One-step construction of a multi-qubit controlled phase gate with ensembles of nitrogen-vacancy centers in hybrid circuit QED

We present a one-step method to realize a multi-qubit controlled phase gate of multiple nitrogen-vacancy-center ensembles (NV ensembles). This multi-qubit phase gate is based on cross-Kerr nonlinearities, which are enabled by a superconducting flux qutrit dispersively coupled to multiple NV ensembles. Since the flux qutrit is not populated during the operation, the effect of qutrit decoherence is greatly suppressed. Moreover, the gate operation time is independent of the number of NV ensembles. Numerical simulations show that high-fidelity construction of a four-qubit controlled phase gate with four NV ensembles is feasible with present hybrid circuit QED technology.