  We propose a hybrid quantum system, where an $LC$ resonator inductively
interacts with a flux qubit and is capacitively coupled to a Rydberg atom.
Varying the external magnetic flux bias controls the flux-qubit flipping and
the flux qubit-resonator interface. The atomic spectrum is tuned via an
electrostatic field, manipulating the qubit-state transition of atom and the
atom-resonator coupling. Different types of entanglement of superconducting,
photonic, and atomic qubits can be prepared via simply tuning the flux bias and
electrostatic field, leading to the implementation of three-qubit Toffoli logic
gate.
