Extended Data Fig. 6: Chern number analysis.

a, The central 12 columns are chosen as the bulk region of the system. b, The measured open Pauli strings, numbered according to ordering on the horizontal axis of Fig. 3c. c, Majorana correlations in the unit-cell basis, obtained from the open strings. The correlation matrix is truncated at distance ± 1 (length-6 strings) to avoid system boundaries when starting from a reference site in the bulk. The (o, e), (o, o) matrices are evaluated similarly, and related to (e, o), (e, e), respectively, through symmetry relations. d, The total variation distance of the measured string distribution (in phase B) from the ideal theory values with increasing error detection. The value is normalized by the point with least postselection and improves by ~ 10% for optimal error detection. e, Discretized Berry curvature F_k whose sum over the 1st Brillouin zone is the Chern number. The red arrows represent the discretized phase potential obtained from normalized eigenstate overlaps, with the arrow vector given by \(\arg \,{\widetilde{{\rm{U}}}}_{{\boldsymbol{k}}}=(\arg \,{{\rm{U}}}_{{\boldsymbol{k}}}^{\widehat{x}},\arg \,{{\rm{U}}}_{{\boldsymbol{k}}}^{\widehat{y}})\). f, The Chern number for different values of loss radius (LR) postselection, evaluated through bootstrapping with 300 trials as a function of a single batch size. The samples are drawn uniformly from the data set with replacement, and the samples from strings identified with each other are afterwards further averaged. g, Change in the Chern number between postselection at loss radius 3 and 0, as a function of batch size. h, Phase diagram of the Chern number as a function of per-layer error and initial plaquette parity values, obtained through noisy numerical simulations. The stars denote points corresponding to the phenomenological noise model inferred from experimental measurements (red with maximal postselection).