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The experimental optimization of a two-qubit controlled-Z (CZ) gate isrealized following two different data-driven gradient ascent pulse engineering(GRAPE) protocols in the aim of optimizing the gate operator and the outputquantum state, respectively. For both GRAPE protocols, the key computation ofgradients utilizes mixed information of the input Z-control pulse and theexperimental measurement. With an imperfect initial pulse in a flattopwaveform, our experimental implementation shows that the CZ gate is quicklyimproved and the gate fidelities subject to the two optimized pulses are around99%. Our experimental study confirms the applicability of the data-driven GRAPEprotocols in the problem of the gate optimization.

Optimization of Controlled-Z Gate with Data-Driven Gradient Ascent Pulse Engineering in a Superconducting Qubit System