Instability in the quantum restart problem

Ruoyu Yin, Eli Barkai

Published 2023-01-15Version 1

We study optimal restart times for the quantum first hitting time problem. Using a monitored one-dimensional lattice quantum walk with restarts, we find an instability absent in the corresponding classical problem. This instability implies that a small change in parameters can lead to a rather large change of the optimal restart time. We show that the optimal restart time versus a control parameter, exhibits sets of staircases and plunges. The plunges, are due to the mentioned instability, which in turn is related to the quantum oscillation of the first hitting time probability, in the absence of restarts. Furthermore, we prove that there are only two patterns of the staircase structures, dependent on the parity of the distance between the target and source in units of lattice constant.