Surface-code memory and biased-noise decoding

Surface codes protect a logical qubit using only local stabilizer checks on a 2D lattice: data qubits sit on edges or vertices, and repeated measurement of local $X$-type and $Z$-type stabilizer operators produces a syndrome without ever measuring the encoded logical state directly. Stacking syndrome rounds over time traces out a space-time syndrome graph; a decoder (typically minimum-weight perfect matching or a neural/tensor-network decoder) infers the most likely error chain consistent with that graph, and the logical observable fails only when the true error and the inferred correction differ by a nontrivial logical operator — an event whose rate drops super-linearly below the physical error rate once the code operates below its threshold. The XZZX variant this record cites reshapes the stabilizers so that a biased (e.g. dephasing-dominated) physical noise channel is matched more efficiently than the standard surface code, without needing a higher weight. This record documents the syndrome-round and logical-observable workflow as an architecture reference; it makes no hardware threshold claim of its own, and — per its caveat — decoder quality, leakage, measurement error, and connectivity determine the useful operating point.