Comparison of the sensitivity to systematic errors between non-adiabatic non-Abelian geometric gates and their dynamical counterparts

TL;DR

This paper compares how non-adiabatic non-Abelian geometric gates and dynamical gates respond to systematic control errors, showing geometric gates are more sensitive and less reliable under such errors.

Contribution

It provides a theoretical comparison of systematic error sensitivities between geometric and dynamical quantum gates, highlighting the impact of control parameter errors.

Findings

Geometric gates are more affected by Rabi frequency errors.

Systematic errors cause non-unitary transformations in geometric gates.

Dynamical gates exhibit higher robustness against systematic errors.

Abstract

We investigate the effects of systematic errors of the control parameters on single-qubit gates based on non-adiabatic non-Abelian geometric holonomies and those relying on purely dynamical evolution. It is explicitly shown that the systematic error in the Rabi frequency of the control fields affects these two kinds of gates in different ways. In the presence of this systematic error, the transformation produced by the non-adiabatic non-Abelian geometric gate is not unitary in the computational space, and the resulting gate infidelity is larger than that with the dynamical method. Our results provide a theoretical basis for choosing a suitable method for implementing elementary quantum gates in physical systems, where the systematic noises are the dominant noise source.