Measurement Based 2-qubit Unitary Gates for Pairs of Nitrogen-Vacancy Centers in Diamond*

The implementation of a high-fidelity 2-qubit quantum gate is an essential, and perhaps the most challenging, ingredient in building a measurement based quantum computer using Nitrogen-vacancy (NV) centers. We propose a measurement-based scheme to generate 2-qubit unitary gates for two NV centers in diamond. We drive a Raman transition in both NV centers simultaneously. We demonstrate that our scheme results in a unitary 2-qubit quantum gate heralded by a Raman photon when the distance between the NV centers is chosen to be a quarter-wavelength of the Raman photon. The generation of the Raman photon goes through multiple excited electronic states of an NV center, and the interference between these paths controls the fidelity of the 2-qubit gate. We find that there is a special value of the drive frequency which should yield essentially perfect fidelity when photon collection efficiency is unity.