Heralded high-fidelity photonic hyper-CNOT gates with quantum scattering in one-dimensional waveguides

Hyper-parallel quantum computation offers irreplaceable advantages in quantum information processing (QIP). In this article, based on the scattering property of photons off emitters coupled to one-dimensional (1D) waveguides, we propose three heralded schemes for implementing hyper-controlled-not (hyper-CNOT) gates on two-photon systems. The four qubits of our hyper-CNOT gates are encoded on the spatial-mode and the polarization degrees of freedom (DOFs) of two-photon systems. In our schemes, the faulty scattering events between photons and quantum emitters caused by system imperfections can be detected and discarded. Besides, no auxiliary photons are needed during the process, reducing the operation time and resource consumption in QIP. We also discuss the success probabilities and fidelities of our schemes, concluding that our schemes may be feasible under current technology.