Photonic hyper-parallel quantum gates play a critical role in high-capacity quantum communication and fast quantum computing. Here, based on photon scattering in one-dimensional (1D) waveguides, we present some heralded schemes for constructing four-qubit hyper-controlled-not (hyper-CNOT) gates in two-photon systems. The qubits are encoded on both the polarization and spatial-mode degrees of freedoms (DOFs) of the photons, which can simplify the quantum circuit and reduce the quantum resource consumption. In our schemes, the faulty scattering events between photons and emitters caused by system imperfections can be filtered out and discarded. That is, our protocols for hyper-CNOT gates work in a heralded way. Our calculations show that, with great progress in the emitter-waveguide systems, our photonic hyper-CNOT gates may be experimentally feasible.
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