Geometry-induced correlated noise in qLDPC syndrome extraction

With code and syndrome-extraction schedule fixed, can routed geometry alone change the correlated fault model enough to impact logical performance? Starting from a geometry-conditioned same-tick interaction Hamiltonian, we derive a controlled retained single-and-pair data-fault model for bivariate-bicycle (BB) layouts. Two geometry metrics emerge in two kernel regimes: under a crossing-local diagnostic kernel, a matching argument reduces the support-level effective fault weight; when every support pair appears in at least one retained round with finite same-round separation, strictly positive kernels saturate the support graph, and weighted exposure becomes the discriminating quantity. Circuit-level Monte Carlo on the $[\![72, 12, 6]\!]$ and $[\![144, 12, 12]\!]$ benchmarks confirms that a biplanar bounded-thickness layout suppresses the monomial single-layer embedding penalty, with weighted exposure tracking logical error rate across 101 operating points (Spearman correlation 0.893). A single-layer logical-family optimization on BB72 reduces worst-case exposure by 26.11% and lowers logical error rate in the tested power-law window. Routed geometry should be optimized together with code, schedule, and decoder.