Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quadrature Photonic Spatial Ising Machine

Wenjia Zhang, Wencheng Sun, Yuanyuan Liu, Qingwen Liu, Jiangbing Du, Zuyuan He

Published Jun 16, 2021• 2 citations
Publisher

Abstract

Abstract The mining in physics and biology for accelerating the hardcore algorithm to solve non-deterministic polynomial (NP) hard problems has inspired a great amount of special-purpose ma-chine models. Ising machine has become an efficient solver for various combinatorial optimization problems. As a computing accelerator, large-scale photonic spatial Ising machine have great advantages and potentials due to excellent scalability and compact system. However, current fundamental limitation of photonic spatial Ising machine is the configuration flexibility of problem implementation in the accelerator model. Arbitrary spin interaction is highly desired for solving various NP hard problems. Moreover, the absence of external magnetic field in the proposed photonic Ising machine will further narrow the freedom to map the optimization applications. In this paper, we propose a novel quadrature photonic spatial Ising machine to break through the limitation of photonic Ising accelerator by synchronous phase manipulation in two and three sections. Max-cut problem solution with graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100 iterations. We derive and verify using simulation the solution for Max-cut problem with more than 1600 nodes and the system tolerance for light misalignment. Moreover, vertex cover problem, modeled as an Ising model with external magnetic field, has been successfully implemented to achieve the optimal solution. Our work suggests flexible problem solution by large-scale photonic spatial Ising machine.

DOI
10.21203/rs.3.rs-611666/v1

Related papers

Quadrature photonic spatial Ising machine

Wenchen Sun, Wenjia Zhang, Yuanyuan Liu +2 more

As a computing accelerator, a large-scale photonic spatial Ising machine has great advantages and potential due to its excellent scalability and compactness. However, the current fundamental limitation of a photonic spatial Ising machine is the configuration flexibility for problem implementation in the accelerator model. Arbitrary spin interactions are highly desired for solving various non-deterministic polynomial (NP)-hard problems. In this paper, we propose a novel quadrature photonic spatial Ising machine to break through the limitation of the photonic Ising accelerator by synchronous phase manipulation in two sections. The max-cut problem solution with a graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100 iterations. Our work suggests flexible problem solving by the large-scale photonic spatial Ising machine.

arXiv:2105.09307•Optics Letters•Feb 9, 2022•35 citations

Ising accelerator with a reconfigurable interferometric photonic processor

Rausell-Campo, José Roberto, Kayed, Nayem Al, Pérez-Lppez, Daniel +3 more

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.

arXiv:2511.13284•Nov 17, 2025•0 citations

General spatial photonic Ising machine based on the interaction matrix eigendecomposition method

Shaomeng Wang, Wenjia Zhang, Xin Ye +1 more

The spatial photonic Ising machine has achieved remarkable advancements in solving combinatorial optimization problems. However, it still remains a huge challenge to flexibly map an arbitrary problem to the Ising model. In this paper, we propose a general spatial photonic Ising machine based on the interaction matrix eigendecomposition method. The arbitrary interaction matrix can be configured in the two-dimensional Fourier transformation based spatial photonic Ising model by using values generated by matrix eigendecomposition. The error in the structural representation of the Hamiltonian decreases substantially with the growing number of eigenvalues utilized to form the Ising machine. In combination with the optimization algorithm, as low as ∼65% of the eigenvalues are required by intensity modulation to guarantee the best probability of optimal solution for a 20-vertex graph Max-cut problem, and this percentage decreases to below ∼20% for near-zero probability. The 4-spin experiments and error analysis demonstrate the Hamiltonian linear mapping and ergodic optimization. Our work provides a viable approach for spatial photonic Ising machines to solve arbitrary combinatorial optimization problems with the help of the multi-dimensional optical property.

Applied Optics•Mar 20, 2024•12 citations

Parallel spatial photonic Ising machine using spatial multiplexing for accelerating combinatorial optimization

Suguru Shimomura, Jun Tanida, Yusuke Ogura

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.

arXiv:2502.18918•Optics Letters•Oct 7, 2025•4 citations

Photonic Spatial-Euler Ising Machine for Solving 20000-vertex Max-cut Problem

Xin Ye, Wenjia Zhang, Shaomeng Wang +3 more

We propose a novel quadrature photonic spatial-Euler Ising machine to realize flexible spin-interaction configuration and spin-flip in a single SLM. A 20000-vertex max-cut problem is experimentally solved, showing 80% improvement compared to simulation results and 49% over heuristic algorithm.

