Enhancing the spreading of quantum walks on star graphs by additional bonds

TL;DR

This paper investigates how adding or removing bonds in star and complete graphs can significantly enhance the spreading of continuous-time quantum walks, outperforming classical random walks by modifying network eigenvalues.

Contribution

It demonstrates that disorder-induced modifications to network topology can optimize quantum walk spreading, a novel insight into quantum network dynamics.

Findings

Spreading is slow on both star and complete graphs without modifications.

Adding bonds to star graphs or removing bonds from complete graphs enhances quantum walk spreading.

Maximum spreading occurs midway between star and complete graph topologies.

Abstract

We study the dynamics of continuous-time quantum walks (CTQW) on networks with highly degenerate eigenvalue spectra of the corresponding connectivity matrices. In particular, we consider the two cases of a star graph and of a complete graph, both having one highly degenerate eigenvalue, while displaying different topologies. While the CTQW spreading over the network - in terms of the average probability to return or to stay at an initially excited node - is in both cases very slow, also when compared to the corresponding classical continuous-time random walk (CTRW), we show how the spreading is enhanced by randomly adding bonds to the star graph or removing bonds from the complete graph. Then, the spreading of the excitations may become very fast, even outperforming the corresponding CTRW. Our numerical results suggest that the maximal spreading is reached halfway between the star graph and the complete graph. We further show how this disorder-enhanced spreading is related to the networks' eigenvalues.