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A UNIFIED SIMULATIONS FRAMEWORK FOR COHERENT ISING MACHINES TO APPROXIMATE COMBINATORIAL OPTIMIZATION PROBLEMS

Vidisha Singhal

Published Jun 26, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.25394/pgs.32788797

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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.
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.
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 machines (CIMs) have emerged as a hybrid form of quantum computing devices designed to solve NP-complete problems, offering an exciting opportunity for discovering optimal solutions. Despite challenges such as susceptibility to noise-induced local minima, we achieved notable advantages in improving the computational accuracy and stability of CIMs. We conducted a successful experimental demonstration of CIM via femtosecond laser pumping that integrates optimization strategies across optical and structural dimensions, resulting in significant performance enhancements. The results are particularly promising. An average success rate of 55% was achieved to identify optimal solutions within a Möbius Ladder graph comprising 100 vertices. Compared with other alternatives, the femtosecond pulse results in significantly higher peak power, leading to more pronounced quantum effects and lower pump power in optical fiber-based CIMs. In addition, we have maintained an impressive success rate for a continuous period of 8 hours, emphasizing the practical applicability of CIMs in real-world scenarios. Furthermore, our research extends to the application of these principles in practical applications such as molecular docking and credit scoring. The results presented substantiate the theoretical promise of CIMs, paving the way for their integration into large-scale practical applications.
Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of the Ising model, tremendous effort has been devoted to developing solvers for Ising-type problems over the past decades. Recent advances in controlling and manipulating both quantum and classical systems have enabled novel computing paradigms such as quantum simulators and coherent Ising machines to tackle hard optimization problems. Here, we examine and benchmark several physics-inspired optimization algorithms, including coherent Ising machines, gain-dissipative algorithms, simulated bifurcation machines, and Hopfield neural networks, which we collectively refer to as stochastic driven nonlinear dynamical systems. Most importantly, we benchmark these algorithms against random Ising problems with planted solutions and compare them to simulated annealing as a baseline leveraging the same software stack for all solvers. We further study how different numerical integration techniques and graph connectivity affect performance. This work provides an overview of a diverse set of new optimization paradigms.
Coherent Ising Machines (CIMs) have emerged as a hybrid form of quantum computing devices designed to solve NP-complete problems, offering an exciting opportunity for discovering optimal solutions. Despite challenges such as susceptibility to noise-induced local minima, we achieved notable advantages in improving the computational accuracy and stability of CIMs. We conducted a successful experimental demonstration of CIM via femto-second laser pumping that integrates optimization strategies across optical and structural dimensions, resulting in significant performance enhancements. The results are particularly promising. An average success rate of 55% was achieved to identify optimal solutions within a Mobius Ladder graph comprising 100 vertices. Compared with other alternatives, the femto-second pulse results in significantly higher peak power, leading to more pronounced quantum effects and lower pump power in optical fiber based CIMs. In addition, we have maintained an impressive success rate for a continuous period of 8 hours, emphasizing the practical applicability of CIMs in real-world scenarios. Furthermore, our research extends to the application of these principles in practical applications such as molecular docking and credit scoring. The results presented substantiate the theoretical promise of CIMs, paving the way for their integration into large-scale practical applications.
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.