An energetic perspective on rapid quenches in quantum annealing

Well-developed theoretical tools exist to analyse how quantum dynamics can solve computational problems by varying Hamiltonians slowly (adiabatically). However, relatively few tools exist for the opposite limit of rapid quenches, used in quantum annealing and quantum walks. We develop a theoretical understanding and several practical tools for this regime. By analysing various energy expectation values, we show that monotonic quenches will yield a better result on average than random guessing. By characterising local dynamics, we identify cases where rapid quenches will lead to a substantially improved numerical scaling. We then use these tools to develop heuristics for choosing control parameters.

The talk is based on the work in Callison et al, NJP 21 123022 (2019) and Callison et al, arXiv:2007.11599 (2020). It offers an introduction to the framework of continuous-time quantum computing, and an explanation of where rapid quenches sit within it. Along with some useful examples, an outline of the theoretical understanding and tools we have developed are presented. Finally, some examples are shown to illustrate how to use the heuristic methods these tools provide; in particular, we show how to choose quantum walk hopping rates and rapid quench schedules.