•Jan 1, 2023•1 citation

General Spatial Photonic Ising Machine Based on Interaction Matrix Eigendecomposition Method

Wang, Shaomeng, Wenjia Zhang, Xin Ye +1 more

The spatial photonic Ising machine has achieved remarkable advancements in solving combinatorial optimization problems. However, it still remains a huge challenge to flexibly mapping an arbitrary problem to Ising model. In this paper, we propose a general spatial photonic Ising machine based on interaction matrix eigendecomposition method. Arbitrary interaction matrix can be configured in the two-dimensional Fourier transformation based spatial photonic Ising model by using values generated by matrix eigendecomposition. The error in the structural representation of the Hamiltonian decreases substantially with the growing number of eigenvalues utilized to form the Ising machine. In combination with the optimization algorithm, as low as 65% of the eigenvalues is required by intensity modulation to guarantee the best probability of optimal solution for a 20-vertex graph Max-cut problem, and this probability decreases to below 20% for zero best chance. Our work provides a viable approach for spatial photonic Ising machines to solve arbitrary combinatorial optimization problems with the help of multi-dimensional optical property.

arXiv:2306.10076•Jun 16, 2023•0 citations
Abstract The mining in physics and biology for accelerating the hardcore algorithm to solve non-deterministic polynomial (NP) hard problems has inspired a great amount of special-purpose ma-chine models. Ising machine has become an efficient solver for various combinatorial optimization problems. As a computing accelerator, large-scale photonic spatial Ising machine have great advantages and potentials due to excellent scalability and compact system. However, current fundamental limitation of photonic spatial Ising machine is the configuration flexibility of problem implementation in the accelerator model. Arbitrary spin interaction is highly desired for solving various NP hard problems. Moreover, the absence of external magnetic field in the proposed photonic Ising machine will further narrow the freedom to map the optimization applications. In this paper, we propose a novel quadrature photonic spatial Ising machine to break through the limitation of photonic Ising accelerator by synchronous phase manipulation in two and three sections. Max-cut problem solution with graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100 iterations. We derive and verify using simulation the solution for Max-cut problem with more than 1600 nodes and the system tolerance for light misalignment. Moreover, vertex cover problem, modeled as an Ising model with external magnetic field, has been successfully implemented to achieve the optimal solution. Our work suggests flexible problem solution by large-scale photonic spatial Ising machine.
As a computing accelerator, a large-scale photonic spatial Ising machine has great advantages and potential due to its excellent scalability and compactness. However, the current fundamental limitation of a photonic spatial Ising machine is the configuration flexibility for problem implementation in the accelerator model. Arbitrary spin interactions are highly desired for solving various non-deterministic polynomial (NP)-hard problems. In this paper, we propose a novel quadrature photonic spatial Ising machine to break through the limitation of the photonic Ising accelerator by synchronous phase manipulation in two sections. The max-cut problem solution with a graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100 iterations. Our work suggests flexible problem solving by the large-scale photonic spatial Ising machine.
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.
The spatial photonic Ising machine has achieved remarkable advancements in solving combinatorial optimization problems. However, it still remains a huge challenge to flexibly map an arbitrary problem to the Ising model. In this paper, we propose a general spatial photonic Ising machine based on the interaction matrix eigendecomposition method. The arbitrary interaction matrix can be configured in the two-dimensional Fourier transformation based spatial photonic Ising model by using values generated by matrix eigendecomposition. The error in the structural representation of the Hamiltonian decreases substantially with the growing number of eigenvalues utilized to form the Ising machine. In combination with the optimization algorithm, as low as ∼65% of the eigenvalues are required by intensity modulation to guarantee the best probability of optimal solution for a 20-vertex graph Max-cut problem, and this percentage decreases to below ∼20% for near-zero probability. The 4-spin experiments and error analysis demonstrate the Hamiltonian linear mapping and ergodic optimization. Our work provides a viable approach for spatial photonic Ising machines to solve arbitrary combinatorial optimization problems with the help of the multi-dimensional optical property.
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 has achieved remarkable advancements in solving combinatorial optimization problems. However, it still remains a huge challenge to flexibly mapping an arbitrary problem to Ising model. In this paper, we propose a general spatial photonic Ising machine based on interaction matrix eigendecomposition method. Arbitrary interaction matrix can be configured in the two-dimensional Fourier transformation based spatial photonic Ising model by using values generated by matrix eigendecomposition. The error in the structural representation of the Hamiltonian decreases substantially with the growing number of eigenvalues utilized to form the Ising machine. In combination with the optimization algorithm, as low as 65% of the eigenvalues is required by intensity modulation to guarantee the best probability of optimal solution for a 20-vertex graph Max-cut problem, and this probability decreases to below 20% for zero best chance. Our work provides a viable approach for spatial photonic Ising machines to solve arbitrary combinatorial optimization problems with the help of multi-dimensional optical property.