An Integrated All-Optical Ising Machine with Unlimited Spin Array Size and Coupling

Abstract

Artificial spin systems are used to solve combinatorial optimization problems by mapping them to the ground state search of the Ising model. Ising machines of various designs, in fields as diverse as photonics and electronics, have been proposed and demonstrated in recent years. One important mathematical operation required in photonic Ising machines for nearly all Hamiltonian minimization algorithms is repeated matrix–vector multiplication with the vector size limited by the physical size of the optical system. Herein, an integrated photonic Ising machine based on matrix partitioning and phase encoding, which effectively allows the use of physically small optical circuits to handle arbitrarily large spin vectors, is proposed. All the complicated calculations are carried out optically, rather than electronically, in this approach. How the required surface area of a hypothetical chip-based photonic Ising machine can be resized according to convenience, with the trade-off being the solution time, and that this trade-off can be done in a way that does not impact the algorithm's efficacy, is shown. Through simulation, the system is predicted to have a high success rate, high noise tolerance, and high error tolerance.