Per-Shot Evaluation of QAOA on Max-Cut: A Black-Box Implementation Comparison with Goemans-Williamson

TL;DR

This paper empirically evaluates QAOA's performance on Max-Cut using a black-box approach with default settings, comparing it to classical algorithms through a per-shot statistical framework on realistic graph instances.

Contribution

It introduces a practical, black-box evaluation methodology for QAOA on Max-Cut, emphasizing default settings and probabilistic performance tracking against classical baselines.

Findings

QAOA's performance varies significantly with default parameters.

QAOA often does not outperform the Goemans-Williamson baseline under default settings.

The per-shot statistical framework provides detailed insights into QAOA's probabilistic success rates.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for addressing combinatorial optimization problems on near-term quantum hardware. In this work, we conduct an empirical evaluation of QAOA on the Max-Cut problem, using the Goemans-Williamson (GW) algorithm as a classical baseline for comparison. Unlike many prior studies, our methodology treats QAOA implementations as black-box optimizers, relying solely on default parameter settings without manual fine-tuning. We evaluate specific off-the-shelf QAOA implementations under default settings, not the algorithmic potential of QAOA with optimized parameters. This reflects a more realistic use case for end users who may lack the resources or expertise for instance-specific optimization. To facilitate fair and informative evaluation, we construct benchmark instances using well-known graph generation models that emulate practical graph structures, avoiding synthetic constructions tailored to either quantum or classical algorithms. A central component of our analysis is a per-shot statistical framework, which tracks the quality of QAOA outputs as a function of the number of circuit executions. This enables probabilistic comparisons with the GW algorithm by examining when and how frequently QAOA surpasses classical performance baselines such as the GW expectation and lower bound. Our results provide insight into the practical applicability of QAOA for Max-Cut and highlight its current limitations, offering a framework that can guide the assessment and development of future QAOA implementations.