Quantum model for coherent Ising machines: Stochastic differential equations with replicator dynamics

摘要

The quantum theory of coherent Ising machines, based on degenerate optical parametric oscillators and measurement-feedback circuits, is developed using the positive P(α,β) representation of the density operator and the master equation. The theory is composed of the c-number stochastic differential equations for describing open dissipative quantum dynamics and the replicator dynamics equations for handling measurement-induced collapse of the density operator. We apply the present theory to simulate two simple Ising spin models and elucidate the unique features of this computing machine.