  Error suppression to the experimental imperfections is a central challenge
for useful quantum computing. Recent studies have shown the advantages of using
single-modulated pulses based on optimal control which can realize
high-fidelity two-qubit gates in neutral-atom arrays. However, typical
optimization only minimizes the ideal gate error in the absence of any decay,
which allows the gate to be passively influenced by all error sources leading
to an exponential increase of sensitivity when the error becomes larger. In the
present work, we propose the realization of two-qubit CZ gates with active
robustness against two-photon detuning errors. Our method depends on a modified
cost function in numerical optimization for shaping gate pulses, which can
minimize, not only the ideal gate error but also the fluctuations of gate
infidelity over a wide error range. We introduce a family of Rydberg blockade
gates with active robustness towards the impacts of versatile noise sources
such as Doppler dephasing and ac Stark shifts. The resulting gates with robust
pulses can significantly increase the insensitivity to any type of errors
acting on the two-photon detuning, benefiting from a relaxed requirement of
colder atomic temperatures or more stable lasers for current experimental
technology.
