Extended Data Fig. 2: State assignment data using 2 rounds of measurements.

As in the case of the SPAM experiment with 1 round of measurements, we prepare each of the four dual-rail basis states. Using the results of the 2 rounds of measurements and our decoding strategy, we assign one of the four states {‘00’, ‘01’, ‘10’, ‘11’}, or the ambiguous outcome ‘A’ in the case where the two measurement outcomes disagree. Results of preparing the two logical state \(\left\vert 01\right\rangle\) and \(\left\vert 10\right\rangle\) are shown in the left two panels; results of intentionally preparing the leakage states \(\left\vert 00\right\rangle\) and \(\left\vert 11\right\rangle\) are shown in the right two panels. The green horizontal lines simulation results modeling the SPAM experiment with two-rounds of measurements. For each state, we repeat the experiment a total of 100, 000 times. The height of the each bar and center of the black line correspond to the mean of the data and error bars represent the standard error, showing ± 1σ.