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