  We study single-qubit gates performed via stimulated Raman adiabatic passage
(STIRAP) on a spin qubit implemented in a quantum dot system in the presence of
phonons. We analyze the interplay of various kinds of errors resulting from the
carrier-phonon interaction as well as from quantum jumps related to
nonadiabaticity and calculate the fidelity as a function of the pulse
parameters. We give quantitative estimates for an InAs/GaAs system and identify
the parameter values for which the error is considerably minimized, even to
values below $10^{-4}$ per operation.
