A quantum advantage over classical for local max cut

TL;DR

This paper demonstrates that a quantum algorithm (QAOA) can outperform classical local algorithms in solving the Local Max Cut problem on degree-3 graphs, indicating potential quantum advantage in combinatorial optimization.

Contribution

It provides the first evidence of a quantum advantage over classical algorithms for a well-studied combinatorial problem on small-scale quantum hardware.

Findings

QAOA outperforms classical local algorithms on degree-3 graphs

Quantum advantage observed with small-scale quantum hardware

Results suggest potential for quantum speedup in practical optimization tasks

Abstract

We compare the performance of a quantum local algorithm to a similar classical counterpart on a well-established combinatorial optimization problem LocalMaxCut. We show that a popular quantum algorithm first discovered by Farhi, Goldstone, and Gutmannn [1] called the quantum optimization approximation algorithm (QAOA) has a computational advantage over comparable local classical techniques on degree-3 graphs. These results hint that even small-scale quantum computation, which is relevant to the current state-of the art quantum hardware, could have significant advantages over comparably simple classical computation.