Neural Deep Operator Networks Representation of Coherent Ising Machine Dynamics

Abstract

Coherent Ising Machines (CIMs) are optical devices that employ parametric oscillators to tackle binary optimization problems, whose simplified dynamics are described by a series of coupled ordinary differential equations (ODEs). In this study, we setup a proof-of-concept experiment to learn the deterministic dynamics of CIMs via the use of neural Deep Operator Networks (DeepONet). After training successfully the systems over multiple initial conditions and problem instances, we benchmark the comparative performance of the neural network versus the simulated ODEs on solving fully-connected quadratic binary optimization problems. In our tests, the network is capable of delivering solutions to the optimization problems of comparative quality to the exact dynamics up to 175 spins. The CIM model used is very simple with respect to the state-of-art, but we do not identify roadblocks to go further: given sufficient training resources more sophisticated CIM solvers could successfully be represented by a neural network at a large scale.