Counterdiabatic driving at Rydberg excitation for symmetric $C_Z$ gates with ultracold neutral atoms

Abstract: We extend the scheme of neutral atom Rydberg $C_Z$ gate based on double sequence of adiabatic pulses applied symmetrically to both atoms using counterdiabatic driving in the regime of Rydberg blockade. This provides substantial reducing of quantum gate operation times (at least five times) compared to previously proposed adiabatic schemes, which is important for high-fidelity entanglement due to finite Rydberg lifetimes. We analyzed schemes of adiabatic rapid passage with counterdiabatic driving for single-photon, two-photon and three-photon schemes of Rydberg excitation for rubidium and cesium atoms. We designed laser pulse profiles with fully analytical shapes and calculated the Bell fidelity taking into account atomic lifetimes and finite blockade strengths. We show that the upper limit of the Bell fidelity reaches ${\mathcal F}\simeq0.9999$ in a room-temperature environment.