  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 specific families of graphs,
however, little is known about the algorithm on arbitrary graphs. We evaluate
the performance of QAOA at depths at most three on the MaxCut problem for all
connected non-isomorphic graphs with at most eight vertices and analyze how
graph structure affects QAOA performance. Some of the strongest predictors of
QAOA success are the existence of odd-cycles and the amount of symmetry in the
graph. 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
allow us to identify classes of combinatorial problems that are likely to
exhibit a quantum advantage.
