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 $p_c=0.052$ ($ν=1.35$). For the hybrid mode, a dense transition-window sweep at $d=3,5,7$ uses $σ\in[0.30,0.50]$ 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 $σ_c=0.4707$ for $(d=3,5)$ and $σ_c=0.3275$ 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 $σ$ and matching-fallback rates up to $0.747$ at $σ=0.50$. In a $d=5$ neural-guidance sensitivity sweep, full learned reweighting reduces the sampled mean LER from $0.1773$ to $0.1663$ over $σ\in[0.35,0.55]$. These results show that estimator resolution and backend fallback diagnostics are part of an auditable decoder comparison.