Exploiting boundary states of imperfect spin chains for high-fidelity state transfer

TL;DR

This paper presents a method to achieve high-fidelity quantum state transfer in imperfect spin chains by combining modulated couplings and boundary states, with an explicit algorithm and a user interface for design.

Contribution

It introduces a novel combined approach using boundary states and modulated couplings, with an exact algorithm and software tool for designing robust spin chains.

Findings

High-fidelity state transfer achieved despite static imperfections.

Explicit construction of modulated couplings from orthogonal polynomial algorithms.

Development of spinGUIn software for spin chain design.

Abstract

We study transfer of a quantum state through XX spin chains with static imperfections. We combine the two standard approaches for state transfer based on (i) modulated couplings between neighboring spins throughout the spin chain and (ii) weak coupling of the outermost spins to an unmodulated spin chain. The combined approach allows us to design spin chains with modulated couplings and localized boundary states, permitting high-fidelity state transfer in the presence of random static imperfections of the couplings. The modulated couplings are explicitly obtained from an exact algorithm using the close relation between tridiagonal matrices and orthogonal polynomials [Linear Algebr. Appl. 21, 245 (1978)]. The implemented algorithm and a graphical user interface for constructing spin chains with boundary states (spinGUIn) are provided as Supplemental Material.