Fluctuation guided search in quantum annealing

Quantum annealing has great promise in leveraging quantum mechanics to solve combinatorial optimisation problems. However, to realize this promise to it's fullest extent we must appropriately leverage the underlying physics. In this spirit, I examine how the well known tendency of quantum annealers to seek solutions where more quantum fluctuations are allowed can be used to trade off optimality of the solution to a synthetic problem for the ability to have a more flexible solution, where some variables can be changed at little or no cost. I demonstrate this tradeoff experimentally using the reverse annealing feature a D-Wave Systems QPU for both problems composed of all binary variables, and those containing some higher-than-binary discrete variables. I further demonstrate how local controls on the qubits can be used to control the levels of fluctuations and guide the search. I discuss places where leveraging this tradeoff could be practically important, namely in hybrid algorithms where some penalties cannot be directly implemented on the annealer and provide some proof-of-concept evidence of how these algorithms could work.