Quantum Networks on Cubelike Graphs

TL;DR

This paper investigates quantum networks modeled by cubelike graphs, providing conditions for perfect state transfer, thereby extending previous results on hypercube and related graph structures.

Contribution

It generalizes existing conditions for perfect state transfer to a broad class of cubelike graphs, enhancing understanding of quantum network capabilities.

Findings

Derived new conditions for perfect state transfer in cubelike graphs.

Extended previous results from hypercubes to more general cubelike structures.

Provided theoretical framework for designing quantum networks with reliable state transfer.

Abstract

Cubelike graphs are the Cayley graphs of the elementary abelian group (Z_2)^n (e.g., the hypercube is a cubelike graph). We give conditions for perfect state transfer between two particles in quantum networks modeled by a large class of cubelike graphs. This generalizes results of Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)] and Facer et al. [Phys. Rev. A 92, 187902 (2008)].