Full state revivals in higher dimensional quantum walks

TL;DR

This paper demonstrates how to construct coin operators for higher-dimensional quantum walks that achieve full state revivals with any desired period, enabling controlled periodic oscillations in quantum simulations.

Contribution

It introduces a method to design coin operators for quantum walks in any dimension that produce full state revivals with arbitrary periods, advancing quantum control techniques.

Findings

Constructed coin operators for any number of dimensions.

Achieved full state revivals with customizable periods.

Potential applications in quantum computation and simulation.

Abstract

Full state revivals in a quantum walk can be viewed as returning of the walker to the initial quantum state in a periodic fashion during the propagation of the walk. In this paper we show that for any given number of spatial dimensions, a coin operator can be constructed to generate a quantum walk having full revivals with any desired period. From the point of view of quantum computation and simulations, these coin operators can be useful in implementing quantum walks which oscillate between any two states with a finite periodicity.