A Quantum Model for Coherent Ising Machine: Stochastic Differential Equations with Replicator Dynamics

摘要

The quantum theory of coherent Ising machines, based on degenerate opticalparametric oscillators and measurement-feedback circuits, is developed usingthe positive $P({\alpha},{\beta})$ representation of the density operator andthe master equation. The theory is composed of the c-number stochasticdifferential equations for describing open dissipative quantum dynamics and thereplicator dynamics equations for handling measurement-induced collapse of thedensity operator. We apply the present theory to simulate two simple Ising spinmodels and elucidate the unique features of this computing machine.