Quantum model for coherent Ising machines: Stochastic differential equations with replicator dynamics
Taime Shoji, Kazuyuki Aihara, Y. Yamamoto · Physical Review A · 2017
The quantum theory of coherent Ising machines, based on degenerate optical parametric oscillators and measurement-feedback circuits, is developed using the positive $P(\ensuremath{\alpha},\ensuremath{\beta})$ 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.