The fixed angle conjecture for QAOA on regular MaxCut graphs
Abstract
The quantum approximate optimization algorithm (QAOA) is a nearterm combinatorial optimization algorithm suitable for noisy quantum devices. However, little is known about performance guarantees for $p>2$. A recent work \cite{Wurtz_guarantee} computing MaxCut performance guarantees for 3regular graphs conjectures that any $d$regular graph evaluated at particular fixed angles has an approximation ratio greater than some worstcase guarantee. In this work, we provide numerical evidence for this fixed angle conjecture for $p<12$. We compute and provide these angles via numerical optimization and tensor networks. These fixed angles serve for an optimizationfree version of QAOA, and have universally good performance on any 3 regular graph. Heuristic evidence is presented for the fixed angle conjecture on graph ensembles, which suggests that these fixed angles are ``close" to global optimum. Under the fixed angle conjecture, QAOA has a larger performance guarantee than the Goemans Williamson algorithm on 3regular graphs for $p\geq 11$.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 DOI:
 10.48550/arXiv.2107.00677
 arXiv:
 arXiv:2107.00677
 Bibcode:
 2021arXiv210700677W
 Keywords:

 Quantum Physics
 EPrint:
 9 pages, 5 figures