A theoretical analysis of the power of pausing

Recent experimental results have shown that adding a pause during quantum annealing can significantly improve the success probability for certain hard optimization problems. An optimal pausing position, where the maximum performance improvement compared to the unpaused case is achieved, has also been observed. In this work, we present a theoretical analysis that explains these observations. We identify the key features of examples known empirically to benefit from pausing. Using these features as building blocks, we then construct a toy model with a simple analytic structure. Using this model, we derive, in an open quantum system setting, a set of sufficient conditions for which an optimal pausing position exists.