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.Introduction-A robust and functional quantum network [1,2] requires the simultaneous achievement of both high-fidelity local quantum operation and efficient distribution of quantum information between remote quantum nodes [3,4]. The combination of these two capabilities would enable a number of important applications, such as long distance quantum communication [5-9], distributed quantum computation [10-14] and quantum metrology [15][16][17][18][19][20]. These two capabilities have been separately demonstrated in various experiments [21,22], but it remains very challenging to combine them into a single physical system. For example, microwave (MW) superconducting qubits feature high quantum operation fidelity [23,24] but suffer severe losses and decoherence during propagation [25]. On the other hand, optical photons are ideal qubits for the purpose of long-distance quantum state distribution [22], but fault-tolerant quantum gates with optical photons remain elusive [26,27]. Naturally, the realization of a practical quantum network would largely benefit from a hybrid platform [28][29][30][31][32][33][34][35][36][37][38][39] which bridges the gap between optical and MW qubits. Therefore, designing a physical photonphoton quantum gate that (1) hybridly processes qubits at different frequencies, (2) has high fidelity is important for achieving this target.Quantum gates involving Rydberg atoms [40] would be able to satisfy the above requirements. For realising a hybrid photon-photon quantum gate, highly excited Rydberg states are employed for interfacing with the MW qubits, while the hyperfine ground states and low lying excited states can be used to process the optical qubit. Meanwhile, the Rydberg states and hyperfine ground states has long lifetime [41], which could help keeping a high fidelity of the gate [42].In this Letter, we propose a new scheme of such a Rydberg quantum CZ-gates, where the optical qubit is interfaced by eletromagnetic induced transparency (EIT) photon storage [43][44][45][46][47] and the MW qubit is processed by high quality MW cavity QED system [48][49][50][51]. The system dynamics and the gate fidelity are analysed in detai...