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Advanced Quantum Technologies

Sliding Mode Control‐Like Accelerated Coherent Ising Machine

Zhi‐guo Nie, Ruo‐xing Guo, Chen‐Rui Fan, Xingyu Wu, Bo Lü, Cong Cao, Yong‐Pan Gao

Published Apr 8, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1002/qute.202500057

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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.
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.
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.
The Ising machine, as a quantum-inspired computing system, can be used to efficiently solve combinatorial optimization problems. Ongoing studies have positioned it to potentially surpass the performance limitations of traditional computers. However, such Ising machines also suffer from scalability as the solution quality becomes sub-optimal when the problem size increases. In this work, we propose an Ising-based framework that uses a distributed Ising algorithm to find the near-optimal solution for large-scale Max-Cut problems through parallel processing via graph segmentation and reassembly. We selected the coherent Ising machine as the hardware solver and successfully found the solution for a 2000-node instance utilizing 20 computational bits on the Gset standard dataset. Additionally, we investigated the key factors influencing the system's performance and discovered that setting the number of reorganizations to one results in higher accuracy. Building on this configuration, we utilized a 100-bit CIM hardware platform (CPQC-1) to solve instances with varying numbers of nodes. The experimental results agree well with the theoretical simulations, confirming the practical feasibility of our method. Moreover, compared to existing Ising-based solvers, our algorithm significantly reduces computational resource requirements while achieving superior performance on large-scale combinatorial optimization problems, highlighting its effectiveness on quantum-inspired hardware.
Coherent Ising machines (CIMs) are an experimentally promising class of physics-based computational architectures that embed hard combinatorial optimization problems into systems of coupled nonlinear optical oscillators. The solution-finding mechanisms employed by CIMs feature complicated dynamical bifurcations occurring on a network scale, posing significant challenges to the development of theory and models for their underlying principles of operation. These difficulties are especially pronounced in the ultra-low-power or quantum regimes where the benefits in computational efficiency over conventional optimization algorithms are expected to be largest. We discuss some of our recent approaches and results at this intersection of dynamical systems theory and quantum model reduction, which have highlighted some potentially useful architectures and applications on the horizon for CIMs.
Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative approach to solve these problems by a specialized physical computing system. To evaluate its potential performance, computational experiments are performed on maximum cut (MAX-CUT) problems against traditional algorithms such as semidefinite programming relaxation of Goemans-Williamson and simulated annealing by Kirkpatrick, et al. The numerical results empirically suggest that the almost constant computation time is required to obtain the reasonably accurate solutions of MAX-CUT problems on a CIM with the number of vertices up to 2×1042 \times 10^42×104 and the number of edges up to 10810^8108.
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.