An Ising Machine Solving Max-Cut Problems based on the Circuit Synthesis of the Phase Dynamics of a Modified Kuramoto Model

Abstract

A promising approach for efficiently solving NP-hard optimization problems is based on mapping the problems onto Ising machines. Oscillator-based Ising machines can be implemented by utilizing sub-harmonic injection locking, which enables binary phase shifts between the oscillators and leads to an improved reliability of Ising machines. Based on a modified Kuramoto model with sub-harmonic injection locking, we synthesize an ideal electrical circuit displaying the phase dynamics of an Ising machine. The ideal circuit can be utilized to specifically take non-ideal effects into account, serving as a starting point for designing Ising machines with increased performance when considering existing electrical components. We furthermore derive a corresponding wave digital model, which is utilized for emulating the synthesized electrical circuit. The emulation results show that the synthesized circuit indeed models the phase dynamics of an Ising machine capable of solving Max-Cut problems with an accuracy of 88% for a 5-node problem and weights between 0 and 31.