Quantum routing in planar graph using perfect state transfer

TL;DR

This paper proposes a novel quantum routing method in planar graphs using perfect state transfer, enabling simultaneous quantum communication between multiple nodes, surpassing classical routing capabilities.

Contribution

It introduces a new static routing schema leveraging hypercube graph properties for efficient quantum communication in planar networks.

Findings

Multiple examples of planar graphs supporting quantum routing.

Quantum routing enables simultaneous communication where classical routing fails.

The approach utilizes hypercube graph combinatorics for network design.

Abstract

In this article, we consider a spin-spin interaction network governed by $XX + YY$ Hamiltonian. The vertices and edges of the network represent the spin objects and their interactions, respectively. We take a privilege to switch on or off any interaction, that assists us to perform multiple perfect state transfers in a graph simultaneously. We also build up a salable network allowing quantum communication between two arbitrary vertices. Later we utilize the combinatorial characteristics of hypercube graphs to propose a static routing schema to communicate simultaneously between a set of senders and a set of receivers in a planar network. Our construction is new and significantly powerful. We elaborate multiple examples of planar graphs supporting quantum routing where classical routing is not possible.