Implementations of two-photon four-qubit Toffoli and Fredkin gates assisted by nitrogen-vacancy centers.

It is desirable to implement an efficient quantum information process demanding fewer quantum resources. We designed two compact quantum circuits for determinately implementing four-qubit Toffoli and Fredkin gates on single-photon systems in both the polarization and spatial degrees of freedom (DoFs) via diamond nitrogen-vacancy (NV) centers in resonators. The gates are heralded by the electron spins associated with the diamond NV centers.