  We study the two-qubit controlled-not gate operating on qubits encoded in the
spin state of a pair of electrons in a double quantum dot. We assume that the
electrons can tunnel between the two quantum dots encoding a single qubit,
while tunneling between the quantum dots that belong to different qubits is
forbidden. Therefore, the two qubits interact exclusively through the direct
Coulomb repulsion of the electrons. We find that entangling two-qubit gates can
be performed by the electrical biasing of quantum dots and/or tuning of the
tunneling matrix elements between the quantum dots within the qubits. The
entangling interaction can be controlled by tuning the bias through the
resonance between the singly-occupied and doubly-occupied singlet ground states
of a double quantum dot.
