Impact of graph structures for QAOA on MaxCut
The quantum approximate optimization algorithm (QAOA) is a promising method of solving combinatorial optimization problems using quantum computing. QAOA on the MaxCut problem has been studied extensively on graphs with specific structure; however, little is known about the general performance of the algorithm on arbitrary graphs. Here, we investigate how different graph characteristics correlate with QAOA performance at depths at most three on the MaxCut problem for all connected non-isomorphic graphs with at most eight vertices. Some good predictors of QAOA success relate to graph symmetries, odd cycles, and density. For example, on eight vertex graphs, the average probability for selecting an optimal solution for graphs that contain no odd cycles after three iterations of QAOA is 60.6% compared to 48.2% for those that do. The data generated from these studies are shared in a publicly accessible database to serve as a benchmark for QAOA calculations and experiments. Knowing the relationship between structure and performance can be used to identify classes of combinatorial problems that are likely to exhibit a quantum advantage.
- Research Organization:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- Defense Advanced Research Projects Agency (DARPA); National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); US Army Research Office (ARO); USDOE
- Grant/Contract Number:
- AC05-00OR22725
- OSTI ID:
- 1819598
- Journal Information:
- Quantum Information Processing, Journal Name: Quantum Information Processing Journal Issue: 9 Vol. 20; ISSN 1570-0755
- Publisher:
- SpringerCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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