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arXiv · 1706.02034

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

Taime Shoji·Kazuyuki Aihara·Yoshihisa Yamamoto
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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.

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Taime Shoji, Kazuyuki Aihara, Yoshihisa Yamamoto. 2017-06-07. A Quantum Model for Coherent Ising Machine: Stochastic Differential Equations with Replicator Dynamics. https://doi.org/10.1103/physreva.96.053833

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