Fixed-angle conjectures for the quantum approximate optimization algorithm on regular MaxCut graphs

Journal Article · 17 November 2021 · Physical Review A - Atomic, Molecular, and Optical Physics

DOI:https://doi.org/10.1103/PhysRevA.104.052419· OSTI ID:1874047

Wurtz, Jonathan; Lykov, Danylo; Glatz, Andreas

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 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 >= 11.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: U.S. Department of Defense (DOD) - Defense Advanced Research Projects Agency (DARPA); National Science Foundation (NSF)
• DOE Contract Number: AC02-06CH11357
• OSTI ID: 1874047
• Journal Information: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 104, Issue 5
• Country of Publication: United States
• Language: English