  We suggest a combined atomic/molecular system for quantum computation, which
takes advantage of highly developed techniques to control atoms and recent
experimental progress in manipulation of ultracold molecules. We show that two
atoms of different species in a given site, {\it e.g.}, in an optical lattice,
could be used for qubit encoding, initialization and readout, with one atom
carrying the qubit, the other enabling a gate. In particular, we describe how a
two-qubit phase gate can be realized by transferring a pair of atoms into the
ground rovibrational state of a polar molecule with a large dipole moment, and
allowing two molecules to interact via their dipole-dipole interaction. We also
discuss how the reverse process of coherently transferring a molecule into a
pair of atoms could be used as a readout tool for molecular quantum computers.
