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Laser & Photonics Review

Wavelength‐Division Multiplexing Scheme Enabling Sparse Spin Interactions For Spatial Photonic Ising Machines

Wanyi Zhang, Li Luo, Yuan Zheng, Zhichao Ruan

Published Sep 30, 2026• 0 citations
Publisher

Abstract

ABSTRACT Spatial photonic Ising machines (SPIMs) offer a promising physical computing architecture for solving NP‐hard combinatorial optimization problems. However, when applied to models with sparse spin interactions, conventional SPIMs still employ a fully connected scheme, which demands digital preprocessing to decompose the interaction matrix and encode full spin interactions, leading to massive resource consumption on spatial light modulators (SLMs) when the spin size is large. Here, we propose and experimentally demonstrate a wavelength‐division multiplexing scheme to enable sparse spin interactions for SPIMs, where only the non‐zero spin interactions are encoded by SLMs, bypassing the need for preprocessing computation. Leveraging the non‐Von Neumann architecture of photonic computing, this method reduces the computational complexity of a single‐spin update in Metropolis–Hastings sampling from to . We successfully applied this system to solve the Max‐Cut problem across various sparse graphs, achieving a considerable probability of finding optimal or near‐optimal solutions, with performance comparable to classical simulated annealing. The proposed spatial encoding scheme requires linear resources scaling with the number of connections between spins, providing a highly scalable and energy‐efficient optical accelerator platform for large‐scale sparse combinatorial optimization.

DOI
10.1002/lpor.71989

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•Sep 9, 2026•0 citations
ABSTRACT Spatial photonic Ising machines (SPIMs) offer a promising physical computing architecture for solving NP‐hard combinatorial optimization problems. However, when applied to models with sparse spin interactions, conventional SPIMs still employ a fully connected scheme, which demands digital preprocessing to decompose the interaction matrix and encode full spin interactions, leading to massive resource consumption on spatial light modulators (SLMs) when the spin size is large. Here, we propose and experimentally demonstrate a wavelength‐division multiplexing scheme to enable sparse spin interactions for SPIMs, where only the non‐zero spin interactions are encoded by SLMs, bypassing the need for preprocessing computation. Leveraging the non‐Von Neumann architecture of photonic computing, this method reduces the computational complexity of a single‐spin update in Metropolis–Hastings sampling from to . We successfully applied this system to solve the Max‐Cut problem across various sparse graphs, achieving a considerable probability of finding optimal or near‐optimal solutions, with performance comparable to classical simulated annealing. The proposed spatial encoding scheme requires linear resources scaling with the number of connections between spins, providing a highly scalable and energy‐efficient optical accelerator platform for large‐scale sparse combinatorial optimization.
Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in unconventional Ising machines. Here, we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. With this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: ± J models, Sherrington-Kirkpatrick models, and only locally connected J 1 - J 2 models and observe the phase transitions. We also demonstrate the ground-state search for solving Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high–power efficiency Boltzmann sampling to a generalized large-scale Ising model.
Photonic Ising machines constitute an emergent new paradigm of computation geared toward tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial photonic Ising machines (SPIMs) have proven advantageous for simulating fully connected large-scale spin systems. Fine control of a general interaction matrix J has been accomplished so far only through matrix decomposition methods. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, allowing the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected value 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 significantly expands the applicability of SPIMs for real-world applications, as it is more efficient than matrix decomposition methods in the case of sparse problems. It paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models on SPIM devices.
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.
Ising machines are an emerging class of hardware that promises ultrafast and energy-efficient solutions to NP-hard combinatorial optimization problems. Spatial photonic Ising machines (SPIMs) exploit optical computing in free space to accelerate the computation, showcasing parallelism, scalability, and low power consumption. However, current SPIMs can implement only a restricted class of problems. This partial programmability is a critical limitation that hampers their benchmark. Achieving full programmability of the device while preserving its scalability is an open challenge. Here, we report a fully programmable SPIM achieved through a novel operation method based on the division of the focal plane. In our scheme, a general Ising problem is decomposed into a set of Mattis Hamiltonians, whose energies are simultaneously computed optically by measuring the intensity on different regions of the camera sensor. Exploiting this concept, we experimentally demonstrate the computation with high success probability of ground-state solutions of up to 32-spin Ising models on unweighted maximum cut graphs with and without ferromagnetic bias. Simulations of the hardware prove a favorable scaling of the accuracy with the number of spin. Our fully programmable SPIM enables the implementation of many quadratic unconstrained binary optimization problems, further establishing SPIMs as a leading paradigm in non-von Neumann hardware.
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.
Abstract Ising machines can efficiently solve real-world combinatorial optimization problems. Among them, photonic Ising machines (PIMs) exploit the parallelism and broadband bandwidth of optical systems to outperform digital computers in certain metrics. However, the bulky footprint of conventional discrete components imposes significant limitations on the miniaturization of current PIMs. Meanwhile, the scalability of problem size and spin connectivity density is constrained by limited computational resources. To address these challenges, we proposed and demonstrated an integrated PIM (IPIM) based on a hybrid architecture on a silicon-based photonic platform with an optical component footprint of 0.065 mm², achieved success rates exceeding 90% in finding global optimal solutions across all three benchmark tests. To tackle the common challenge in PIMs, where large-scale and high-connectivity-density problems naturally incur high computational complexity, we developed a joint algorithm with sparsity, inverse sparsity, and decomposition operations (JA-SID). Using this approach, we successfully solved Ising problems with sparse and dense spin connectivity, involving 102,400 spins. In addition, we introduced an optimized parameter configuration scheme (OPCS), which reduced the iteration count by over 50% for slowly converging problems, thereby lowering time complexity and power consumption. In practice, we used the IPIM to successfully partition a Facebook social network with over 60,000 users, demonstrating its capability to handle ultra-large-scale real-world problems. Our research substantially extended the applicability of IPIM, offering a promising solution to the increasing global demand for computational resources.