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Up to now, all the works about constructing quantum logic gates, an essentialpart in quantum computing, are focused on operating on one degree of freedom(DOF) of quantum systems. Here, we investigate the possibility to achieve ascalable photonic quantum computing based on two DOFs of quantum systems andconstruct a deterministic hyper-controlled-not (hyper-CNOT) gate operating onboth spatial-mode and polarization DOFs of a photon pair simultaneously, byusing the giant optical Faraday rotation induced by a single-electron spin in aquantum dot inside a one-side optical microcavity as a result of cavity quantumelectrodynamics. With this hyper-CNOT gate and linear optical elements,two-photon four-qubit cluster entangled states can be prepared and analyzed,which gives an application to manipulate more information with less resources.We analyze the experimental feasibility of this hyper-CNOT gate and show thatit can be implemented with current technology.

Deterministic photonic spatial-polarization hyper-controlled-not gate assisted by quantum dot inside one-side optical microcavity