Variational diabatic annealing schedules with Landau-Zener-Stückelberg interference

In recent years there have been great advances in improving the coherence of quantum annealing hardware. However, exponentially closing spectral gaps are a major obstacle to solving computational problems with adiabatic quantum annealers. In a recent paper, variational diabatic annealing schedules were investigated and an exponential speed-up over the adiabatic model was observed. Here, we propose a theoretical explanation for this observation. We identify the interference between amplitudes of different energy levels after consecutive Landau-Zener crossings, also known as Landau-Zener-Stückelberg (LZS) interference, as the basic mechanism of the observed speed-up. Based on this observation, we define a class of variational diabatic annealing schedules that drastically reduces the search space for the optimal parameters. We prove that if an efficient, optimal annealing schedule is in this schedule class, it can be found efficiently, which also allows us to state conditions when variational schedules provide an exponential speed-up over adiabatic annealing, even considering the optimization cost. We analyze the impact of decoherence and show that it impairs the effectiveness of the variational schedules, thus showing the utility of coherence for analogue quantum computation.