Fig. 8: Exponential suppression of the sub-threshold logical failure probabilities p_L with respect to code distance.

We use code distances d or d_eff depending on the noise model and compare different Floquet codes: CSS (green), XYZ² (orange), P⁶ (red), and X³Z³ (blue). Results are calculated for different noise models: (a, b) code-capacity and (c, d) SDEM3 noise models, with a subthreshold physical error rate p = 0.55%, which is small enough, yet can still be simulated using our computational resources up to code distance d = 24 or d_eff = 12, for all the different codes and parameters corresponding to different curves in the plots. The same physical error rates are chosen for all curves such that the subthreshold performance under different noise bias strengths and noise models can be compared. Plots are computed using two different bias strengths; one representing noise near the depolarizing regime: (a,c) η = 1 and the other representing noise in the strongly dephasing regime: (b, d) η = 99. All curves can be fitted to an exponential decay function \(f\propto \exp (-\gamma d)\) or \(f\propto \exp (-\gamma {d}_{{\rm{eff}}})\) where γ depends on the bias strength η and is an increasing function of (p_th − p). Each data point is averaged over 10⁵ − 10⁹ shots.