Discretization of continuous-time quantum walks via the staggered model with Hamiltonians

TL;DR

This paper explores the relationship between continuous-time and discrete-time quantum walks using the staggered model with Hamiltonians, revealing new phenomena and connections in quantum walk behaviors.

Contribution

It establishes a close connection between continuous-time and staggered discrete-time quantum walks and provides examples of phenomena unique to the staggered model.

Findings

Connection between continuous-time and staggered quantum walks

Examples of perfect state transfer in the staggered model

Instances of uniform mixing not reproducible by continuous-time walks

Abstract

We characterize a close connection between the continuous-time quantum-walk model and a discrete-time quantum-walk version, based on the staggered model with Hamiltonians in a class of Cayley graphs, which can be considered as a discretization of continuous-time quantum walks. This connection provides examples of perfect state transfer and instantaneous uniform mixing in the staggered model. On the other hand, we provide some more examples of perfect state transfer and instantaneous uniform mixing in the staggered model that cannot be reproduced by the continuous-time model.