Quantum Walk on the Line through Potential Barriers

TL;DR

This paper demonstrates that quantum walks maintain their ballistic dispersion even when tunneling through potential barriers, with only the hopping rate affected, which aids in experimental error detection.

Contribution

It provides an explicit calculation showing that potential barriers do not destroy quantum walk dispersion, offering a method to detect hopping errors in experiments.

Findings

Quantum walks retain their ballistic spread despite potential barriers.

Hopping errors can be detected and quantified through dispersion analysis.

The dispersion coefficient changes but the overall ballistic nature remains.

Abstract

Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the particle may need to tunnel through a potential barrier to hop, and a naive calculation suggests this could eliminate the ballistic transport. We show by explicit calculation, however, that such a loss does not occur. Rather, the $\Theta(t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.