  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 fast controlled-phase (c-phase) 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 Josephsonjunction superconducting phase qubit. The fidelity of
our state-transfer protocol is about 99.65% within the operation time of 70.60
ns. The fidelity of our c-phase gate is about 98.23% within the operation time
of 93.87 ns. Furthermore, using the c-phase gate, we construct a
two-dimensional cluster state on NVEs in n*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.
