Distributions of steady states in a network of degenerate optical parametric oscillators in solving combinatorial optimization problems
Distributions of steady states in a network of degenerate optical parametric oscillators in solving combinatorial optimization problems
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DOI：
10.1103/physreva.98.053839
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发表时间：
2018-08
影响因子：
2.9
通讯作者：
R. Miyazaki;Masayuki Ohzeki
中科院分区：
文献类型：
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作者：
R. Miyazaki;Masayuki Ohzeki
我们研究了简并光参量振荡器（DOPO）网络作为相干伊辛机的模型，相干伊辛机是一种解决伊辛问题的架构。该网络代表 Ising 模型中的交互，该模型是先前针对两个 DOPO 情况提出的模型的推广。 DOPO 的动力学由 Fokker-Planck 方程以正 $P$ 表示来描述。我们获得了在某些 ansatz 下任意 Ising 问题的稳态的近似分布。使用统计力学的方法，我们分析证明，特定参数范围内的最可能状态对应于两个相当简单的问题的真正最佳状态，即没有或有二元随机场的全连接铁磁耦合。特别是，对于随机场问题，该分布可以正确检测目标伊辛模型中随场大小变化而发生的相变。
We investigate a network of degenerate optical parametric oscillators (DOPOs) as a model of the coherent Ising machine, an architecture for solving Ising problems. The network represents the interaction in the Ising model, which is a generalization of a previously proposed one for the two-DOPO case. Dynamics of the DOPOs is described by the Fokker-Planck equation in the positive $P$ representation. We obtain approximate distribution of steady states for arbitrary Ising problems under some ansatz. Using the method of statistical mechanics, we analytically demonstrate that the most probable states in a particular range of the parameters correspond to the true optimal states for two rather simple problems, i.e., fully connected ferromagnetic coupling without or with binary random fields. In particular, for the random-field problem, the distribution correctly detects the phase transition that occurs in the target Ising model with varying the magnitude of the fields.