Truncated Wigner function theory of coherent Ising machines based on degenerate optical parametric oscillator network

TL;DR

This paper develops a quantum theoretical framework for coherent Ising machines using networks of degenerate optical parametric oscillators, demonstrating how quantum correlations and noise reduction techniques improve ground state probability.

Contribution

It introduces a truncated Wigner representation approach to analyze quantum effects in coherent Ising machines with various reservoir fields, highlighting noise reduction benefits.

Findings

Quantum correlations exist between coupled DOPOs despite dissipation.

Reducing thermal noise increases the likelihood of finding the ground state.

Squeezing vacuum fluctuations enhances the performance of the Ising machine.

Abstract

We present the quantum theory of coherent Ising machines based on networks of degenerate optical parametric oscillators (DOPOs). In a simple model consisting of two coupled DOPOs, both positive-$P$ representation and truncated Wigner representation predict quantum correlation and inseparability between the two DOPOs in spite of the open-dissipative nature of the system. Here, we apply the truncated Wigner representation method to coherent Ising machines with thermal, vacuum, and squeezed reservoir fields. We find that the probability of finding the ground state of a one-dimensional Ising model increases substantially as a result of reducing excess thermal noise and squeezing the incident vacuum fluctuation on the out-coupling port.