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

Abstract

The quantum theory of coherent Ising machines, based on degenerate optical parametric oscillators and measurement-feedback circuits, is developed using the positive $P(\alpha ,\beta )$ 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.

9 pages, 5 figures

References in corpus (3)

• Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
• A Quantum Model for Coherent Ising Machines: Discrete-time Measurement Feedback Formulation
• Cauchy-Schwarz characterization of tripartite quantum correlations in an optical parametric oscillator