  We analyze the optically driven dynamics of a qubit implemented on a
singlet-triplet subspace of two-electron states in a self-assembled quantum dot
molecule. We study two possible control schemes based on the coupling to an
excited (four-particle) state either by two spectrally separated laser pulses
or by a single spectrally broad pulse. We quantitatively characterize the
imperfections of the qubit operation resulting from non-adiabatic evolution and
from limited spectral selectivity in a real system, as compared to the ideal
adiabatic Raman transfer of occupation in the $\Lambda$-system. Next, we study
the effects of decoherence induced by the coupling to the phonons of the
surrounding crystal lattice and by radiative recombination. As a result, we are
able to identify the optimization trade-offs between different sources of
errors and indicate the most favorable conditions for quantum control of the
singlet-triplet qubit in the two optical control schemes.
