TY - JOUR

T1 - Distributions of steady states in a network of degenerate optical parametric oscillators in solving combinatorial optimization problems

AU - Miyazaki, Ryoji

AU - Ohzeki, Masayuki

N1 - Funding Information:
The authors thank A. Ichiki and K. Ohki for helpful discussions and comments on the manuscript. R.M. thanks T. Leleu and Y. Yamamoto for valuable discussions. This research is supported by JST through its ImPACT program. M.O. acknowledges JSPS KAKENHI Grants No. 15H03699, No. 16H04382, and No. 16K13849.
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/11/21

Y1 - 2018/11/21

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85057128209&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057128209&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.98.053839

DO - 10.1103/PhysRevA.98.053839

M3 - Article

AN - SCOPUS:85057128209

SN - 2469-9926

VL - 98

JO - Physical Review A

JF - Physical Review A

IS - 5

M1 - 053839

ER -