We present benchmarking results for the nonvariational quantum walk-based optimization algorithm (nonvariational 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 behavior contrasts with that of classical heuristics, which, for NP-hard optimization 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 nonvariational QWOA may offer a meaningful advantage by scaling more favorably 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 nonvariational QWOA is designed to generalize.

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• Quantum benchmarking
• Quantum computation
• Quantum walks