  The high fidelity storage, distribution and processing of quantum information
prefers qubits with different physical properties. Thus, hybrid quantum gates
interfacing different types of qubits are essential for the realization of
complex quantum network structures. A Rydberg-atom based physical quantum CZ
gate is proposed to hybridly process the polarisation-encoded single-photon
optical qubit and the "Schroedinger cat" microwave qubit. The degradation of
the fidelity under the influence of various noise channels, such as microwave
cavity loss, sponetanous emission of atom states, and non-adiabaticity effect,
etc, has been analyised through detailed theoretical analysis by deriving
input-output relation of qubit fields. The feasibility and the challenges of
the protocol within current technology are also discussed by analysing the
possible experimental parameter settings.
