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arXiv:2309.04043 · Journal of Applied Physics

Mean-field coherent Ising machines with artificial Zeeman terms

Mastiyage Don Sudeera Hasaranga Gunathilaka, Yoshitaka Inui, Satoshi Kako, Y. Yamamoto, Toru Aonishi

Published Dec 20, 2023• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/5.0176248

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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.
Abstract A coherent Ising machine (CIM) is an open-dissipative Ising solver using optical pulses generated from a degenerate optical parametric oscillator as analog magnetizations. When solving real-world optimization problems with CIM, this solver has two difficulties: mutual coupling induced amplitude inhomogeneity and absence of natural way to implement Zeeman terms. For the approximate Gaussian formulation of CIMs with amplitude control feedback, we add artificial Zeemam terms using the target amplitude information. Here we show, for 16-spin CIM with Zeeman terms, the amplitude control increases the performance, particularly when Zeeman terms are competing against mutual coupling coefficients.
The coherent Ising machine (CIM) enables efficient sampling of low-lying energy states of the Ising Hamiltonian with all-to-all connectivity by encoding the spins in the amplitudes of pulsed modes in an optical parametric oscillator (OPO). The interaction between the pulses is realized by means of measurement-based optoelectronic feedforward, which enhances the gain for lower-energy spin configurations. We present an efficient method of simulating the CIM on a classical computer that outperforms the CIM itself, as well as the noisy mean-field annealer in terms of both the quality of the samples and the computational speed. It is furthermore advantageous with respect to the CIM in that it can handle Ising Hamiltonians with arbitrary real-valued node coupling strengths. These results illuminate the nature of the faster performance exhibited by the CIM and may give rise to a new class of quantum-inspired algorithms of classical annealing that can successfully compete with existing methods.
Abstract A Coherent Ising machine (CIM) is an oscillator-network-based analog computing system to circumvent the bottleneck in von Neumann digital computing architectures. The CIM consists of a network of degenerate optical parametric oscillators (DOPOs) and is designed to find a ground state or perform Boltzmann sampling for all degenerate ground states and low-energy excited states in combinatorial optimization problems. A nonlinear measurement feedback scheme, called chaotic amplitude control (CAC), has recently been proposed to correct pulse amplitude inhomogeneity and thereby faithfully map the Ising Hamiltonian to the loss landscape of the DOPO network. However, the quantum limit of the CIM-CAC performance is not fully explored yet. This work clarifies how the quantum noise squeezing and the measurement-induced state shift in repeated indirect quantum measurements improve the system performance. From the numerical simulation on the Ising model with the Zeeman terms, obtained from combinatorial clustering problems formulated as constrained optimization problems, it is revealed that the CIM-CAC operating in a single photon per pulse regime dramatically outperforms the standard CIM-CAC with a large photon number per pulse. This is because the standard CIM-CAC is often trapped in a periodic trajectory and cannot escape from there. On the other hand, the significant improvement is brought by the noise-induced amplitude jump in the single photon CIM-CAC.
The coherent Ising machine is an optical processor that uses coherent laser pulses, but does not employ coherent quantum dynamics in a computational role. Core to its operation is the iterated simulation of all-to-all spin coupling via mean-field calculation in a classical FPGA coprocessor. Although it has been described as "operating at the quantum limit" and a "quantum artificial brain", interaction with the FPGA prevents the coherent Ising machine from exploiting quantum effects in its computations. Thus the question naturally arises: Can the optical portion of the coherent Ising machine be replaced with classical mean-field arithmetic? Here we answer this in the affirmative by showing that a straightforward noisy version of mean-field annealing closely matches CIM performance scaling, while running roughly 20 times faster in absolute terms.
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.
ABSTRACT The coherent Ising machine (CIM) is a quantum‐inspired computing platform that leverages optical parametric oscillation dynamics to solve combinatorial optimization problems by searching for the ground state of Ising Hamiltonian. Conventional CIM implementations face challenges in handling non‐uniform coupling strengths and maintaining amplitude stability during computation. In this paper, a new Global mean‐amplitude Feedback‐enhanced spiking neural network CIM (GF‐SNN‐CIM) is introduced with a physics‐driven amplitude stabilization mechanism to dynamically balance nonlinear gain saturation and coupling effects. This modification enhances synchronization in the optical pulse network, leading to more robust convergence under varying interaction strengths. Numerical simulation validation on Max‐Cut problems demonstrates that the GF‐SNN‐CIM achieves improvements in average cut rate compared to conventional spiking neural network CIM. Further application to the traffic assignment problem (TAP) confirms the method's generality. The GF‐SNN‐CIM achieves near‐continuous accuracy (deviations 0.035%) even at coarse discretization, while large‐scale tests on Beijing's road network (481 spins) validate its real‐world applicability. These advances establish a physics‐consistent optimization framework, where optical pulse dynamics directly encode combinatorial problems, paving the way for scalable, high‐performance CIM implementations in complex optimization tasks.