  We show how state-dependent optical potentials can be used to trap a pair of
molecules in different internal states at a separation much smaller than the
wavelength of the trapping light. This close spacing greatly enhances the
dipole-dipole interaction and we show how it can be used to implement two-qubit
gates between molecules that are 100 times faster than existing protocols and
than rotational coherence times already demonstrated. We analyze complications
due to hyperfine structure, tensor light shifts, photon scattering and
collisional loss, and conclude that none is a barrier to implementing the
scheme.
