In this talk I will describe a quantum protocol for the non-destructive measurement of single molecule's electronic, vibrational, rotational or Zeeman state [J. Mur-Petit et al, Phys. Rev. A 85, 022308 (2012)]. The protocol is based on a quantum logic scheme between an atomic ion and a 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 individual molecular ions, but it also has applications in the fields of quantum information and quantum computing.