  The performance of the quantum approximate optimization algorithm is
evaluated by using three different measures: the probability of finding the
ground state, the energy expectation value, and a ratio closely related to the
approximation ratio. The set of problem instances studied consists of weighted
MaxCut problems and 2-satisfiability problems. The Ising model representations
of the latter possess unique ground states and highly-degenerate first excited
states. The quantum approximate optimization algorithm is executed on quantum
computer simulators and on the IBM Q Experience. Additionally, data obtained
from the D-Wave 2000Q quantum annealer is used for comparison, and it is found
that the D-Wave machine outperforms the quantum approximate optimization
algorithm executed on a simulator. The overall performance of the quantum
approximate optimization algorithm is found to strongly depend on the problem
instance.
