Discrete-time quantum walk with feed-forward quantum coin

TL;DR

This paper introduces a generalized discrete-time quantum walk with a feed-forward quantum coin, revealing anomalous slow diffusion behavior distinct from the ballistic transport of traditional models.

Contribution

The paper proposes a novel feed-forward quantum coin model for discrete-time quantum walks, linking it to anomalous diffusion described by the porous-medium equation.

Findings

The model exhibits anomalous slow diffusion.

Contrasts with conventional quantum walk showing ballistic transport.

Abstract

Constructing a discrete model like a cellular automaton is a powerful method for understanding various dynamical systems. However, the relationship between the discrete model and its continuous analogue is, in general, nontrivial. As a quantum-mechanical cellular automaton, a discrete-time quantum walk is defined to include various quantum dynamical behavior. Here we generalize a discrete-time quantum walk on a line into the feed-forward quantum coin model, which depends on the coin state of the previous step. We show that our proposed model has an anomalous slow diffusion characterized by the porous-medium equation, while the conventional discrete-time quantum walk model shows ballistic transport.