With the local resonant interaction between a nitrogen-vacancy-center ensemble (NVE) and a superconducting coplanar resonator, and the single-qubit operation, we propose two protocols for the state transfer between two remote NVEs and for a fast controlled-phase (cphase) gate on these NVEs, respectively. This hybrid quantum system is composed of two distant NVEs coupled to separated high-$Q$ transmission line resonators (TLRs), which are interconnected by a current-biased Josephson-junction superconducting phase qubit. The fidelity of our state-transfer protocol is about $99.63\%$ within the operation time of $70.60$ ns. The fidelity of our cphase gate is about $98.15\%$ within the operation time of $93.87$ ns. Furthermore, using the cphase gate, we construct a two-dimensional cluster state on NVEs in a $n\times n$ square grid based on the hybrid quantum system for the one-way quantum computation. Our protocol may be more robust, compared with the one based on the superconducting resonators, due to the long coherence time of NVEs at room temperature.

• Received 27 February 2015

DOI:https://doi.org/10.1103/PhysRevA.91.062325