Fast and efficient long-distance quantum state transfer in long-range spin-$\frac{1}{2}$ models

TL;DR

This paper demonstrates a method for fast, high-fidelity quantum state transfer in long spin chains using minimal engineering and exploiting the dispersion relation, with potential applications in quantum communication.

Contribution

It introduces a minimal engineering scheme for quantum state transfer in long-range spin chains, achieving over 99% fidelity with linear time scaling.

Findings

Average transfer fidelity exceeds 99%

Transfer time scales linearly with chain length

Method applies to arbitrary next-nearest neighbor couplings

Abstract

Quantum state transfer is investigated beyond the nearest-neighbour coupling scheme in long spin-$\frac{1}{2}$ linear chains. Exploiting the properties of the next-nearest neighbour Hamiltonian's dispersion relation, it is shown that with minimal engineering, i.e., an on-site magnetic field on the two end sites and only a few symmetrically-modified end inter-site couplings, an average transfer fidelity above $99\%$ can be achieved. To leading order, the required time scales linearly with the length of the chain. Such a fast, high-quality quantum state transfer is based on the ballistic propagation of the wave packet centred in the linear region of the dispersion relation by means of the on-site magnetic field. At the same time, the wave packet width, modulated by the inter-site couplings at the chain ends, whose values are found via a carefully designed genetic algorithm, is constrained mostly in the linear region of the dispersion relation. Our coupling scheme is shown to hold for arbitrary values of the next-nearest inter-site coupling and can be straightforwardly applied to longer range coupling schemes.