High-fidelity control-Z (CZβ) 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 CZβ gates. Here we numerically investigate the
time-optimal pulses to generate a high-fidelity Rydberg CZβ 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 CZβ gate with a high Bell fidelity up to 0.9998. 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.Comment: 6 figure