Improved quantum annealer performance from oscillating transverse fields

Quantum annealing is a promising application of quantum hardware for solving hard classical optimization problems. The runtime of the quantum annealing algorithm, in absence of noise or other effects such as the constructive interference of multiple diabatic crossings, and at constant adiabatic evolution rate, is proportional to the inverse minimum gap squared. In this article, we show that for a large class of problem Hamiltonians, one can improve in the runtime of a quantum annealer (relative to minimum gap squared scaling) by adding local oscillating fields, which are not amenable to efficient classical simulation. For many hard N-qubit problems these fields can act to reduce the difficulty exponent of the problem, providing a polynomial runtime improvement. We argue that the resulting speedup should be robust against local qubit energy fluctuations, in contrast to variable-rate annealing, which is not. We consider two classes of hard first order transition (the Grover problem and N-spin transitions between polarized semiclassical states), and provide analytical arguments and numerical evidence to support our claims. The oscillating fields themselves can be added through current flux-qubit based hardware by simply incorporating oscillating electric and magnetic lines, and could thus be implemented immediately.