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

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Cited by in corpus (10)

• Destabilization of local minima in analog spin systems by correction of amplitude heterogeneity
• Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators
• Order-of-magnitude differences in computational performance of analog Ising machines induced by the choice of nonlinearity
• Coherent Ising machines with error correction feedback
• Entanglement and quantum discord in optically coupled coherent Ising machines
• A Benchmarking Study of Quantum Algorithms for Combinatorial Optimization
• The coherent Ising machine with quantum feedback: the total and conditional master equation methods
• Initial states and apodisation for quantum field simulations in phase-space
• Phase-space simulations of feedback coherent Ising machines
• Steady state distributions of network of degenerate optical parametric oscillators in solving combinatorial optimization problems