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Physical Review Applied

Enhanced, fully connected 360 000-spin spatial photonic Ising machine

Junze Yao, Rongwei Zhu, Junjie Yu

Published Sep 25, 2025• 5 citations
Publisher

Abstract

The spatial photonic Ising machine (SPIM) is a promising architecture that leverages the scalability and parallelism of photons to solve Ising problems in combinatorial optimization. SPIMs have been held back fundamentally by limited computational accuracy. This study overcomes that limitation through a hybrid approach, integrating aberration correction with a dynamic algorithm to update simultaneously a number of flipped spins, rather than just one. The method demonstrably improves computational accuracy and presents a way for SPIMs to scale to significantly larger systems (order 10${}^{5}$ spins), a milestone on the path to practical application.

DOI
10.1103/c792-d3n9

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The spatial photonic Ising machine (SPIM) is a promising architecture that leverages the scalability and parallelism of photons to solve Ising problems in combinatorial optimization. SPIMs have been held back fundamentally by limited computational accuracy. This study overcomes that limitation through a hybrid approach, integrating aberration correction with a dynamic algorithm to update simultaneously a number of flipped spins, rather than just one. The method demonstrably improves computational accuracy and presents a way for SPIMs to scale to significantly larger systems (order 105{}^{5}5 spins), a milestone on the path to practical application.
The spatial photonic Ising machine (SPIM) is a simple and elegant architecture capable of expanding the spin scale with ease, and thus this optical architecture is attractive for its potential in solving large-scale combinatorial optimization problems. Here, we propose a scheme for aberration compensation to improve the computing accuracy of the SPIM based on a spatial light modulator (SLM), resulting in good scalability. First, the gamma curve of the SLM is corrected with the help of double-hole interference fringes. Then, an enhanced phase shift interferometry is used to measure the aberration of the entire optical system, and this aberration is compensated by loading the compensation phase on the SLM. Moreover, an iterative algorithm using self-adaptive cluster flipping is proposed for accelerating the convergence of SPIM. During the converging process, the number of flipped spins within the cluster is updated dynamically according to the convergence speed and accuracy, which makes it possible to achieve a good balance between high speed and high accuracy. Further, a proof-of-principle experimental set-up of the optimized SPIM is implemented, and the ground-state search of an antiferromagnetic Ising model is demonstrated. As an example, this optimized Ising machine is used for solving the number partitioning problem. It is shown that the partition of 40,000 random numbers is well demonstrated, and the final partitioning accuracy is as high as 99.88%.
A spatial photonic Ising machine (SPIM) handles large-scale combinatorial optimization problems due to optical processing with spatial parallelism. However, iterative feedback in the search for an optimal solution limits processing speed, even though the Ising Hamiltonian is computed optically. We propose a parallel spatial photonic Ising machine (pSPIM) utilizing spatial multiplexing to search for an optimal solution efficiently. By employing grating patterns and encoding multiple configurations of Ising spins in a phase distribution, several Ising Hamiltonians are computed simultaneously. We demonstrated that the optimal solutions of max-cut problems with 100 Ising spins were obtained more frequently as the number of processing units increased. In addition, combining the multicomponent model with parallel processing provides an efficient search for optimal solutions to problems represented by using interaction matrices with a rank greater than one. The spin-update strategy of pSPIM offers an effective approach for efficiently solving large-scale combinatorial optimization problems.
The spatial photonic Ising machine (SPIM) [13D. Pierangeli et al., Large-Scale Photonic Ising Machine by Spatial Light Modulation, Phys. Rev. Lett. 122, 213902 (2019).PRLTAO0031-900710.1103/PhysRevLett.122.213902] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems efficiently. The primitive version of the SPIM, however, can accommodate Ising problems with only rank-one interaction matrices. In this Letter, we propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. Moreover, it acquires the learning ability of Boltzmann machines. We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using the model with low-rank interactions. Thus, the proposed model exhibits higher practical applicability to various problems of combinatorial optimization and statistical learning, without losing the scalability inherent in the SPIM architecture.
Combinatorial optimization problems are challenging for classical computing architectures, motivating the development of specialized hardware like Ising machines. The Spatial Photonic Ising Machine (SPIM) and its enhanced versions have shown promise in solving such problems by mapping them to the Ising model and leveraging optical parallelism to compute Hamiltonian energies efficiently. However, the 0-1 knapsack problem, as a representative combinatorial optimization problem, has only been reported to be solved effectively in small-scale SPIM. In this work, we analyze the factors that limit the spin scalability and propose a novel hardware-aware Hamiltonian mapping scheme to overcome this limitation. Based on this enhanced SPIM, the scheme is validated through simulated annealing experiments on a 102400-spin 0-1 knapsack problem, achieving high solution accuracy. Our method not only enables efficient solutions to large-scale 0-1 knapsack problems but also offers generalizability to other combinatorial optimization problems with similar coupling configurations. This work demonstrates the potential of SPIMs as scalable and adaptable solvers for real-world optimization challenges.
Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising Machines have proven to be advantageous for simulating fully connected large-scale spin systems. However, fine control of a general interaction matrix JJJ has so far only been accomplished through eigenvalue decomposition methods that either limit the scalability or increase the execution time of the optimization process. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, enabling the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected values and then proceed to solve both the unweighted and weighted graph partitioning problems, showcasing a systematic convergence to an optimal solution via simulated annealing. Our approach greatly expands the applicability of SPIMs for real-world applications without sacrificing any of the inherent advantages of the system, and paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models, on SPIM devices.
We explore the potential of spatial-photonic Ising machines (SPIMs) to address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically affected by the rank and precision of the coupling matrices. By developing and assessing advanced decomposition techniques, we expand the range of problems SPIMs can solve, overcoming the limitations of traditional Mattis-type matrices. Our approach accommodates a diverse array of coupling matrices, including those with inherently low ranks, applicable to complex NP-complete problems. We explore the practical benefits of low-rank approximation in optimization tasks, particularly in financial optimization, to demonstrate the real-world applications of SPIMs. Finally, we evaluate the computational limitations imposed by SPIM hardware precision and suggest strategies to optimize the performance of these systems within these constraints.