General quantum computation on distant phonons assisted by hybrid systems.

• The system consists of two acoustic wave resonator, two ensembles of nitrogen-vacancy centers, and a superconducting resonator. • The interaction is nonlocal. • Generate the Bell state and construct the controlled-phase gate. We study the generation of entanglement and the realization of controlled quantum phase gates in hybrid quantum systems. Based on the researches on acoustic wave resonators (AWRs) in recent years, we propose a hybrid system which consists of two high quality-factor AWRs, two ensembles of nitrogen-vacancy-centers (NVEs), and a superconducting resonator used to interact two NVEs. Utilizing this hybrid system we present detailed schemes to produce entangled states and carry out controlled-phase gates on two distant AWRs. The numerical simulation shows that from our protocols the fidelities of the entangled states and the controlled-phase gates can reach 99.19 % and 98.56 %, respectively, by taking into account the dissipation and dephasing of the whole system. [ABSTRACT FROM AUTHOR]