Encoding computing qubits in multiple degrees of freedom (DOFs) of a photonic system allows hyperparallel quantum computation to enlarge channel capacity with less quantum resource, and constructing high-fidelity hyperparallel quantum gates is always recognized as a fundamental prerequisite for hyperparallel quantum computation. Herein, we propose an approach for implementing a high-fidelity photonic hyperparallel controlled-phase-flip (CPF) gate working with polarization, spatial-mode, and frequency DOFs, through utilizing the practical interaction between the single photon and the diamond nitrogen vacancy (NV) center embedded in the cavity. Particularly, the desired output state of the gate without computation errors coming from the practical interaction is obtained, and the robust fidelity is guaranteed in the nearly realistic condition. Meanwhile, the requirement for the experimental realization of the gate is relaxed. In addition, this approach can be generalized to complete the high-fidelity photonic three-DOF hyperparallel CPFN gate and parity-check gate. These interesting features may make the present scheme have potential for applications in the hyperparallel quantum computation.
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