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Usually, the hyperparallel quantum computation can speed up quantumcomputing, reduce the quantum resource consumed largely, resist to noise, andsimplify the storage of quantum information. Here, we present the first schemefor the self-error-corrected hyperparallel photonic quantum computation workingwith both the polarization and the spatial-mode degrees of freedom of photonsystems simultaneously. It can prevent bit-flip errors from happening with animperfect nonlinear interaction in the nearly realistic condition. We give theway to design the universal hyperparallel photonic quantum controlled-NOT(CNOT) gate on a two-photon system, resorting to the nonlinear interactionbetween the circularly polarized photon and the electron spin in the quantumdot in a double-sided microcavity system, by taking the imperfect interactionin the nearly realistic condition into account. Its self-error-correctedpattern prevents the bit-flip errors from happening in the hyperparallelquantum CNOT gate, guarantees the robust fidelity, and relaxes the requirementfor its experiment. Meanwhile, this scheme works in a failure-heralded way.Also, we generalize this approach to achieve the self-error-correctedhyperparallel quantum CNOT$^N$ gate working on a multiple-photon system. Thesegood features make this scheme more useful in the photonic quantum computationand quantum communication in the future.

Self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom