Two-walker discrete-time quantum walks on the line with percolation

TL;DR

This paper investigates how two non-interacting quantum walkers behave on a line with missing links, revealing how symmetry affects outcomes and exploring the potential for estimating link failures despite noise.

Contribution

It analyzes the impact of lattice imperfections on two-particle quantum walks, highlighting the role of particle symmetry and proposing methods to estimate broken links.

Findings

Symmetry under particle exchange influences walk outcomes.

Bunching phenomena do not reliably indicate indistinguishability.

Multiple walkers can help estimate link failure probabilities.

Abstract

One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles performing a quantum walk on the line when the possibility of lattice imperfections, in the form of missing links, is considered. We investigate two regimes, statical and dynamical percolation, that correspond to different time scales for the imperfections evolution with respect to the quantum-walk one. By studying the qualitative behaviour of three two-particle quantities for different probabilities of having missing bonds, we argue that the chosen symmetry under particle-exchange of the input state strongly affects the output of the walk, even in noisy and highly non-ideal regimes. We provide evidence against the possibility of gathering information about the walkers indistinguishability from the observation of bunching phenomena in the output distribution, in all those situations that require a comparison between averaged quantities. Although the spread of the walk is not substantially changed by the addition of a second particle, we show that the presence of multiple walkers can be beneficial for a procedure to estimate the probability of having a broken link.