  We propose a scheme to implement quantum controlled NOT gate and quantum
phase gate in an optomechanical system based on phonon blockade. For
appropriate choices of system parameters, fidelities of both the quantum gate
operations are very close to unity in the absence of dissipation. Using
recently achieved experimental values in a mechanical resonator coupled to a
microwave cavity, we show that the quantum gate can be realized experimentally
with very high fidelity.
