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Optics Express

Gain optimization for enhanced solution quality of optoelectronic Ising machines

Yanbo Ren, Zhewen Hu, Ye Xiao, Miaomiao Wei, Ming Li

Published Apr 7, 2026• 0 citations
Publisher

Abstract

The Ising machine is an emerging hardware platform for combinatorial optimization, offering orders-of-magnitude speedups over conventional computing. However, due to its reliance on intrinsic physical dynamics, systematic strategies for improving solution quality remain limited, making optimal operation difficult to identify. Here, we investigate the optoelectronic Ising machine and systematically analyze the impact of pump gain on solution quality, considering both the final gain and the gain control scheme. Based on the system's evolutionary dynamics, we explain the experimentally observed behaviors and propose a gain-optimization strategy to determine the optimal operating point. Using this strategy, the solution quality of the optoelectronic Ising machine is improved for Max-Cut problems with graph densities of 10%, 50%, and 100%.

DOI
10.1364/oe.588617

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The Ising machine is an emerging hardware platform for combinatorial optimization, offering orders-of-magnitude speedups over conventional computing. However, due to its reliance on intrinsic physical dynamics, systematic strategies for improving solution quality remain limited, making optimal operation difficult to identify. Here, we investigate the optoelectronic Ising machine and systematically analyze the impact of pump gain on solution quality, considering both the final gain and the gain control scheme. Based on the system's evolutionary dynamics, we explain the experimentally observed behaviors and propose a gain-optimization strategy to determine the optimal operating point. Using this strategy, the solution quality of the optoelectronic Ising machine is improved for Max-Cut problems with graph densities of 10%, 50%, and 100%.
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.
The photonic Ising machine, a promising non-von Neumann computational paradigm, offers a feasible way to address combinatorial optimization problems.We develop a digital noise injection method for spatial photonic Ising machines based on smoothed analysis, where noise level acts as a parameter that quantifies the smoothness degree.Through experiments with 20736-node Max-Cut problems, we establish a stable performance within a smoothness degree of 0.04 to 0.07.Digital noise injection results in a 24% performance enhancement, showing a 73% improvement over heuristic Sahni-Gonzales (SG) algorithms.Furthermore, to address noise-induced instability concerns, we propose an optoelectronic co-optimization method for a more streamlined smoothing method with strong stability.
Combinatorial optimization problems are difficult to solve due to the space explosion in an exhaustive search. Using Ising model-based solvers can efficiently find near-optimal solutions by minimizing the energy of a nonlinear Hamiltonian system. In contrast to Ising machines based on quantum mechanics, classical Ising machines using conventional technologies, such as the complementary metal-oxide-semiconductor, offer efficient implementations with competitive performance. In this paper, we briefly review recently developed simulation algorithms of classical Ising machines. These algorithms are classified by considering various inherent mechanisms in the simulation of physical phenomena. Then, strategies to improve the simulation efficiency are discussed by generalizing their characteristics and behaviours. These simulation algorithms are key for improving the efficiency of classical Ising machines in solving combinatorial optimization problems.
An Ising machine (IM), as a type of analog computer tailored for tackling intractable combinatorial optimization problems, has attracted remarkable attention in recent years. In contrast to the blossoming field of bespoke IM hardware, developing metaheuristics from IMs remains largely uninvestigated. Here, we propose a physics-inspired evolutionary computation paradigm, termed the Ising optimization framework (IOF); it comprises a unique Ising algorithm and a hybrid annealing scheme, which together are well-suited for solving quadratic unconstrained binary optimization (QUBO) problems embedded in Ising system energy. The Ising algorithm leverages a set of iterated self-mapping functions to evolve an Ising-spin swarm, enabling efficient energy minimization in artificial Ising systems while mitigating detrimental chaos. Complementing the algorithm, a hybrid annealing scheme integrating singular value dropout, bifurcation control, and a nudging strategy, is devised to augment the overall optimization capacity. The effectiveness of the IOF is validated on various Ising and Max-cut problems with decision variables ranging from 625 to 5000 in number. In comparison to four major types of methods for solving QUBOs, including IM simulations, nature-inspired algorithms, a state-of-the-art heuristic, and the commercial solver Gurobi, the IOF consistently demonstrates notable optimization quality and computational efficiency. This paper provides a theoretical foundation and practical guidelines for bridging Ising-inspired approaches with evolutionary computation, offering an evolutionary perspective on Ising optimizations and suggesting a fertile avenue for future research and application.
We numerically demonstrate that introducing XY-spin dynamics enabled by phase-insensitive optical parametric gain enhances the performance of coherent Ising machines (CIMs). Whereas conventional CIMs based on phase-sensitive optical parametric gain confine spins to two discrete Ising states, nondegenerate optical parametric oscillators with phase-insensitive gain support continuous-phase XY spins, facilitating spin flips that enable the system to escape local minima. Benchmarking on Wishart-planted problem instances shows that gradually transitioning from XY to Ising spins reduces the time-to-solution by roughly an order of magnitude relative to purely Ising-based dynamics. Furthermore, tailoring the transitions between XY-like and Ising-like regimes yields additional improvements beyond a simple unidirectional XY-to-Ising transition. Our results establish a new framework for engineering CIM dynamics in full phase-quadrature space and point toward fully optical architectures for efficient combinatorial optimization.
The Ising machine (IM) has emerged as a promising tool for tackling nondeterministic polynomial-time hard combinatorial optimization problems in real-world applications. Among various types of IMs, optoelectronic IMs based on electro-optical (EO) modulators stand out as an impressive platform for Ising computations. They offer a simple and stable architecture, with the EO modulator providing a natural inline nonlinear transfer function for the Ising model. However, integrated optoelectronic IMs have not been demonstrated until now, and exploring large-scale computations within the constraints of digital hardware resources remains an open challenge for these systems. In this paper, an integrated optoelectronic IM based on a thin-film lithium niobate (TFLN) photonic chip is presented, in conjunction with a sparse matrix–vector multiplication algorithm embedded in a field-programmable gate array that optimizes hardware resource utilization and minimizes computational latency. This setup allows us to solve multiple types of MAX-CUT problems with up to 2048 spins and achieve a remarkably low iteration latency of 1.78 μs. To further address the constraints posed by digital devices when tackling larger-scale Ising problems, we extend the application of the TFLN chip to yet another new scheme in which the single, compact on-chip modulator concurrently performs operations of linear multiplication and nonlinear transformation. This scheme demonstrates the capability to address large-scale MAX-CUT problems involving up to 16,384 spins, which, to the best of our knowledge, are the largest-scale problems solved on an on-chip IM, highlighting its potential to overcome digital limitations. The TFLN-based optoelectronic IMs provide a compact solution with high scalability for potentially practical applications in addressing complex combinatorial optimization problems.