Assessing the performance of quantum annealing with nonlinear driving

Current generation quantum annealers have already proven to be successful problem-solvers. Yet, quantum annealing is still very much in its infancy, with suboptimal applicability. For instance, to date it is still an open question which annealing protocol causes the fewest diabatic excitations for a given eigenspectrum, and even whether there is a universally optimal strategy. Therefore, in this paper, we report analytical and numerical studies of the diabatic excitations arising from nonlinear protocols applied to the transverse field Ising chain, the exactly solvable model that serves as a quantum annealing playground. Our analysis focuses on several driving schemes that inhibit or facilitate the dynamic phases discussed in a previous work. Rather remarkably, we find that the paradigmatic Kibble-Zurek behavior can be suppressed with ``pauses'' in the evolution, both for crossing and for stopping at the quantum critical point of the system.