Reexamination of decoherence in quantum walks on the hypercube

TL;DR

This paper revisits decoherence effects on quantum walks on the hypercube, introducing a new model inspired by quantum state transfer, with a perturbative solution showing a dimension-independent lower bound on hitting probability.

Contribution

It presents a novel decoherence model that breaks tensor-product structure and provides a perturbative analysis with new insights into hitting probabilities.

Findings

Lower bound on hitting probability independent of hypercube dimension

New decoherence model inspired by quantum state transfer

Perturbative solution for non-tensor-product dynamics

Abstract

The effect of decoherence on the continuous-time quantum walk on the hypercube is revisited. Previously, an exact solution was found for a decoherence model that preserved the effective tensor-product form of the dynamics. Here a new model is presented, inspired by perfect quantum state transfer in qubit networks. A perturbative solution is found for the dynamics of this model which is not of a tensor-product form. In contrast to previous results, the hitting probability has a lower bound that is independent of the hypercube dimension.