High probability state transfer in spin-1/2 chains: Analytical and numerical approaches

TL;DR

This paper develops analytical and numerical methods to analyze high-probability quantum state transfer in spin-1/2 chains, comparing different Hamiltonian models and interaction ranges to optimize transfer efficiency.

Contribution

It introduces exact diagonalization techniques for specific spin chain configurations and compares transfer times across various Hamiltonians and interaction types.

Findings

End-to-end state transfer times vary with chain configuration and Hamiltonian.

Numerical simulations confirm analytical predictions for chain dynamics.

Different interaction models influence transfer efficiency and speed.

Abstract

This article is devoted to the development of analytical and numerical approaches to the problem of the end-to-end quantum state transfer along the spin-1/2 chain using two methods: (a) a homogeneous spin chain with week end bonds and equal Larmor frequencies and (b) a homogeneous spin chain with end Larmor frequencies different from inner ones. A tridiagonal matrix representation of the XY Hamiltonian with nearest neighbor interactions relevant to the quantum state transfer is exactly diagonalized for a combination of the above two methods. In order to take into account interactions of the remote spins we used numerical simulations of the quantum state transfer in ten-node chains. We compare the state transfer times obtained using the two above methods for chains governed by the both XY and XXZ Hamiltonians and using both nearest neighbor and all node interactions.