  The interaction between the electric dipole moment of a trapped molecular ion
and the configuration of the confined Coulomb crystal couples the orientation
of the molecule to its motion. We consider the practical feasibility of
harnessing this interaction to initialize, process, and read out quantum
information encoded in molecular ion qubits without optically illuminating the
molecules. We present two schemes wherein a molecular ion can be entangled with
a co-trapped atomic ion qubit, providing, among other things, a means for
molecular state preparation and measurement. We also show that virtual phonon
exchange can significantly boost range of the intermolecular dipole-dipole
interaction, allowing strong coupling between widely-separated molecular ion
qubits.
