# Non-Abelian holonomic transformation in the presence of classical noise

## TL;DR

This paper explores how classical noise affects the fidelity of non-Abelian holonomic quantum gates, identifying noise sensitivities and optimal control parameter regions for high-speed quantum computing.

## Contribution

It provides a detailed analysis of noise impacts on non-Abelian holonomic gates and identifies 'sweet spots' for robust quantum gate implementation.

## Key findings

- Nonadiabatic gates are more sensitive to noise in the envelop function than control phases.
- Identification of 'sweet spots' in control parameters for noise resilience.
- Extension of analysis to two-qubit quantum gates.

## Abstract

It is proposed that high-speed universal quantum gates can be realized by using non-Abelian holonomic transformation. A cyclic evolution path which brings the system periodically back to a degenerate qubit subspace is crucial to holonomic quantum computing. The cyclic nature and the resulting gate operations are fully dependent on the precise control of driving parameters, such as the modulated envelop function of Rabi frequency and the control phases. We investigate the effects of fluctuations in these driving parameters on the transformation fidelity of a universal set of single-qubit quantum gates. We compare the damage effects from different noise sources and determine the "sweet spots" in the driving parameter space. The nonadiabatic non-Abelian quantum gate is found to be more susceptible to classical noises on the envelop function than that on the control phases. We also extend our study to a two-qubit quantum gate.