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A cavity QED implementation of the non-adiabatic holonomic quantumcomputation in decoherence-free subspaces is proposed with nitrogen-vacancycenters coupled commonly to the whispering-gallery mode of a microspherecavity, where a universal set of quantum gates can be realized on the qubits.In our implementation, with the assistant of the appropriate driving fields,the quantum evolution is insensitive to the cavity field state, which is onlyvirtually excited. The implemented non-adiabatic holonomies, utilizing opticaltransitions in the {\Lambda} type of three-level configuration of thenitrogen-vacancy centers, can be used to construct a universal set of quantumgates on the encoded logical qubits. Therefore, our scheme opens up thepossibility of realizing universal holonomic quantum computation with cavityassisted interaction on solid-state spins characterized by long coherencetimes.

Cavity QED implementation of non-adiabatic holonomies for universal quantum gates in decoherence-free subspaces with nitrogen-vacancy centers