Switching and partially switching the hypercube while maintaining perfect state transfer

TL;DR

This paper explores how perturbing the hypercube graph can preserve perfect state transfer properties, which are crucial for quantum information transfer, even under certain structural modifications.

Contribution

It introduces methods for switching and partially switching hypercube graphs while maintaining perfect state transfer and related properties.

Findings

PST is preserved under specific graph perturbations.

Sensitivity to readout time errors remains unchanged.

Perturbations can be physically motivated or necessary.

Abstract

A graph is said to exhibit perfect state transfer (PST) if one of its corresponding Hamiltonian matrices, which are based on the vertex-edge structure of the graph, gives rise to PST in a quantum information-theoretic context, namely with respect to inter-qubit interactions of a quantum system. We perform various perturbations to the hypercube graph---a graph that is known to exhibit PST---to create graphs that maintain many of the same properties of the hypercube, including PST as well as the distance for which PST occurs. We show that the sensitivity with respect to readout time errors remains unaffected for the vertices involved in PST. We give motivation for when these perturbations may be physically desirable or even necessary.