Oscillatory quantum optimization methods applied to problems with large ground state bands

RFQA is a promising new quantum method for solving optimization problems, where by adding local oscillations to transverse fields, it can provide a polynomial quantum speedup over traditional quantum annealing methods. Inspired both by the performance of RFQA in trial problems with few ground states, and by the phenomenology of NP-complete problems, we consider RFQA applied to problems with exponentially many ground states, but where these states are an exponentially small fraction of the total configuration space. We explore how accelerated thermalization in low energy bands can provide a potentially noise tolerant quantum speedup for optimization and machine learning.