Effects of noise on fidelity in spin-orbit qubit transformations

TL;DR

This paper investigates how white noise affects the fidelity of non-adiabatic holonomic spin-qubit transformations in a time-dependent harmonic trap with Rashba interaction, providing exact results and optimization strategies.

Contribution

It offers an exact analytical framework for analyzing noise effects on spin transformations and introduces methods to optimize fidelity in spin-qubit operations.

Findings

Exact spin rotation angle derivation under noise

Fidelity probability distributions for cyclic transformations

Strategies for optimizing final fidelity

Abstract

We analyse non-adiabatic non-Abelian holonomic transformations of spin-qubits confined to a linear time dependent harmonic trap with time dependent Rashba interaction. For this system exact results can be derived for spin rotation angle which also enables exact treatment of white gate-noise effects. We concentrate in particular on the reliability of cyclic transformations quantified by fidelity defined by the probability that the qubit after one full cycle remains in the ground-state energy manifold. The formalism allows exact analysis of spin transformations that optimise final fidelity. Various examples of time dependent fidelity probability distributions are presented and discussed.