Using continuation methods to analyse the difficulty of problems solved by Ising machines

TL;DR

This paper uses continuation methods to analyze how the bifurcation structure of problems influences the success probability of Ising machines in finding optimal solutions, highlighting the impact of implementation choices.

Contribution

It introduces a bifurcation-based analysis framework for Ising machines, revealing how implementation affects solution difficulty and success rates.

Findings

Bifurcation sequences determine solution difficulty.

Proper implementation drastically improves success probability.

Continuation methods reveal problem landscape structure.

Abstract

Ising machines are dedicated hardware solvers of NP-hard optimization problems. However, they do not always find the most optimal solution. The probability of finding this optimal solution depends on the problem at hand. Using continuation methods, we show that this is closely linked to the bifurcation sequence of the optimal solution. From this bifurcation analysis, we can determine the effectiveness of solution schemes. Moreover, we find that the proper choice of implementation of the Ising machine can drastically change this bifurcation sequence and therefore vastly increase the probability of finding the optimal solution.