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 paper, 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 admit such a protocol. Moreover, we modify the quantity known as the Pólya 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.
|Journal||Physical Review A|
|State||Published - Mar 2022|
Bibliographical noteFunding Information:
We wish to thank C. Cedzich and two anonymous referees for helpful comments. M.N.J. was supported by the President Scholarship and the BINA Scholarship at Bar-Ilan University. E.C. acknowledges support from the Israel Innovation Authority under Projects No. 70002 and No. 73795 from the Quantum Science and Technology Program of the Israeli Council of Higher Education, from the Pazy Foundation, and from the Ministry of Science and Technology. This work was supported by Grant No. FQXi-RFP-CPW-2006 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor advised fund of Silicon Valley Community Foundation.
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