Percolation assisted excitation transport in discrete-time quantum walks

TL;DR

This paper investigates how percolation can enhance excitation transport in discrete-time quantum walks on a ring, showing that dynamical percolations can eliminate trapping effects and improve transport efficiency.

Contribution

It demonstrates that dynamical percolations in lazy quantum walks can overcome trapping, leading to efficient excitation transport in symmetric ring graphs.

Findings

Exponential decay of survival probability in non-lazy quantum walks.

Trapping effects in lazy quantum walks reduce transport efficiency.

Dynamical percolations eliminate trapping, restoring high transport efficiency.

Abstract

Coherent transport of excitations along chains of coupled quantum systems represents an interesting problem with a number of applications ranging from quantum optics to solar cell technology. A convenient tool for studying such processes are quantum walks. They allow to determine in a quantitative way all the process features. We study the survival probability and the transport efficiency on a simple, highly symmetric graph represented by a ring. The propagation of excitation is modeled by a discrete-time (coined) quantum walk. For a two-state quantum walk, where the excitation (walker) has to leave its actual position to the neighboring sites, the survival probability decays exponentially and the transport efficiency is unity. The decay rate of the survival probability can be estimated using the leading eigenvalue of the evolution operator. However, if the excitation is allowed to stay at its present position, i.e. the propagation is modeled by a lazy quantum walk, then part of the wave-packet can be trapped in the vicinity of the origin and never reaches the sink. In such a case, the survival probability does not vanish and the excitation transport is not efficient. The dependency of the transport efficiency on the initial state is determined. Nevertheless, we show that for some lazy quantum walks dynamical percolations of the ring eliminate the trapping effect and efficient excitation transport can be achieved.