High-Fidelity Geometric Gates with Single Ions Doped in Crystals

Single rare-earth ions doped in solids are one kind of the promising candidates for quantum nodes towards a scalable quantum network. Realizing a universal set of high-fidelity gate operations is a central requirement for functional quantum nodes. Here we propose geometric gate operations using the hybridized states of electron spin and nuclear spin of an ion embedded in a crystal. The fidelities of these geometric gates achieve 0.98 in the realistic experimental situations. We also show the robustness of geometric gates to pulse fluctuations and to environment decoherence. These results provide insights for geometric phases in dissipative systems and show a potential application of high fidelity manipulations for future quantum internet nodes.