  The experimental optimization of a two-qubit controlled-Z (CZ) gate is
realized following two different data-driven gradient ascent pulse engineering
(GRAPE) protocols in the aim of optimizing the gate operator and the output
quantum state, respectively. For both GRAPE protocols, the key computation of
gradients utilizes mixed information of the input Z-control pulse and the
experimental measurement. With an imperfect initial pulse in a flattop
waveform, our experimental implementation shows that the CZ gate is quickly
improved and the gate fidelities subject to the two optimized pulses are around
99%. Our experimental study confirms the applicability of the data-driven GRAPE
protocols in the problem of the gate optimization.
