Computational phase transitions: benchmarking Ising machines and quantum optimisers

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.

QPack: Quantum Approximate Optimization Algorithms as universal benchmark for quantum computers

“…The model is also supported in Qiskit [66], alongside the popular MaxCut algorithm. The Ising model has in recent publishing been compared for both classical and QAOA algorithms [67]. It becomes apparent that for large clause density, QAOA shows reachability deficits [28] and is therefore no improvement on the classical algorithms.…”

Game of Life on Graphs

“…Random instances of many different problems and families of structures in computer science undergo a phase transition with respect to one or more parameters. Moreover, the most challenging and complex instances are observed around the transition point, while the instances far from the transition are usually simpler [5,13,15]. One of the first famous results on this topic was about 3-SAT phase transition [8,3].…”