Skew-Gaussian model of small-photon-number coherent Ising machines

TL;DR

This paper introduces a skew-Gaussian model for small-photon-number coherent Ising machines that incorporates third-order fluctuations, improving the accuracy of success probability predictions over traditional Gaussian models.

Contribution

The authors develop a skew-Gaussian model including third-order fluctuation products, enhancing the description of CIMs in strong-gain-saturation regimes beyond Gaussian approximations.

Findings

Skew-Gaussian model better matches quantum master equation predictions.

Inclusion of skewness improves success probability estimates.

Skew variables influence CIM performance analysis.

Abstract

A Gaussian quantum theory of bosonic modes has been widely used to describe quantum optical systems, including coherent Ising machines (CIMs) that consist of $\chi^{(2)}$ degenerate optical parametric oscillators (DOPOs) as nonlinear elements. However, Gaussian models have been thought to be invalid in the extremely strong-gain-saturation limit. Here, we develop an extended Gaussian model including two third-order fluctuation products, $\langle \delta \hat{X}^3\rangle$ and $\langle \delta \hat{X}\delta \hat{P}^2\rangle$, which we call self-skewness and cross-skewness, respectively. This new model which we call skew-Gaussian model more precisely replicates the success probability predicted by the quantum master equation (QME), relative to Gaussian models. We also discuss the impact of skew variables on the performance of CIMs.