squeezed vacuum state of light is an important concept of quantum optics which has an uncertainty reduction in a specific quadrature compared to the coherent vacuum state. The coherent Ising machines (CIMs) based on the squeezed state are capable of searching the ground state of the Ising model, which can be used to solve combinatorial optimization problems and have been experimentally demonstrated to have excellent computational performance. This review introduces the recent progress of a CIM hardware solver based on optical parametric oscillators, including the delayed optical path scheme and a measurement feedback scheme. Also, the basic principles, unique advantages, and potential challenges are described. We expect that the applications of large-scale CIM hardware solvers will have a huge impact on the acceleration of the computation power.
We introduce the recent progress of coherent Ising machine (CIM), which finds solutions to complex combinatorial optimization problems using a network of degenerate optical parametric oscillators (DOPO). We describe our effort to generate time-multiplexed DOPOs using long-distance fiber cavities including telecom-band phase sensitive amplifiers [1-4]. We then present our experiments where we found solutions to complex combinatorial optimization problems using a CIM with measurement-feedback scheme [5]. Finally, a future perspective of the CIM project will briefly described.
Coherent Ising Machines (CIMs) are an emerging class of computational architectures that embed hard combinatorial optimization problems in the continuous dynamics of a physical system with analog degrees of freedom. While crisp theoretical results on the ultimate performance and scaling of such architectures are lacking, large-scale experimental prototypes have begun to exhibit promising results in practice. Our team at Stanford has begun to study the fundamental properties of CIM dynamics using a combination of techniques from statistical physics, random matrices, and dynamical systems theory. Many connections to recent work in neuroscience and deep learning are noted. Our work focuses specifically on CIMs that utilize the nonlinear threshold behavior of optical parametric oscillators to effect a soft (potentially glassy) transition between linear and binary dynamical regimes.