Computational Phase Transitions: Benchmarking Ising Machines and Quantum Optimisers

TL;DR

This paper reviews how computational phase transitions serve as benchmarks for Ising machines and quantum optimisers, highlighting their role in understanding problem hardness and algorithm performance.

Contribution

It surveys recent findings on computational phase transitions in physical processors, emphasizing their application in benchmarking Ising machines and quantum optimisation algorithms.

Findings

Hard instances are concentrated in narrow parameter regions

Quantum algorithms' success depends on problem density

Phase transition analysis aids benchmarking and understanding performance

Abstract

While there are various approaches to benchmark physical processors, recent findings have focused on computational phase transitions. This is due to several factors. Importantly, the hardest instances appear to be well-concentrated in a narrow region, with a control parameter allowing uniform random distributions of problem instances with similar computational challenge. It has been established that one could observe a computational phase transition in a distribution produced from coherent Ising machine(s). In terms of quantum approximate optimisation, the ability for the quantum algorithm to function depends critically on the ratio of a problems constraint to variable ratio (called density). The critical density dependence on performance resulted in what was called, reachability deficits. In this perspective we recall the background needed to understand how to apply computational phase transitions in various bench-marking tasks and we survey several such contemporary findings.