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.
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.
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 Machines (CIMs) are emerging hardware solvers for approximating solutions to combinatorial optimization problems, and may offer advantages in energy-efficiency, speed, and scalability across applications. However, CIM computing is a nascent and methodologically fragmented field, and substantial research is required to determine its utility for real-world combinatorial optimization problems. The core argument of this thesis is that several complementary efforts are required: (1) developing a unified simulations framework that systematically evaluates CIM variations by isolating implementation and methodological differences from architectural ones; (2) introducing layers of abstraction, analogous to those in mature CMOS-based computing, to enable effort (1); and (3), by extension of efforts (1) and (2), potentially enabling CIM-inspired dynamics -- which, when simulated, are simply classical algorithms that run on conventional computers -- for efficient in-silico approximation of combinatorial optimization problems.As a concrete example of the utility of the unified simulations framework, this thesis compares several CIM modifications proposed to address spin amplitude inhomogeneity (an artifact of the CIM's analog nature) that can hinder convergence to the ground state. These variations have been analyzed under varying assumptions and methodologies, and no prior work has systematically compared their performance by isolating architectural differences. This thesis presents the first side-by-side evaluation of six promising CIM architectures using a unified simulation model. We develop implementation-agnostic stochastic differential equations, find optimal hyperparameters via Bayesian optimization per problem-architecture pair, and assess the performance on multiple metrics using MaxCut instances from the Gset and BiqMac datasets. CIM-SNN outperforms the rest on most metrics, with a 54.21% average success probability (SP) improvement and 1.36× faster time-to-solution (TTS) at 96% GS energy compared to the Standard CIM on BiqMac graphs. Other CIMs show some advantages on certain Gset graphs. CIM-QA is usually the worst-performing, with an 18.55% average SP loss and a 1.30× slower TTS at 96% GS compared to the Standard CIM on BiqMac graphs. CIM-SNN demonstrates the greatest noise robustness and promise for further tuning via a linear pump schedule. CIM-QA benefits from high noise levels. These analyses were made possible only by the unified simulations framework developed in this thesis, which can also be used to evaluate future architectural modifications against existing ones. Lastly, we present a potential abstraction stack that further extends the unified simulations framework, which can benefit future research and introduce a new direction in the field.
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.
Coherent Ising machines (CIMs), leveraging the bistable physical properties of coherent light to emulate Ising spins, exhibit great potential as hardware accelerators for tackling complex combinatorial optimization problems. Recent advances have demonstrated that the performance of CIMs can be enhanced either by incorporating large random noise or higher-order nonlinearities, yet their combined effects on CIM performance remain mainly unexplored. In this work, we develop a numerical CIM model that utilizes a tunable fifth-order polynomial nonlinear dynamic function under large noise levels, which has the potential to be implemented in all-optical platforms. We propose a normal form of a CIM model that allows for both supercritical and subcritical pitchfork bifurcation operational regimes, with fifth-order nonlinearity and tunable hyperparameters to control the Ising spin dynamics. In the benchmark studies, we simulate various sets of MaxCut problems using our fifth-order polynomial CIM model. The results show a significant performance improvement, achieving an average of 59.5% improvement in median time-to-solution (TTS) and an average of 6 times improvement in median success rate (SR) for dense Maxcut problems in the BiqMac library, compared to the commonly used third-order polynomial CIM model with low noise. The fifth-order polynomial CIM model in the large-noise regime also shows better performance trends as the problem size scales up. These findings reveal the enhancements on the computational performance of Ising machines in the large-nose regime from fifth-order nonlinearity, showing important implications for both simulation and hardware perspectives.
Coherent Ising Machines (CIMs) have emerged as promising hardware solvers for NP-hard combinatorial optimization problems, potentially offering energy-efficiency, accuracy, speed, and scalability. These problems span applications including scheduling, routing, resource allocation, and machine learning. Spin amplitude inhomogeneity (an artifact of its analog nature) can hinder CIM convergence to the ground state. Several CIM modifications have been proposed to address this issue. However, no prior work has systematically compared the performance of these concepts. This paper presents the first side-by-side evaluation of six promising CIM architectures using a unified simulation model. We develop stochastic differential equations, find optimal hyperparameters via Bayesian optimization per problem-architecture pair, and assess the performance on multiple metrics using MaxCut instances from the Gset and BiqMac datasets. CIM-SNN outperforms the rest on most metrics, with a 54.21% average success probability (SP) improvement and 1.36× less time-to-solution (TTS) at 96% GS energy compared to the Standard CIM on BiqMac graphs. Other CIMs show some advantages on certain Gset graphs. CIM-QA is usually the worst-performing, with an 18.55% average SP loss and a 1.30× higher TTS at 96% GS compared to the Standard CIM on BiqMac graphs. CIM-SNN demonstrates the greatest noise robustness and promise for further tuning via a linear pump schedule. CIM-QA benefits from high noise levels. This study makes two key contributions: (1) identifying promising CIM architectures to guide targeted research and accelerate practical adoption, and (2) providing a unified framework for evaluating future architectural modifications against existing ones.