Decoder Dependence in Surface-Code Threshold Estimation Under Digitized Hybrid Continuous-Variable and Discrete Noise

Abstract

Surface-code threshold estimates depend on the inference pipeline, including decoder and estimator choices. We compare decoders within a single LiDMaS+ workflow under Pauli-reference and digitized hybrid continuous-variable/discrete sweeps. In the Pauli-reference mode, the matching-style backend outperforms Union-Find and yields crossing median $p_c=0.0531$ (bootstrap interval [0.0415,0.0572]) and collapse fit $p_c=0.052$ ($\nu =1.35$). For the hybrid mode, a dense transition-window sweep at $d=3,5,7$ uses $\sigma \in [0.30,0.50]$ with step 0.01 and 3000 trials per point. After the initial exact-zero plateau is excluded from crossing localization, the matching-style backend gives interior crossing estimates ${\sigma }_c=0.4707$ for $(d=3,5)$ and ${\sigma }_c=0.3275$ for $(d=5,7)$; the latter lies in a low-LER region and remains estimator-sensitive. A targeted $d=9$ extension shows larger Union-Find LER at moderate-to-high $\sigma$ and matching-fallback rates up to 0.747 at $\sigma =0.50$. In a $d=5$ neural-guidance sensitivity sweep, full learned reweighting reduces the sampled mean LER from 0.1773 to 0.1663 over $\sigma \in [0.35,0.55]$. These results show that estimator resolution and backend fallback diagnostics are part of an auditable decoder comparison.