Nonlocal Corrections from Dual Boundary Condition Inference\\in Quantum Error Correction

Most standard decoders used for quantum error correction are formulated as forward inference from syndrome and readout data. Here we test whether an explicit structural backward prior can add useful information beyond matched forward-only baselines. We introduce Dual Boundary Condition Inference (DBCI), a classical inference framework inspired by the Aharonov-Bergmann-Lebowitz rule that combines calibrated forward likelihoods with a structural backward prior encoding code geometry. On IBM quantum hardware, DBCI outperforms four standard decoders (lookup table, MWPM, Union-Find, and BP-OSD) and a matched forward Bayesian baseline at every distance tested. Per-shot analysis reveals a coupling-matrix anti-symmetry diagnostic that cleanly separates boundary-interaction shots from agreement shots. At intermediate forward–backward coupling, the fused decoder produces correct decodings on d=7 shots that neither boundary alone recovers. The weaker Union-Find baseline yields slightly more anomalous shots than MWPM, possibly suggesting that weaker forward decoders leave more room for backward-boundary contributions. Spatial analysis shows these corrections are spatially extended, spanning Manhattan distance 11 on a 7 × 7 qubit grid. All inference is classical Bayesian fusion on classical measurement data, yet exhibits boundary tension, intermediate-coupling amplification, and spatially extended information effects consistent with the weak value literature. All results are obtained in the single-round, bit-flip-sector setting; broader implications are discussed but not claimed.