Robust √swap gate on nitrogen-vacancy centres via quantum Zeno dynamics

A robust root swap gate is directly put forward by manipulating two diamond nitrogen-vacancy (NV) centres coupled to a photonic crystal nanocavity within quantum Zeno subspaces. This quantum gate is immune to both the loss of cavity and spontaneous emission of the NV centre, since no cavity photon or excited level of the NV centre is populated during the whole operation. The strictly numerical simulation shows that the average fidelity of the root swap gate is high corresponding to the current experimental parameters.