Training a quantum optimizer

We study a variant of the quantum approximate optimization algorithm [E. Farhi, J. Goldstone, and S. Gutmann, arXiv: 1411.4028] with a slightly different parametrization and a different objective: rather than looking for a state which approximately solves an optimization problem, our goal is to find a quantum algorithm that, given an instance of the maximum 2-satisfiability problem (MAX-2-SAT), will produce a state with high overlap with the optimal state. Using a machine learning approach, we chose a training set of instances and optimized the parameters to produce a large overlap for the training set. We then tested these optimized parameters on a larger instance set. As a training set, we used a subset of the hard instances studied by Crosson, Farhi, C. Y.-Y. Lin, H.-H. Lin, and P. Shor (CFLLS) (arXiv: 1401.7320). When tested, on the full set, the parameters that we find produce a significantly larger overlap than the optimized annealing times of CFLLS. Testing on other random instances from 20 to 28 bits continues to show improvement over annealing, with the improvement being most notable on the hardest instances. Further tests on instances of MAX-3-SAT also showed improvement on the hardest instances. This algorithm may be a possible application for near-term quantum computers with limited coherence times.