Fig. 5. Leakage analysis.

a Repeated measurement sequence for extracting leakage error during the measurement. The X_π/2 pulse allows us to randomly sample leakage events from $∣0⟩$ or $∣1⟩$ states. b The leakage probability ($p_{\mathrm{leak}}^{\mathrm{meas}}$) to the $∣2⟩$ state measured at Q_F14. The leakage and seepage rate is obtained by fitting the data with Eq. (15). c, d Qubit leakage in the system as a function of syndrome measurement rounds for Z − and X − basis logical states. Bar plots show the $p_{\mathrm{leak}}^{\mathrm{tot}}$ as computed from the gate and measurement leakage rates, obtained from randomized benchmarking (2Q gates) and from the sequence shown in a, respectively. Experimental results, $p_{\mathrm{leak}}^{\exp }=1-p_{\mathrm{accept}}$, where p_accept is the acceptance probability calculated from the method outlined in Methods “Post-selection method”, are shown as black symbols for comparison. The experimental results plotted here do not include initialization leakage. e Readout calibration data for Q_F12 (see Fig. 4a). The qubit is prepared in its $∣0⟩$, $∣1⟩$, and $∣2⟩$ states and measured. The collected statistics can be seen in as blue ($∣0⟩$), red ($∣1⟩$), and grey ($∣2⟩$) where the dot-dashed lines represent 3-σ for each distribution. f 3-state classification results for Q_F12 after qubit initialization, and g after the first X − syndrome measurement.