Universal set of quantum gates for electron defect spin qubits in diamond and silicon carbide

Electron spin qubits based on nitrogen-vacancy centers in diamond and defects in silicon carbide have become a rapidly developing direction in quantum information and computing due to their potential in room temperature quantum computing. While single-qubit manipulations have been proposed and experimentally realized, the design of a realistic deterministic two-qubit entangling gate currently remains an important challenge. We propose fast optically controlled design where a two-qubit gate between spatially separate qubits is mediated by a photonic microcavity mode. The proposed gate scheme is compatible with available single-qubit operations. In addition, our design provides an opportunity to perform individual single qubit operations without the need to spatially resolve the qubits. As a result, for the first time a universal set of deterministic gates is proposed that can be implemented with current experimental capabilities in these systems.