Efficient Generation of Quantum Cluster Entangled States for Distant Diamond Nitrogen-Vacancy Centers

We present an efficient scheme for creating electronic quantum cluster entangled states associated with distant diamond nitrogen-vacancy (NV) centers coupled to microtoroidal resonators using parity-check and controlled-phase gates. These two gates are constructed by exploiting the input-output processes of single photons as a result of cavity quantum electrodynamics. Our schemes provides an efficient route to solid-state one-way quantum computation as diamond NV centers exhibit the ultralong coherent time and fast electron-spin manipulation. The time scale of the quantum cluster entangled states is a parity-check gate and a controlled-phase gate. Moreover, the prior entanglement is not required, and a higher fidelity and a higher efficiency of the quantum cluster states can be achieved, compared with other protocols.