  We use quantum optimal control theory algorithms to design external electric
fields that drive the coupled spin and orbital dynamics of an electron in a
double quantum dot, subject to the spin-orbit interaction and Zeeman magnetic
fields. We obtain time-profiles of multi-frequency electric pulses which
increase the rate of spin-flip transitions by several orders of magnitude in
comparison with monochromatic fields, where the spin Rabi oscillations were
predicted to be very slow. This precise, with the accuracy higher than
$10^{-4}$, and fast, at the timescale of the order of 0.1 ns, simultaneous
control of the electron spin orientation and position is achieved while keeping
the electron in the four lowest tunneling- and Zeeman-split levels through the
duration of the pulse, facilitating high fidelity and suggesting useful
applications in spintronics and quantum information devices.
