Figure 6
From: Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
Vertices on the rough boundaries that do not satisfy the trailing vertex condition. In (a), we highlight such a vertex, v, in blue on the top rough boundary. Consider the highlighted qubit (blue face) and its syndrome (light yellow edges). For the sweep directions \(\vec {\omega } = (1,-1,-1)\) and \(\vec {\omega }' = (-1,1,-1)\), v does not satisfy the trailing vertex condition because the blue face is not in \({{{\uparrow }\,}}(v)\). In (b), we highlight a vertex in red on the right rough boundary that does not satisfy the trailing vertex condition for the same reason as (a), where the problematic sweep direction is \(\vec {\omega } = (-1, -1, 1)\).
