General quantum computation on photons assisted with double single-sided cavity system

We propose a physical system consisting of two optical cavities and a two-level system (TLS), which can be viewed as a double single-sided cavity system. The two cavities are crossed each other in a mutually perpendicular way and are both single-sided. The TLS is coupled to the two cavities. The universal input-output relation of the system, the reflection and transmission coefficients are derived by exploiting the probability amplitude method. Then by using the nitrogen-vacancy center instead of the TLS, we generate the controlled-phase gate and the controlled-controlled-phase gate on the photon qubits, with simple protocols that can be accomplished in both weak and strong coupling regimes. The protocols are shown to give rise to high fidelities and gate efficiencies.