  We propose an approach for studying quantum information and performing high
resolution spectroscopy of rotational states of trapped molecular ions using an
on-chip superconducting microwave resonator. Molecular ions have several
advantages over neutral molecules. Ions can be loaded into deep (1 eV) RF traps
and are trapped independent of the electric dipole moment of their rotational
transition. Their charge protects them from motional dephasing and prevents
collisional loss, allowing 1 s coherence times when used as a quantum memory,
with detection of single molecules possible in <10 ms. An analysis of the
detection efficiency and coherence properties of the molecules is presented.
