Evaluation of QAOA based on the approximation ratio of individual samples

TL;DR

This paper evaluates the performance of QAOA on the Max-Cut problem, showing that optimized settings can significantly improve its efficiency and bring it closer to classical algorithms, especially on certain graph types.

Contribution

It introduces performance metrics based on sample quality probabilities and demonstrates that optimized QAOA settings can reduce the performance gap with classical solvers.

Findings

QAOA performance varies with graph type.

Optimizing the variational parameters improves performance by up to 100 times.

QAOA can approach classical solver performance on 3-regular random graphs.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm to solve binary-variable optimization problems. Due to the short circuit depth and its expected robustness to systematic errors, it is one of the promising candidates likely to run on near-term quantum devices. We simulate the performance of QAOA applied to the Max-Cut problem and compare it with some of the best classical alternatives, for exact, approximate and heuristic solution. When comparing solvers, their performance is characterized by the computational time taken to achieve a given quality of solution. Since QAOA is based on sampling, we utilize performance metrics based on the probability of observing a sample above a certain quality. In addition, we show that the QAOA performance varies significantly with the graph type. By selecting a suitable optimizer for the variational parameters and reducing the number of function evaluations, QAOA performance improves by up to 2 orders of magnitude compared to previous estimates. Especially for 3-regular random graphs, this setting decreases the performance gap with classical alternatives. Because of the evolving QAOA computational complexity-theoretic guidance, we utilize a framework for the search for quantum advantage which incorporates a large number of problem instances and all three classical solver modalities: exact, approximate, and heuristic.