Benchmarking Quantum Heuristics: Non-Variational QWOA for Weighted Maxcut

TL;DR

This paper benchmarks the non-variational Quantum Walk Optimization Algorithm (QWOA) on weighted Maxcut problems, showing promising scaling advantages over classical heuristics in simulation for problem sizes up to 31 nodes.

Contribution

It provides the first comprehensive benchmarking of non-variational QWOA on weighted Maxcut, demonstrating its potential for quantum advantage in combinatorial optimization.

Findings

Achieves constant average-case success probability for optimal solutions up to n=31.

Scales more favorably than classical heuristics as problem size increases.

Suggests potential for quantum advantage in solving NP-hard problems.

Abstract

We present benchmarking results for the non-variational Quantum Walk Optimisation Algorithm (non-variational QWOA) applied to the weighted maxcut problem, using classical simulations for problem sizes up to $n = 31$. The amplified quantum state, prepared using a quadratic number of alternating unitaries, achieves a constant average-case measurement probability for globally optimal solutions across these problem sizes. This behaviour contrasts with that of classical heuristics, which, for NP-hard optimisation problems, typically exhibit solve probabilities that decay as problem size increases. Performance comparisons with two local-search heuristics on the same benchmark instances suggest that the non-variational QWOA may offer a meaningful advantage by scaling more favourably with problem size. These results provide supporting evidence for the potential of this quantum heuristic to achieve quantum advantage, though further work is needed to assess whether the observed performance scaling persists at larger problem sizes, and to confirm whether similar performance trends are observed for the other problem classes to which the non-variational QWOA is designed to generalise.