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.
@article{arxiv.1603.00065,
title = {Continuous variables quantum computation over the vibrational modes of a single trapped ion},
author = {Luis Ortiz-Gutiérrez and Bruna Gabrielly and Luis F. Muñoz and Kainã T. Pereira and Jefferson G. Filgueiras and Alessandro S. Villar},
journal= {arXiv preprint arXiv:1603.00065},
year = {2017}
}