Effect of Randomness on Quantum Data Buses of Heisenberg Spin Chains

TL;DR

This paper investigates how static randomness in exchange couplings and magnetic fields affects the fidelity and properties of a Heisenberg spin chain used as a quantum data bus, revealing effects on energy levels, eigenstates, and effective couplings.

Contribution

It provides a detailed analysis of the impact of static disorder on the quantum data bus performance and ground state properties in Heisenberg spin chains, highlighting differences caused by exchange randomness and magnetic fields.

Findings

Non-uniform exchange couplings preserve isotropy but vary local energy levels.

Random magnetic fields induce avoided level crossings and anisotropic couplings.

Ground state magnetic moment can misalign with the average magnetic field.

Abstract

A strongly coupled spin chain can mediate long-distance effective couplings or entanglement between remote qubits, and can be used as a quantum data bus. We study how the fidelity of a spin-1/2 Heisenberg chain as a spin bus is affected by static random exchange couplings and magnetic fields. We find that, while non-uniform exchange couplings preserve the isotropy of the qubit effective couplings, they cause the energy levels, the eigenstates, and the magnitude of the couplings to vary locally. On the other hand, random local magnetic fields lead to an avoided level crossing for the bus ground state manifold, and cause the effective qubit couplings to be anisotropic. Interestingly, the total magnetic moment of the ground state of an odd-size bus may not be parallel to the average magnetic field. Its alignment depends on both the direction of the average field and the field distribution, in contrast with the ground state of a single spin which always aligns with the applied magnetic field to minimize the Zeeman energy. Lastly, we calculate sensitivities of the spin bus to such local variations, which are potentially useful for evaluating decoherence when dynamical fluctuations in the exchange coupling or magnetic field are considered.