A coherent Ising machine for MAX-CUT problems : Performance evaluation against semidefinite programming relaxation and simulated annealing

TL;DR

This paper evaluates the performance of a coherent Ising machine (CIM) based on optical parametric oscillators for solving large MAX-CUT problems, showing it requires almost constant time for reasonably accurate solutions even at large scales.

Contribution

It provides the first empirical performance comparison of a CIM with traditional algorithms like SDP relaxation and simulated annealing for large-scale MAX-CUT problems.

Findings

CIM achieves near-constant computation time for large MAX-CUT instances.

CIM produces reasonably accurate solutions for problems with up to 20,000 vertices.

Performance suggests CIM as a promising physical computing approach for combinatorial optimization.

Abstract

Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative approach to solve these problems by a specialized physical computing system. To evaluate its potential performance, computational experiments are performed on maximum cut (MAX-CUT) problems against traditional algorithms such as semidefinite programming relaxation of Goemans-Williamson and simulated annealing by Kirkpatrick, et al. The numerical results empirically suggest that the almost constant computation time is required to obtain the reasonably accurate solutions of MAX-CUT problems on a CIM with the number of vertices up to $2 \times 10^4$ and the number of edges up to $10^8$.