  Quantum Approximate Optimization Algorithm (QAOA) is one of the most
promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ)
era. Quantifying the performance of QAOA in the near-term regime is of utmost
importance. We perform a large-scale numerical study of the approximation
ratios attainable by QAOA is the low- to medium-depth regime. To find good QAOA
parameters we perform 990 million 10-qubit QAOA circuit evaluations. We find
that the approximation ratio increases only marginally as the depth is
increased, and the gains are offset by the increasing complexity of optimizing
variational parameters. We observe a high variation in approximation ratios
attained by QAOA, including high variations within the same class of problem
instances. We observe that the difference in approximation ratios between
problem instances increases as the similarity between instances decreases. We
find that optimal QAOA parameters concentrate for instances in out benchmark,
confirming the previous findings for a different class of problems.
