High-Fidelity Entangling Gates for Electron and Nuclear Spin Qubits in Diamond

Motivated by the recent experimental progress in exploring the use of a nitrogen-vacancy (NV) center in diamond as a quantum computing platform, we propose schemes for fast and high-fidelity entangling gates on this platform. Using both analytical and numerical calculations, we demonstrate that synchronization effects between resonant and off-resonant transitions may be exploited such that spin-flip errors due to strong driving may be eliminated by adjusting the gate time or the driving field. This allows for fast, high fidelity entangling operations between the electron spin and one or several nuclear spins. We investigate a two-qubit system where the NV center is comprised of a $^{15}$N atom and a qubit-qutrit system for the case of a $^{14}$N atom. In both cases, we predict a complete suppression of off-resonant driving errors for two-qubit gates when addressing the NV electron spin conditioned on states of nuclear spins of the nitrogen atom of the defect. Additionally, we predict fidelities $>0.99$ for multi-qubit gates when including the surrounding $^{13}$C atoms in the diamond lattice in the conditioned logic.