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With the local resonant interaction between a nitrogen-vacancy-centerensemble (NVE) and a superconducting coplanar resonator, and the single-qubitoperation, we propose two protocols for the state transfer between two remoteNVEs and for fast controlled-phase (c-phase) on these NVEs, respectively. Thishybrid quantum system is composed of two distant NVEs coupled to separatedhigh-Q transmission line resonators (TLRs), which are interconnected by acurrent-biased Josephsonjunction superconducting phase qubit. The fidelity ofour state-transfer protocol is about 99.65% within the operation time of 70.60ns. The fidelity of our c-phase gate is about 98.23% within the operation timeof 93.87 ns. Furthermore, using the c-phase gate, we construct atwo-dimensional cluster state on NVEs in n*n square grid based on the hybridquantum system for the one-way quantum computation. Our protocol may be morerobust, compared with the one based on the superconducting resonators, due tothe long coherence time of NVEs at room temperature.

Quantum information processing on nitrogen-vacancy ensembles with the local resonance assisted by circuit QED