Restart Expedites Quantum Walk Hitting Times

R. Yin, E. Barkai

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

Classical first-passage times under restart are used in a wide variety of models, yet the quantum version of the problem still misses key concepts. We study the quantum hitting time with restart using a monitored quantum walk. The restart strategy eliminates the problem of dark states, i.e., cases where the particle evades detection, while maintaining the ballistic propagation which is important for a fast search. We find profound effects of quantum oscillations on the restart problem, namely, a type of instability of the mean detection time, and optimal restart times that form staircases, with sudden drops as the rate of sampling is modified. In the absence of restart and in the Zeno limit, the detection of the walker is not possible, and we examine how restart overcomes this well-known problem, showing that the optimal restart time becomes insensitive to the sampling period.

Original languageEnglish
Article number050802
JournalPhysical Review Letters
Volume130
Issue number5
DOIs
StatePublished - 3 Feb 2023

Bibliographical note

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© 2023 American Physical Society.

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