Stroboscopic quantum walks

TL;DR

This paper introduces stroboscopic quantum walks, a new framework linking quantum walks with quantum resonances observed in chaotic systems, through numerical simulations.

Contribution

It presents the concept of stroboscopic quantum walks by reformulating discrete quantum walks as periodic perturbations, connecting them to quantum resonances in nonlinear quantum systems.

Findings

Established the link between stroboscopic walks and quantum resonances

Numerical simulations demonstrate the connection with quantum chaos systems

Recast quantum walks in the context of periodic perturbations

Abstract

Discrete time (coined) quantum walks are produced by the repeated application of a constant unitary transformation to a quantum system. By recasting these walks into the setting of periodic perturbations to an otherwise freely evolving system we introduce the concept of a stroboscopic quantum walk. Through numerical simulation, we establish the link between families of stroboscopic walks and quantum resonances. These are observed in the nonlinear systems of quantum chaos theory such as the delta-kicked rotator or the delta-kicked accelerator.