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arXiv · 2201.03307

Induced on-demand revival in coined quantum walks on infinite $d$-dimensional lattices

Mahesh N. Jayakody·Ismael L. Paiva·Asiri Nanayakkara·Eliahu Cohen
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Abstract

The study of recurrences and revivals in quantum systems has attracted a great deal of interest because of its importance in the control of quantum systems and its potential use in developing new technologies. In this work, we introduce a protocol to induce full-state revivals in a huge class of quantum walks on a $d$-dimensional lattice governed by a $c$-dimensional coin system. The protocol requires two repeated interventions in the coin degree of freedom. We also present a characterization of the walks that admits such a protocol. Moreover, we modify the quantity known as P\'olya number, typically used in the study of recurrences in classical random walks and quantum walks, to create a witness of the first revival of the walk.

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Mahesh N. Jayakody, Ismael L. Paiva, Asiri Nanayakkara, Eliahu Cohen. 2022-01-10. Induced on-demand revival in coined quantum walks on infinite $d$-dimensional lattices. https://doi.org/10.1103/physreva.105.032413

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