Hyperparallel optical quantum computation assisted by atomic ensembles embedded in double-sided optical cavities

We propose an effective, scalable, hyperparallel photonic quantum computation scheme in which photonic qubits are hyperencoded both in the spatial degrees of freedom (DOF) and the polarization DOF of each photon. The deterministic hyper-controlled-not (hyper-cnot) gate on a two-photon system is attainable with our interesting interface between the polarized photon and the collective spin wave (magnon) of an atomic ensemble embedded in a double-sided optical cavity, and it doubles the operations in the conventional quantum cnot gate. Moreover, we present a compact hyper-cnot^N gate on N +1 hyperencoded photons with only two auxiliary cavity-magnon systems, not more, and it can be faithfully constituted with current experimental techniques. Our proposal enables various applications with the hyperencoded photons in quantum computing and quantum networks.