Discrete-time quantum walks generated by aperiodic fractal sequence of space coin operators

TL;DR

This paper investigates how aperiodic fractal sequences of coin operators influence the dynamics of one-dimensional discrete-time quantum walks, revealing sensitive quantum effects and peculiar wave function behaviors.

Contribution

It introduces a two-coin model based on fractal Cantor set rules, exploring inhomogeneities' effects on quantum walk properties and entanglement entropy.

Findings

Wave function exhibits peculiar properties due to fractal inhomogeneities

Entanglement entropy is highly sensitive to subtle quantum effects

Probability distribution and variance are affected by the aperiodic coin sequence

Abstract

Properties of one dimensional discrete-time quantum walks are sensitive to the presence of inhomogeneities in the substrate, which can be generated by defining position dependent coin operators. Deterministic aperiodic sequences of two or more symbols provide ideal environments where these properties can be explored in a controlled way. This work discusses a two-coin model resulting from the construction rules that lead to the usual fractal Cantor set. Although the fraction of the less frequent coin $\rightarrow 0$ as the size of the chain is increased, it leaves peculiar properties in the walker dynamics. They are characterized by the wave function, from which results for the probability distribution and its variance, as well as the entanglement entropy were obtained. A number of results for different choices of the two coins are presented. The entanglement entropy has shown to be very sensitive to uncover subtle quantum effects present in the model.