Extended Data Fig. 6: Comparison of different models for QEC result.

Comparison of the fitting results of quadratic (a + cp² + dp³), third-order polynomial (a + bp + cp² + dp³) and linear functions (a + bp). The coefficients a, b, c and d are the fitting parameters. We obtain a = 0.879 ± 0.006, c = −2.72 ± 0.06 and d = 1.89 ± 0.06 (quadratic function), a = 0.88 ± 0.01, b = 0.0 ± 0.1, c = −2.75 ± 0.24 and d = 1.91 ± 0.16 (third-order polynomial function), and a = 0.94 ± 0.02 and b = −1.00 ± 0.03 (linear function) from the fitting results. To compare the fitting results by different models, we calculate the Bayesian information criterion⁴³ (BIC) and the Akaike information criterion⁴⁴ (AIC). Models with lower BIC are preferred, whereas models with lower AIC provide better prediction of the experimental behaviour. The difference between the linear fit and the others is found to be decisive⁴⁵ (|ΔBIC| ≈ 50). In addition, although the difference is not as large (|ΔBIC| ≈ 3), the quadratic fit without the first-order term is more preferred than the polynomial function including the first-order term. The errors are 1σ from the mean.