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Hybrid quantum gates hold great promise for quantum information processingsince they preserve the advantages of different quantum systems. Here wepresent compact quantum circuits to deterministically implement controlled-NOT,Toffoli, and Fredkin gates between a flying photon qubit and diamondnitrogen-vacancy (NV) centers assisted by microcavities. The target qubits ofthese universal quantum gates are encoded on the spins of the electronsassociated with the diamond NV centers and they have long coherence time forstoring information, and the control qubit is encoded on the polarizations ofthe flying photon and can be easily manipulated. Our quantum circuits arecompact, economic, and simple. Moreover, they do not require additional qubits.The complexity of our schemes for universal three-qubit gates is much reduced,compared to the synthesis with two-qubit entangling gates. These schemes havehigh fidelities and efficiencies, and they are feasible in experiment.

Hybrid quantum gates between flying photon and diamond nitrogen-vacancy centers assisted by optical microcavities