High-fidelity Rydberg controlled-Z gates with optimal pulses

High-fidelity control-$Z$ ($C_Z$) gates are essential and mandatory to build a large-scale quantum computer. In neutral atoms, the strong dipole-dipole interactions between their Rydberg states make them one of the pioneering platforms to implement $C_Z$ gates. Here we numerically investigate the time-optimal pulses to generate a high-fidelity Rydberg $C_{Z}$ gate in a three-level ladder-type atomic system. By tuning the temporal shapes of Gaussian or segmented pulses, the populations on the intermediate excited states are shown to be suppressed within the symmetric gate operation protocol, which leads to a $C_{Z}$ gate with a high Bell fidelity up to $99.92\%$. These optimized pulses are robust to thermal fluctuations and the excitation field variations. Our results promise a high-fidelity and fast gate operation under amenable and controllable experimental parameters, which goes beyond the adiabatic operation regime under a finite Blockade strength.