Spin degrees of freedom of charged nitrogen-vacancy $\left({\mathrm{NV}}^{-}\right)$ centers in diamond have large decoherence times even at room temperature, can be initialized and read out using optical fields, and are therefore a promising candidate for solid-state qubits. Recently, quantum manipulations of ${\mathrm{NV}}^{-}$ centers using rf fields were experimentally realized. In this paper, we provide a theoretical demonstration, first, that such operations can be controlled by varying the frequency of the signal, instead of its amplitude, and ${\mathrm{NV}}^{-}$ centers can be selectively addressed even with spacially uniform rf signals; second, that when several ${\mathrm{NV}}^{-}$ centers are placed in an off-resonance optical cavity, a similar application of classical optical fields provides a controlled coupling and enables a universal two-qubit gate (CPHASE). rf and optical control together promise a scalable quantum computing architecture.

• Received 7 March 2007

DOI:https://doi.org/10.1103/PhysRevB.76.014122