  Quantum operations with a charge solid-state qubit whose logical states are
formed by two spatially separated localized states of an electron in the
double-dot structure are studied theoretically. We show that it is possible to
perform various one-qubit rotations making use of the microwave pulses tuned to
the resonances between the localized states and the excited state delocalized
over the nanostructure. Explicit analytic expression for the time-dependent
electron state vector is derived, and the appropriate pulse parameters are
determined.
