We study the two-qubit controlled-not gate operating on qubits encoded in thespin state of a pair of electrons in a double quantum dot. We assume that theelectrons can tunnel between the two quantum dots encoding a single qubit,while tunneling between the quantum dots that belong to different qubits isforbidden. Therefore, the two qubits interact exclusively through the directCoulomb repulsion of the electrons. We find that entangling two-qubit gates canbe performed by the electrical biasing of quantum dots and/or tuning of thetunneling matrix elements between the quantum dots within the qubits. Theentangling interaction can be controlled by tuning the bias through theresonance between the singly-occupied and doubly-occupied singlet ground statesof a double quantum dot.
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