Decoder Performance in Hybrid CV-Discrete Surface-Code Threshold Estimation Using LiDMaS+

TL;DR

This study compares different decoders for surface-code threshold estimation under various noise models, highlighting how decoder choice influences threshold accuracy and robustness in quantum error correction.

Contribution

It provides a detailed comparison of MWPM, Union-Find, and neural-guided MWPM decoders in hybrid quantum error correction regimes, emphasizing their impact on threshold estimation.

Findings

MWPM outperforms Union-Find in baseline scenarios.

Neural-guided MWPM closely tracks MWPM performance.

Decoder choice significantly affects threshold inference.

Abstract

Threshold estimation is central to fault-tolerant quantum computing, but the reported threshold depends not only on the code and noise model, but also on the decoder used to interpret syndrome data. We study this dependence for surface-code threshold estimation under both a standard Pauli noise model and a hybrid continuous-variable/discrete model motivated by GKP-style digitization. Using LiDMaS+ as a common experimental platform, we compare minimum-weight perfect matching (MWPM) and Union-Find under matched sweep grids, matched distances, and deterministic seeding, and we additionally evaluate trained neural-guided MWPM in the hybrid regime. In the Pauli baseline at distance $d=5$, MWPM consistently outperforms Union-Find, reducing the mean sampled logical error rate from $0.384$ to $0.260$, and producing a stable threshold summary with crossing median $p_c \approx 0.053$. In the hybrid fixed-distance run, Union-Find is substantially worse than MWPM (mean LER $0.1657$ versus $0.1195$), while trained neural-guided MWPM tracks MWPM closely (mean LER $0.1158$). Across hybrid multi-distance sweeps, the distance-dependent reversal in logical-error ordering remains visible, but the grid-based crossing estimator still returns boundary-valued $\sigma_c=0.05$ for all decoders. Neural-guided runs also show elevated decoder-failure diagnostics at high noise ($\max$ decoder-failure rate $0.1335$ at $d=7,\sigma=0.60$), indicating that learned guidance quality and decoder robustness must be reported alongside threshold curves. These results show that decoder choice and estimator design both materially affect threshold inference.