Glued trees algorithm under phase damping

TL;DR

This paper investigates how phase damping decoherence affects the performance of the glued trees quantum walk algorithm, exploring whether weak decoherence can enhance the probability of reaching the target vertex.

Contribution

It provides a discrete time reformulation of the glued trees quantum walk and analyzes the impact of phase damping decoherence on its success probability.

Findings

Phase damping reduces the success probability of the quantum walk.

Weak decoherence may facilitate spreading across the graph.

Decoherence effects depend on damping strength and timing.

Abstract

We study the behaviour of the glued trees algorithm described by Childs et al. in [STOC `03, Proc. 35th ACM Symposium on Theory of Computing (2004) 59] under decoherence. We consider a discrete time reformulation of the continuous time quantum walk protocol and apply a phase damping channel to the coin state, investigating the effect of such a mechanism on the probability of the walker appearing on the target vertex of the graph. We pay particular attention to any potential advantage coming from the use of weak decoherence for the spreading of the walk across the glued trees graph.