Decoder Comparability Across Quantum Software Stacks: Repeated-Round Surface and Digitized-GKP Syndrome Replay

Abstract

We present a contract-preserving, family-aware comparison of decoder behavior across four syndrome-generation stacks (PennyLane, Qiskit, Cirq, and a LiDMaS+ reference) under a fixed replay interface. Request streams from repeated-round surface-code and digitized-GKP circuits are replayed through BP, MWPM, and UF with matched controls. The unified matrix spans 24 cells and achieves line-level integrity: $24000$ request lines, $24000$ response lines, response ratio $=1.0$ in every cell, zero parse failures, and zero decoder-name mismatches. Fifteen warning-no-syndrome events occur only in GKP-Cirq rows. Within-family ordering is stable in both families ($\mathrm{BP}<\mathrm{MWPM}<\mathrm{UF}$); source-averaged flip counts are 2.435, 4.768, and 5.870 for surface and 1.595, 2.908, and 3.681 for GKP. Relative to MWPM, BP reduces mean intervention volume by $48.9\%$ in surface and $45.1\%$ in GKP. Source-vs-reference effects are family dependent, with larger coherent shifts in GKP. Source-bootstrap ranks remain unchanged, and hidden-truth sidecars add an outer-code logical-parity error-rate check in which UF has the largest source-mean rate in both families. The comparison is stack-aware, contract-verified, and avoids raw cross-family threshold-equivalence claims.