Perfect state transfer over distance-regular spin networks

TL;DR

This paper presents a spectral and algebraic combinatorics-based method for designing spin Hamiltonians on distance-regular graphs to achieve perfect quantum state transfer without dynamic control.

Contribution

It introduces a novel approach using stratification and Bose-Mesner algebra to determine coupling constants for perfect state transfer in distance-regular spin networks.

Findings

Method successfully applied to cycle networks with even vertices

Effective for hypercube networks and other distance-regular graphs

Provides explicit parameters for perfect state transfer

Abstract

By considering distance-regular graphs as spin networks, first we introduce some particular spin Hamiltonians which are extended version of those of Refs.\cite{8,9''}. Then, by using spectral analysis techniques and algebraic combinatoric structure of distance-regular graphs such as stratification introduced in \cite{obata, js} and Bose-Mesner algebra, we give a method for finding a set of coupling constants in the Hamiltonians so that a particular state initially encoded on one site of a network will evolve freely to the opposite site without any dynamical controls, i.e., we show that how to derive the parameters of the system so that perfect state transfer (PST) can be achieved. As examples, the cycle networks with even number of vertices and $d$-dimensional hypercube networks are considered in details and the method is applied for some important distance-regular networks in appendix.