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Universal hyperparallel hybrid photonic quantum gates with dipole-induced transparency in the weak-coupling regime

We present the dipole induced transparency (DIT) of a diamond nitrogen-vacancy center embedded in a photonic crystal cavity coupled to two waveguides, and it is obvious with the robust and flexible reflectance and transmittance difference of circularly polarized lights between the uncoupled and the coupled cavities even in the bad cavity regime (the Purcell regime). With this DIT, we propose two universal hyperparallel hybrid photonic quantum logic gates, including a hybrid hyper-controlled-not gate and a hybrid hyper-Toffoli gate, on photon systems in both the polarization and the spatial-mode degrees of freedom (DOFs), which are equal to two identical quantum logic gates operating simultaneously on the systems in one DOF. They can be used to perform more quantum operations with less resources in the quantum information protocols with multi-qubit systems in several DOFs, which may depress the resources consumed and the photonic dissipation. Moreover, they are more robust against asymmetric environment noise in the weak-coupling regime, compared with the integration of two cascaded quantum logic gates in one DOF.