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

TL;DR

This paper introduces a protocol for inducing full-state revivals in quantum walks on infinite lattices using coin interventions, with a new recurrence witness based on the Pólya number.

Contribution

The work presents a novel protocol for on-demand revivals in quantum walks and characterizes walks that support this, advancing control over quantum recurrence phenomena.

Findings

Protocol enables full-state revivals with coin interventions

Characterization of walks supporting revival protocol

Modified Pólya number as a revival witness

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.