Fig. 2: Experimental results of MEADD on CZ gates (excitation-conserving two-qubit gates close to the ideal CZ).

All data are collected from a 69-qubit Google Sycamore processor, see Supplementary Information in ref. ¹⁷ for details of the processor. a Fidelities obtained using the context-aware fidelity estimation (CAFE) protocol¹⁹. These fidelities indicate how well a particular unitary characterization corresponds to the implementation of the CZ gate, and are presented for unitaries characterized by MEADD (blue), cross-entropy benchmarking (XEB, orange), and the perfect CZ unitary (gray). Solid lines with markers are the median over 85 different CZ gates of a single Sycamore device, and the shaded regions are the inner quartile regions. A higher CAFE fidelity corresponds to a more accurate unitary characterization of the gate, see text for details. The inset shows the empirical cumulative distribution functions (CDF) of the coherent errors inferred from the CAFE curves of every CZ gate, with median values reported in the legend. Also shown are the results obtained using the unitary tomography (UT, green) and the phase method (PM, red) characterization protocols. b Empirical CDFs of run-to-run standard deviations in the characterized controlled phase ϕ, and c swap angle θ, measured over 12 sequential characterizations of the 85 CZ gates. The different protocols were interleaved with one another over several hours to average out device inconsistencies. The median standard deviations of the different methods are reported in milliradian in the plots.