Observing a Phase Transition in a Coherent Ising Machine

TL;DR

This paper investigates how a coherent Ising machine (CIM) simulates the thermodynamic phase transition of a 2D Ising model, revealing that CIM can replicate phase transition behavior more accurately than mean field approximations.

Contribution

It demonstrates that CIM samples can be regarded as a canonical ensemble, allowing estimation of an effective temperature and revealing phase transition-like behavior.

Findings

CIM samples can be modeled as a canonical ensemble.

Estimated effective temperature aligns with thermodynamic properties.

CIM exhibits a phase transition more accurately than mean field models.

Abstract

A coherent Ising machine (CIM) is known to deliver the low-energy states of the Ising model. Here, we investigate how well the CIM simulates the thermodynamic properties of a two-dimensional square-lattice Ising model. Assuming that the spin sets sampled by the CIM can be regarded as a canonical ensemble, we estimate the effective temperature of the spins represented by degenerate optical parametric oscillator pulses by using maximum likelihood estimation. With the obtained temperature, we confirmed that the thermodynamic quantities obtained with the CIM exhibited a phase-transition-like behavior that better matches the analytical and numerical results than the mean field one.