  We introduce an approach to quantum information processing where the
information is stored in the motional degrees of freedom of nanomechanical
devices. The qubits of our approach are formed by the two lowest energy levels
of mechanical resonators which are tuned to be strongly anharmonic by suitable
electrostatic fields. Single qubit rotations are conducted by radio frequency
voltage pulses that are applied to individual resonators. Two qubit entangling
gates in turn are implemented via a coupling of two qubits to a common optical
resonance of a high finesse cavity. We find that gate fidelities exceeding 99%
can be achieved for realistic experimental parameters.
