Continuous variables quantum computation over the vibrational modes of a   single trapped ion
  We consider the quantum processor based on a chain of trapped ions to propose an architecture wherein the motional degrees of freedom of trapped ions (position and momentum) could be exploited as the computational Hilbert space. We adopt a continuous-variables approach to develop a toolbox of quantum operations to manipulate one or two vibrational modes at a time. Together with the intrinsic non-linearity of the qubit degree of freedom, employed to mediate the interaction between modes, arbitrary manipulation and readout of the ionic wave function could be achieved. 
Luis Ortiz-Guti\'errez, Bruna Gabrielly, Luis F. Mu\~noz, Kain\~a T.   Pereira, Jefferson G. Filgueiras and Alessandro S. Villar
quant-ph