Universal quantum gates between nitrogen-vacancy centers in a levitated nanodiamond

We propose a scheme to realize the controlled-phase gates between nitrogen-vacancy (NV) centers in an optically trapped nanodiamond, through a uniform magnetic field-induced coupling between the NV centers and the torsional mode of the levitated nanodiamond. The gates are insensitive to the thermal noise of the torsional mode. By combining the scheme with the dynamical decoupling, it is found that the high-fidelity universal quantum gates are possible with present experimental technology. The proposed scheme is useful for an NV-center-based quantum network and distributed quantum computation.