  We propose purely electric manipulation of spin qubits by means of the
spin-orbit interaction (SOI) {\it without magnetic field or magnets} in a
double-quantum dot. All the unitary transformations can be constructed by the
time-dependent Dzyaloshinsky-Moriya interaction between the two spins, which
arises from the Rashba SOI modulated by electric field. As a few
demonstrations, we study both analytically and numerically the three
operations, i.e., (A) the spin initialization, (B) the two-spin rotation in the
opposite directions, and (C) the two-spin rotation in the same direction. The
effects of the relaxation and the feasibility of this proposal are also
discussed.
