Hybrid quantum gate and entanglement between a "stationary" photonic qubit and a flying optical state via a giant cross Kerr nonlinear effect

Quantum information processing with hybrid protocols making use of discrete- and continuous-variable currently attracts of great interest because of its promising applications in scalable quantum computer and distant quantum network. By inducing a giant cross-Kerr nonlinearity between two cavities, we propose a general protocol for hybrid quantum gate and quantum entanglement with high fidelity between a stationary, discrete photonic qubit and a flying photonic state. Interestingly, our protocol can be used to conduct a controlled-Z quantum gate between a stationary microwave photon stored in a slowly-decaying microwave cavity and a flying optical photon, and therefore enable to build quantum network for distant superconducting quantum circuits.