Noise-Biased Surface Code Thresholds Under Realistic Gate Sets

Abstract

Biased-noise threshold claims for surface-code families are often expressed in terms of the nominal hardware dephasing ratio η, yet realistic gate decompositions, measurement asymmetries, and syndrome-extraction schedules can convert a substantial fraction of the nominal Z-dominant noise into less favorable error components. This mismatch matters well beyond quantum error correction because it exemplifies a broader problem in reliable scientific computing: analytical control parameters are useful only if the implementation preserves the semantics that make them predictive. We study this issue for realistic biased-noise surface-code threshold estimation by introducing an effective-bias renormalization, ηeff , that aggregates compiled Pauli components and a temporal-fragility factor into a decoder-visible bias observable. We couple that observable to three formal results: a reference biased-Pauli closure identity, a convex-mixture representation for gate-class attribution, and a schedule-sensitivity transfer bound connecting changes in ηeff to threshold residuals. We then instantiate the resulting analysis on a matched validation suite that mirrors the planned sweep over code families, distances, schedules, and bias ratios. Across four code families, reparameterizing thresholds by ηeff reduces leave-one-schedule-out RMSE by 40.6%–50.5%, the convex-mixture interval bound has zero empirical violations, and the schedule-transfer residual remains within the predicted bound across all held-out settings. These gains are interpreted as a conditional first-order result that holds when boundary fragility and backend semantic mismatch remain within audited ranges. The current evidence is surrogate-based rather than direct Stim or Qiskit Aer execution, so the manuscript should be read as a rigorous mechanism paper with an executable validation scaffold rather than as a final hardware-faithful threshold benchmark.