Gaussian and skew-Gaussian quantum optical models of coherent Ising machines (CIMs)

Gaussian models of bosonic systems, which approximate quasi-phase-space distribution by mean

amplitudes and variances, have been used to describe quantum optical phenomena. To numerically

simulate coherent Ising machines (CIMs), which are nonlinear-optical-and-digital hybrid solvers for

quadratic unconstrained binary optimization (QUBO), we have derived models which replicate the

results of quantum master equation (QME) even when the optical nonlinearity per photon is large.

When the Gaussian model is obtained by linearization of stochastic differential equations, that derived

from positive-P quasi-distribution function can be more accurate than that derived from Wigner

function (Commun. Phys. 5, 154). The Gaussian model beyond linearization, including cumulant

decomposition of fourth-order fluctuation products into the products of variances (PRRes. 4, 013009),

provides more accurate below-threshold characteristics than those by linearization. In addition to these

developments, we have developed a ‘skew-Gaussian model’ (2403.00200), including the third-order

fluctuation products. In comparison with QME, skew-Gaussian model was more accurate than

Gaussian models.