  We present a scheme for ground-state cooling of a mechanical resonator by
simultaneously coupling it to a superconducting qubit and a cavity field. The
Hamiltonian describing the hybrid system dynamics is systematically derived.
The cooling process is driven by a red-detuned ac drive on the qubit and a
laser drive on the optomechanical cavity. We have investigated cooling in the
weak and the strong coupling regimes for both the individual system, i.e.,
qubit assisted cooling and optomechanical cooling, and compared them with the
effective hybrid cooling. It is shown that hybrid cooling is more effective
compared to the individual cooling mechanisms, and could be applied in both the
resolved and the unresolved sideband regimes.
