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arXiv:2512.21587

Incorporating rank-free coupling and external field via an incoherent modulated spatial photonic Ising machine

Ze Zheng, Yuegang Li, Hang Xu, Jingzheng Huang, Tailong Xiao, Guihua Zeng

Published Dec 25, 2025• 0 citations
arXivHTMLPDF

Abstract

Spatial photonic Ising machines offer a novel optical platform for optimization and spin-model simulation, but existing diffraction-based schemes rely on auxiliary spins or multiplexing to encode high-rank couplings and external fields, reducing either speed or spin count. We demonstrate an amplitude-only, rank-free spatial photonic Ising machine in which arbitrary Ising Hamiltonians are encoded as Hadamard products on aligned amplitude and binary spatial modulators and read out by a single-pixel intensity measurement. The machine directly programs fully connected 797-spin Ising models with external fields at nearly 9-bit precision and operates at a constant iteration rate of ~200 Hz. By removing zero-valued product terms, the same architecture scales to sparse problems and experimentally solves a Max-Cut instance on a 424,108-vertex Mobius ladder graph. We also observe the phase transition of the Sherrington-Kirkpatrick model, demonstrating programmable optical simulation beyond low-rank couplings. These results establish amplitude modulation as a scalable route to programmable photonic Ising machines.

DOI
10.48550/arxiv.2512.21587

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Spatial photonic Ising machines offer a novel optical platform for optimization and spin-model simulation, but existing diffraction-based schemes rely on auxiliary spins or multiplexing to encode high-rank couplings and external fields, reducing either speed or spin count. We demonstrate an amplitude-only, rank-free spatial photonic Ising machine in which arbitrary Ising Hamiltonians are encoded as Hadamard products on aligned amplitude and binary spatial modulators and read out by a single-pixel intensity measurement. The machine directly programs fully connected 797-spin Ising models with external fields at nearly 9-bit precision and operates at a constant iteration rate of ~200 Hz. By removing zero-valued product terms, the same architecture scales to sparse problems and experimentally solves a Max-Cut instance on a 424,108-vertex Mobius ladder graph. We also observe the phase transition of the Sherrington-Kirkpatrick model, demonstrating programmable optical simulation beyond low-rank couplings. These results establish amplitude modulation as a scalable route to programmable photonic Ising machines.
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.
Abstract Drawing inspiration from the physical Ising model, optical Ising machines have emerged as a promising paradigm in optical computing. These machines typically utilize optical phase or amplitude modulators to represent the analog spin variables, which determine the final Hamiltonian by the combinatorial configuration of the complex optical field. However, current optical modulators exhibit relatively low modulation resolution and significant technical challenges arise when scaling up optical Ising systems to maintain consistent performance across integrated device clusters. Here we propose a programmable optical differential Ising machine that provides direct access to changes in the Hamiltonian. This system streamlines unnecessary matrix calculations, thereby reducing the requirements for the size and precision of the modulator matrix. Through numerical simulations on 60 to 100 spin MaxCut benchmark problems, we determine that the minimum required resolutions for the DAC and ADC are 6 bits and 5 bits, respectively, along with a significant tolerance of 0.3 rad for phase errors and over 10 multiplexing operations. Additionally, 100-spin experiments with a dual-channel system demonstrate its potential for phase transition simulation and solving complex 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.
The general-purpose programmable photonic processors offer a scalable and reconfigurable solution for a wide range of RF and optical applications. Therefore, implementing photonic Ising machines using programmable processors leverages the advantages of high speed and parallelism, enabling efficient hardware acceleration for finding ground-state solutions to combinatorial optimization problems. In this work, we demonstrate a novel programmable photonic Ising solver based on a hexagonal mesh general-purpose programmable photonic platform. The integrated system allows reconfigurable matrix multiplication and computes the Hamiltonian iteratively using an annealing algorithm that facilitates spin updates and effectively searches for the ground state. As a proof of concept, we experimentally solve two benchmark optimization problems, a fundamental three-node ferromagnetic coupling problem with external bias that demonstrates nontrivial spin interactions, and a four-node Max-Cut problem with arbitrary coupling matrices. Furthermore, to establish a large-scale capability, we emulated Ising problems with sizes up to N = 50, achieving success probabilities exceeding 80\%. Additionally, we examined the impact of errors, such as phase and coupling, on the performance of the programmable photonic Ising machine. Our general-purpose photonic Ising machine paves the way for implementing large-scale, programmable architectures for solving optimization problems.
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.
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.