Experimental Observation of Phase Transitions in Spatial Photonic Ising Machine

TL;DR

This paper experimentally investigates phase transitions in a spatial photonic Ising machine, validating mean-field theory predictions and exploring its robustness in solving optimization problems.

Contribution

It introduces gauge transformations for the photonic Ising machine and experimentally maps its phase diagram with 100 spins, confirming theoretical predictions.

Findings

Observation of paramagnetic, ferromagnetic, and spin-glass phases.

Experimental validation of mean-field theory in the photonic system.

Robustness of the system with many-spin interactions despite optical imperfections.

Abstract

Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Thanks to gauge transformation, we experimentally evaluate the phase diagram of high-dimensional spin-glass equilibrium system with $100$ fully-connected spins. We observe the presence of paramagnetic, ferromagnetic as well as spin-glass phases and determine the critical temperature $T_c$ and the critical probability ${{p}_{c}}$ of phase transitions, which agree well with the mean-field theory predictions. Thus the approximation of the mean-field model is experimentally validated in the spatial photonic Ising machine. Furthermore, we discuss the phase transition in parallel with solving combinatorial optimization problems during the cooling process and identify that the spatial photonic Ising machine is robust with sufficient many-spin interactions, even when the system is associated with the optical aberrations and the measurement uncertainty.