Mean-Matched Controls Fail to Preserve Logical Risk in Rotated Surface-Code Memories with Spatially Resolved Noise

Abstract Spatially concentrated noise is a central concern in modular quantum error correction, yet its effect is often estimated by replacing a heterogeneous device with a uniform effective error rate. We show that matching the expected number of physical faults does not preserve the logical failure probability in rotated surface-code memories. First, we reanalyse a published 2.6-million-shot proxy benchmark and identify six specific implementation issues that constrain its interpretation: an undocumented seam fraction of 0.5 instead of the configured 0.3, noise injection outside the repeated circuit body, an X error appended after measurement that cannot flip the recorded outcome, an unused p_ebit field, an algebraically generated decay curve presented as data, and a resource annotation not matching any circuit layout. Second, we perform 14.4 million additional sampled memory experiments across 72 conditions, covering code distances three to nine, both logical memory bases, spatially resolved seam noise, a channel-wise mean-matched control, and decoder mismatch. All numerical comparisons use recorded failure counts, with binomial confidence intervals and multiplicity-adjusted hypothesis tests. At code distance three, X-basis memory, and the largest tested noise severity, the geometric seam produces 977 failures while a channel-wise mean-matched homogeneous control produces 1430 failures in 200,000 shots, giving a risk ratio of 0.683 with a 95% confidence interval of 0.630 to 0.741 (Holm-adjusted p = 4.6 × 10⁻¹⁹). Only this d = 3 X-basis comparison is statistically decisive at the available shot count; the larger-distance observations are consistent with the same effect but are individually under-powered. Decoding the same geometric-noise samples with calibrated matching weights reduces failures from 2060 to 977 relative to baseline weights. Z-basis point estimates show the opposite geometry trend, although the selected largest-severity comparisons do not survive familywise adjustment. A simple repetition-code calculation explains why matching the mean physical error probability cannot generally preserve logical risk. The results establish a reproducible method for separating spatial exposure, temporal exposure, and decoder assumptions in seam-noise studies. They support geometry-aware modeling and calibrated decoding within the tested memory circuits; they do not implement a distributed gate, a Bell-pair channel, or classical feedforward, and they do not establish a distributed-gate threshold or hardware-level resource advantage.