We investigate the theoretically achievable fidelities when coherently controlling an effective three-qubit system consisting of a negatively charged nitrogen vacancy (15NV−) center in diamond with an additional nearby carbon 13C spin via square and two frequency component radio and microwave frequency pulses in different magnetic field regimes. Such a system has potentially interesting applications in quantum information-related tasks such as distributed quantum computation or quantum repeater schemes. We find that the best fidelities can be achieved in an intermediate magnetic field regime. However, with only square pulses it will be challenging to reach the fidelity threshold(s) predicted by current models of fault-tolerant quantum computing.
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