Driving quantum walk spreading with the coin operator

TL;DR

This paper explores how a time-dependent coin operator in quantum walks can control the spread of the wave function, enabling various asymptotic behaviors such as ballistic and localized spreading.

Contribution

It introduces a generalized framework for discrete quantum walks with a time-dependent coin, establishing analytical relations for long-term spreading behaviors.

Findings

Analytical relation between coin operator and wave-function spreadings

Ability to engineer desired asymptotic behaviors through coin sequence

Demonstration of diverse spreading regimes including localization

Abstract

We generalize the discrete quantum walk on the line using a time dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time sequence allows to obtain a variety of predetermined asymptotic wave-function spreadings: ballistic, sub-ballistic, diffusive, sub-diffusive and localized.