  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.
