Fig. 2: Sliding window decoding schematic for 2D decoding problem, for example representing the repetition code with phenomenological noise.

At each decoding step a number of syndrome rounds (window) is selected for decoding (orange region in left columns), and tentative corrections acquired. The corrections in the older n_com rounds (green region in right columns) are of high confidence and are committed to, while the corrections in the remaining (buffer) n_buf rounds are discarded. The window is then moved up to the edge of the commit region and the process repeated. We decide to commit to the edges going from the commit region out of it, producing artificial defects defined by nodes outside of the region belonging to such an edge. All numerics performed using a generalisation of this method to the 3D decoding problem representing the surface code with circuit-level noise.