Swift chiral quantum walks

TL;DR

This paper demonstrates that adding complex phases to the edges of a graph can transform sedentary continuous-time quantum walks into swift chiral quantum walks, significantly reducing return probabilities and expanding the understanding of chiral CTQW capabilities.

Contribution

It introduces a method to achieve swift chiral quantum walks by adding complex phases, and provides a no-go theorem for Laplacian-type chiral CTQWs, advancing the theoretical understanding of quantum walk dynamics.

Findings

Adding complex phases enables swift chiral quantum walks.

Laplacian-type swift chiral CTQWs are impossible (no-go theorem).

Characterization of tasks achievable with chiral CTQWs.

Abstract

A continuous-time quantum walk (CTQW) is sedentary if the return probability in the starting vertex is close to one at all times. Recent results imply that, when starting from a maximal degree vertex, the CTQW dynamics generated by the Laplacian and adjacency matrices are typically sedentary. In this paper, we show that the addition of appropriate complex phases to the edges of the graph, defining a chiral CTQW, can cure sedentarity and lead to swift chiral quantum walks of the adjacency type, which bring the returning probability to zero in the shortest time possible. We also provide a no-go theorem for swift chiral CTQWs of the Laplacian type. Our results provide one of the first, general characterization of tasks that can and cannot be achieved with chiral CTQWs.