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arXiv:2509.13917 · Advanced Quantum Technologies

Global Mean‐Amplitude Enhanced Spiking Neural Network Coherent Ising Machine

Yan‐Chen Jiang, Lu Ma, Chuan Wang, Tie-Jun Wang

Published Apr 1, 2026• 0 citations

Abstract

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.

DOI: 10.1002/qute.202500607

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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.

Coherent Ising machines (CIMs) are a promising approach for quantum computation. It exhibits excellent per-formance in solving the combinatorial optimization problems, however, the existence of amplitude heterogeneity limits the applications of CIMs. Here in this work, we present a system of the spiking neural network composed of antisymmetrically coupled degenerate optical parametric oscillator pulses and dissipative pulses. It works based on the principles of CIM during solving the combinatorial optimization problems. Moreover, a nonlinear transfer function is chosen to mitigate the amplitude inhomogeneities and destabilize the resulting local minima ac-cording to the dynamical behavior of spiking neurons.

Coherent Ising machine (CIM) is a hardware solver that simulates the Ising model and finds optimal solutions to combinatorial optimization problems. However, for practical tasks, the computational process may be trapped in local minima, which is a key challenge for CIM. In this work, we design a CIM structure with a spiking neural network by adding dissipative pulses, which are anti-symmetrically coupled to the degenerate optical parametric oscillator pulses in CIM with a measurement feedback system. We find that the unstable oscillatory region of the spiking neural network could assist the CIM to escape from the trapped local minima. Moreover, we show that the machine has a different search mechanism than CIM, which can achieve a higher solution success probability and speed-up effect.

Spiking neural network is a kind of neuromorphic computing that is believed to improve the level of intelligence and provide advantages for quantum computing. In this work, we address this issue by designing an optical spiking neural network and find that it can be used to accelerate the speed of computation, especially on combinatorial optimization problems. Here the spiking neural network is constructed by the antisymmetrically coupled degenerate optical parametric oscillator pulses and dissipative pulses. A nonlinear transfer function is chosen to mitigate amplitude inhomogeneities and destabilize the resulting local minima according to the dynamical behavior of spiking neurons. It is numerically shown that the spiking neural network-coherent Ising machines have excellent performance on combinatorial optimization problems, which is expected to offer new applications for neural computing and optical computing.

Abstract Coherent Ising Machine (CIM) emerge as powerful tools for solving large‐scale combinatorial optimization problems by mapping them to the ground state search of the Ising model. Traditional CIM models face two major challenges when addressing large‐scale problems: slowness in convergence and susceptibility to local minima. To address these limitations, the Sliding Mode Control‐Like Coherent Ising Machine (SMCL‐CIM) integrates sliding mode control principles into the feedback mechanism of the CIM, inspired by classical dynamic control methods. Experimental results on random graphs and G‐set benchmarks demonstrate that for the max‐cut problem, SMCL‐CIM achieves an approximately 79. 93% reduction in solution time while improving solution accuracy by 11.4%–15.3% under the same simulation conditions. This scheme provides an efficient and scalable approach to combinatorial optimization, thereby facilitating the broader application of CIM.

Combinatorial optimization problems (COPs) constitute a fundamental class of computational challenges with extensive applications across scientific and industrial domains. The emergence of the coherent Ising machine (CIM) as a computational paradigm has demonstrated exceptional capabilities in rapidly generating arbitrary spin configurations and effectively solving large-scale COPs. Despite its promising potential, the CIM framework encounters an inherent limitation related to amplitude heterogeneity. Current approaches to this limitation primarily rely on Gaussian approximations to model quantum noise in the system's amplitude dynamics within the original CIM framework. However, these methods generally fail to account for the temporal and periodic non-Markovian characteristics of pulses in practical environments. In this study, we introduce temporally correlated non-Markovian noise into the dynamics of both conventional and spiking neural network-based CIM systems, investigating their performance through comprehensive hyperparameter analysis. Our method incorporates a detailed examination of hyperparameter selection and its influence on algorithmic efficiency. Through extensive numerical simulations, we demonstrate that the integration of non-Markovian noise significantly accelerates variance evolution in both canonical coordinates and amplitude dynamics over time. The proposed approach not only exhibits enhanced computational performance but also shows superior scalability for large-scale problem instances. These findings suggest that our approach offers distinct advantages in addressing complex COPs, potentially opening new avenues for efficient optimization in various applications.

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.