  We have studied theoretically the possibility of ultra-fast manipulation of a
single electron spin in 2D semiconductor quantum dots, by means of
high-frequency time-dependent electric fields. The electron spin degree of
freedom is excited through spin-orbit coupling, and the procedure may be
enhanced by the presence of a static magnetic field. We use quantum optimal
control theory to tailor the temporal profile of the electric field in order to
achieve the most effective manipulation. The scheme predicts significant
control over spin operations in times of the order of picoseconds -- an
ultrafast time scale that permits to avoid the effects of decoherence if this
scheme is to be used as a tool for quantum information processing.
