Hardware-in-the-Loop Syndrome-to-Decoder Validation for Repetition, Surface, CSS-LDPC, and Digitized-GKP Codes

Abstract

Quantum error-correction experiments increasingly require a verified interface between measured syndrome bits and decoder-native correction requests. We report a four-branch syndrome-to-decoder study spanning three IBM gate-model hardware circuits and one PennyLane-backed digitized-GKP model. The hardware branches implement a five-data-qubit repetition code, a distance-five rotated-surface-code Z-check extraction layer, and the Z-check half of the Steane CSS code as a compact CSS-LDPC benchmark. The GKP branch samples finite-squeezed Gaussian-CV q-readout and injected q-shifts, then bins wrapped quadrature coordinates into the same outer surface-code Z-check interface. All cases use 4096 shots per stream, clean and injected streams, LiDMaS+ request construction, and MWPM/minimum-weight correction as the plotted baseline, with union-find and hard-decision belief-propagation/min-sum policies replayed for interface validation. The correction-volume panels additionally report mean minimum-weight correction weight for each decoded stream. Repetition and CSS-LDPC hardware preserve the dominant expected syndrome and correction for every injected target. The routed 56-qubit surface circuit exhibits broad hardware-induced syndrome activation: exact localization drops to $0.003$--$0.108$, but target-containing localization remains $0.279$--$0.642$. The digitized-GKP study gives exact q-shift localization of $0.350$--$0.495$ and target-containing localization of $0.417$--$0.608$. The results support an auditable syndrome-to-decoder interface rather than a threshold claim.