  We theoretically investigate electron spin operations driven by applied
electric fields in a semiconductor double quantum dot (DQD). Our model
describes a DQD formed in semiconductor nanowire with longitudinal potential
modulated by local gating. The eigenstates for two electron occupation,
including spin-orbit interaction, are calculated and then used to construct a
model for the charge transport cycle in the DQD taking into account the spatial
dependence and spin mixing of states. The dynamics of the system is simulated
aiming at implementing protocols for qubit operations, that is, controlled
transitions between the singlet and triplet states. In order to obtain fast
spin manipulation, the dynamics is carried out taking advantage of the
anticrossings of energy levels introduced by the spin-orbit and interdot
couplings. The theory of optimal quantum control is invoked to find the
specific electric-field driving that performs qubit logical operations. We
demonstrate that it is possible to perform within high efficiency a universal
set of quantum gates $\{$CNOT, H$\otimes$I, I$\otimes$H, T$\otimes$I, and
T$\otimes$I$\}$, where H is the Hadamard gate, T is the $\pi/8$ gate, and I is
the identity, even in the presence of a fast charge transport cycle and charge
noise effects.
