Quadrature Photonic Spatial Ising Machine

TL;DR

This paper introduces a novel quadrature photonic spatial Ising machine that enhances configuration flexibility and external magnetic field implementation, enabling efficient solutions to large-scale combinatorial optimization problems like Max-cut and vertex cover.

Contribution

The paper proposes a new quadrature approach for photonic spatial Ising machines, allowing arbitrary spin interactions and external magnetic fields, thus broadening their application scope.

Findings

Successfully solved Max-cut problem with 100 nodes experimentally.

Simulated solutions for Max-cut with over 1600 nodes.

Implemented vertex cover problem with external magnetic field.

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 optimizationproblems. As a computing accelerator, large-scale photonic spatial Ising machine have great advan-tages and potentials due to excellent scalability and compact system. However, current fundamentallimitation of photonic spatial Ising machine is the configuration flexibility of problem implementationin the accelerator model. Arbitrary spin interactions is highly desired for solving various NP hardproblems. Moreover, the absence of external magnetic field in the proposed photonic Ising machinewill further narrow the freedom to map the optimization applications. In this paper, we propose anovel quadrature photonic spatial Ising machine to break through the limitation of photonic Isingaccelerator by synchronous phase manipulation in two and three sections. Max-cut problem solutionwith graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100iterations. We derive and verify using simulation the solution for Max-cut problem with more than1600 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 achievethe optimal solution. Our work suggests flexible problem solution by large-scale photonic spatialIsing machine.