  We propose a fast and non-destructive spectroscopic method for single
molecular ions that implements quantum logic schemes between an atomic ion and
the molecular ion of interest. Our proposal relies on a hybrid coherent
manipulation of the two-ion system, using optical or magnetic forces depending
on the types of molecular levels to be addressed (Zeeman, rotational,
vibrational or electronic degrees of freedom). The method is especially suited
for the non-destructive precision spectroscopy of single molecular ions, and
sets a starting point for new hybrid quantum computation schemes that combine
molecular and atomic ions, covering the measurement and entangling steps.
