Thermodynamic quantities of two-dimensional Ising models obtained by noisy mean field annealing and coherent Ising machine

TL;DR

This paper compares the thermodynamic quantities of two-dimensional Ising models obtained by noisy mean field annealing (NMFA) and coherent Ising machines (CIM), revealing that NMFA aligns with mean field results but not with CIM, especially near phase transitions.

Contribution

The study demonstrates that NMFA reproduces mean field thermodynamic features but fails to capture the phase transition behavior observed in CIM, highlighting the limitations of NMFA in modeling CIM performance.

Findings

NMFA matches mean field thermodynamics.

CIM captures phase transitions beyond mean field.

NMFA cannot replicate CIM's thermodynamic features.

Abstract

Noisy mean field annealing (NMFA) is an algorithm that mimics a coherent Ising machine (CIM), which is an optical system for solving Ising problems. The NMFA has reproduced the solver performance of the CIM for systems of limited size even though it simplifies the interaction between spins with a mean-field approximation. However, recent experiments observing various thermodynamic quantities have revealed that the CIM can capture the phase transitions of the two-dimensional Ising models that the mean field cannot capture. This situation leads to a fundamental question as to how well the NMFA can capture the features of the thermodynamic quantities around the phase transition. This paper answers that the NMFA reproduces the thermodynamic features of the mean field, but cannot reproduce the CIM results. This suggests that, in terms of sampling, the level of performance of the CIM is beyond that of the NMFA.