Experimental Demonstration of a Reconfigurable Coupled Oscillator Platform to Solve the Max-Cut Problem

TL;DR

This paper demonstrates an integrated circuit of 30 reconfigurable coupled oscillators that efficiently approximates solutions to the NP-hard Max-Cut problem, showing high accuracy especially in dense graphs.

Contribution

It introduces a reconfigurable oscillator platform that solves Max-Cut problems with high accuracy, advancing hardware-based combinatorial optimization methods.

Findings

Achieved solutions within 99% of optimal for most graphs.

Effectively solved dense graphs with high edge density.

Demonstrated room-temperature operation of the oscillator-based solver.

Abstract

In this work, we experimentally demonstrate an integrated circuit (IC) of 30 relaxation oscillators with reconfigurable capacitive coupling to solve the NP-Hard Maximum Cut (Max-Cut) problem. We show that under the influence of an external second-harmonic injection signal, the oscillator phases exhibit a bi-partition which can be used to calculate a high quality approximate Max-Cut solution. Leveraging the all-to-all reconfigurable coupling architecture, we experimentally evaluate the computational properties of the oscillators using randomly generated graph instances of varying size and edge density . Further, comparing the Max-Cut solutions with the optimal values, we show that the oscillators (after simple post-processing) produce a Max-Cut that is within 99% of the optimal value in 28 of the 36 measured graphs; importantly, the oscillators are particularly effective in dense graphs with the Max-Cut being optimal in seven out of nine measured graphs with edge density 0.8. Our work marks a step towards creating an efficient, room-temperature-compatible non-Boolean hardware-based solver for hard combinatorial optimization problems.