Three-Photon Polarization-Spatial Hyperparallel Quantum Fredkin Gate Assisted by Diamond Nitrogen Vacancy Center in Optical Cavity

The construction of a near-deterministic photonic hyperparallel quantum Fredkin (hyper-Fredkin) gate is investigated for a three-photon system with the optical property of a diamond nitrogen vacancy center embedded in an optical cavity (cavity-NV center system). This hyper-Fredkin gate can be used to perform double Fredkin gate operations on both the polarization and spatial-mode degrees of freedom (DOFs) of a three-photon system with a near-unit success probability, compared with those on the double three-photon systems in one DOF. In this proposal, the hybrid quantum logic gate operations are the key elements of the hyper-Fredkin gate, and only two cavity-NV center systems are required. Moreover, the possibility of constructing a high-fidelity and high-efficiency hyper-Fredkin gate in the experimental environment of a cavity-NV center system is discussed, which may be used to implement high-fidelity photonic computational tasks in two DOFs with a high efficiency.