  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.
