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arXiv · 2107.00677

The fixed angle conjecture for QAOA on regular MaxCut graphs

Jonathan Wurtz·Danylo Lykov
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Abstract

The quantum approximate optimization algorithm (QAOA) is a near-term 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 3-regular graphs conjectures that any $d$-regular graph evaluated at particular fixed angles has an approximation ratio greater than some worst-case 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 optimization-free 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 3-regular graphs for $p\geq 11$.

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Jonathan Wurtz, Danylo Lykov. 2021-07-19. The fixed angle conjecture for QAOA on regular MaxCut graphs. https://arxiv.org/abs/2107.00677

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