Quantum walks with sequential aperiodic jumps

TL;DR

This paper investigates how binary aperiodic sequences like Fibonacci, Thue-Morse, and Rudin-Shapiro affect the dynamics of discrete-time quantum walks, revealing slowed wavepacket spreading and enhanced entanglement.

Contribution

It introduces a detailed analysis of quantum walks with aperiodic jumps, highlighting the influence of different sequences and coin operators on spreading behavior and entanglement.

Findings

Wavepacket spreading slows down with aperiodic jumps, with the exponent depending on the sequence.

Superdiffusive behavior is predominant, with sensitivity to the type of coin operator.

Aperiodicity affects measures like Shannon entropy, IPR, and kurtosis, and enhances spin-lattice entanglement.

Abstract

We analyze a set of discrete-time quantum walks for which the displacements on a chain follow binary aperiodic jumps according to three paradigmatic sequences: Fibonacci, Thue-Morse and Rudin-Shapiro. We use a generalized Hadamard coin $\widehat C_{H}$ as well as a generalized Fourier coin $\widehat C_{K}$. We verify the QW experiences a slowdown of the wavepacket spreading --- $\sigma ^2 (t) \sim t^\alpha $ --- by the aperiodic jumps whose exponent, $\alpha$, depends on the type of aperiodicity. Additional aperiodicity-induced effects also emerge, namely: (i) while the superdiffusive regime ($1<\alpha<2$) is predominant, $\alpha$ displays an unusual sensibility with the type of coin operator where the more pronounced differences emerge for the Rudin-Shapiro and random protocol; (ii) even though the angle $\theta$ of the coin operator is homogeneous in space and time, there is a nonmonotonic dependence of $\alpha$ with $\theta$. Fingerprints of the aperiodicity in the hoppings are also found when additional distributional measures such as Shannon entropy, IPR, Jensen-Shannon dissimilarity, and kurtosis are computed. Finally, we argue the spin-lattice entanglement is enhanced by aperiodic jumps.