Quantum phase flip gate between distant nitrogen-vacancy-center ensembles coupled to superconducting flux qubits

We propose a scheme for realizing a quantum controlled phase flip (CPF) gate between two distant nitrogen-vacancy-center spin ensembles (NVEs). The two NVEs couple magnetically with two inductively coupled superconducting flux qubits (FQs). By using an additional energy level of the nitrogen-vacancy (NV) center, the CPF gate can be implemented within the null- and single-excitation subspaces and the external classical driven field is needless in our scheme. Because of the adoption of NVE instead of single NV center, the CPF operation can be greatly speeded up. Besides, we show that this gate provides us a source of cluster states generation on NVEs. Analyses on the influences of dissipation show that this gate is robust.