Fidelity of optically induced single-spin rotations in semiconductor quantum dots in the presence of nuclear spins

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.