  We examine the influence of nuclear spins on the performance of optically
induced rotations of single electron spins in semiconductor quantum dots. We
consider Raman type optical transitions between electron spin states and take
into account the additional effect of the Overhauser field. We calculate
average fidelities of rotations around characteristic axes in the presence of
nuclear spins analytically with perturbation theory up to second order in the
Overhauser field. Moreover, we calculate the fidelity using numerical averaging
over the nuclear field distribution, including arbitrary orders of the
hyperfine interaction.
