Efficient scheme for implementing a hybrid Toffoli gate with two NV ensembles simultaneously controlling a single superconducting qubit

The Toffoli gate is a three-qubit controlled-controlled-NOT gate, which plays a central role in quantum information processing and quantum computing. Recently, hybrid systems and hybrid quantum gates have attracted much attention. We propose an efficient scheme to implement a hybrid Toffoli gate with two nitrogen-vacancy center ensembles (NV ensembles) as the control qubits and a single superconducting flux qubit as the target qubit. This hybrid Toffoli gate is realized by employing two NV ensembles coupled to a superconducting qutrit. The hybrid Toffoli gate is constructed by a controlled-controlled-phase (CCPHASE) gate sandwiched between two Hadamard gates applied on the target qubit. Since the CCPHASE gate is realized using only a single-step operation and no conventional gate decomposition protocol is applied, the Toffoli-gate implementation is greatly simplified. Because the higher energy level of the flux qutrit is not populated, the decoherence of this level is greatly suppressed. In addition, our hybrid Toffoli gate can be used to generate a hybrid Greenberger-Horne-Zeilinger entangled state of a flux qubit and two NV ensembles. Numerical simulations demonstrate that high-fidelity implementation of a hybrid Toffoli gate is feasible within current experimental technology. This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems.