Evaluating Quantum Approximate Optimization Algorithm: A Case Study

TL;DR

This study evaluates the performance of the Quantum Approximate Optimization Algorithm (QAOA) in the low- to medium-depth regime through extensive numerical simulations, revealing limited improvements with increased depth and high variability in results.

Contribution

It provides a large-scale numerical analysis of QAOA's approximation ratios, highlighting the challenges in parameter optimization and the variability across problem instances.

Findings

Approximation ratio increases marginally with depth.

Optimization complexity offsets gains from increased depth.

High variability in approximation ratios across instances.

Abstract

Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We perform a large-scale numerical study of the approximation ratios attainable by QAOA is the low- to medium-depth regime. To find good QAOA parameters we perform 990 million 10-qubit QAOA circuit evaluations. We find that the approximation ratio increases only marginally as the depth is increased, and the gains are offset by the increasing complexity of optimizing variational parameters. We observe a high variation in approximation ratios attained by QAOA, including high variations within the same class of problem instances. We observe that the difference in approximation ratios between problem instances increases as the similarity between instances decreases. We find that optimal QAOA parameters concentrate for instances in out benchmark, confirming the previous findings for a different class of problems.