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We propose purely electric manipulation of spin qubits by means of thespin-orbit interaction (SOI) {\it without magnetic field or magnets} in adouble-quantum dot. All the unitary transformations can be constructed by thetime-dependent Dzyaloshinsky-Moriya interaction between the two spins, whicharises from the Rashba SOI modulated by electric field. As a fewdemonstrations, we study both analytically and numerically the threeoperations, i.e., (A) the spin initialization, (B) the two-spin rotation in theopposite directions, and (C) the two-spin rotation in the same direction. Theeffects of the relaxation and the feasibility of this proposal are alsodiscussed.

Manipulation of two spin qubits in a double quantum dot using an electric field