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

Dennis Delali Kwesi Wayo, Chinonso Onah, Vladimir Milchakov, Leonardo Goliatt, Sven Groppe

TL;DR

Results show that decoder choice and estimator design both materially affect threshold inference and that learned guidance quality and decoder robustness must be reported alongside threshold curves.

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 $σ_c=0.05$ for all decoders. Neural-guided runs also show elevated decoder-failure diagnostics at high noise ($\max$ decoder-failure rate $0.1335$ at $d=7,σ=0.60$), 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.

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

TL;DR

Results show that decoder choice and estimator design both materially affect threshold inference and that learned guidance quality and decoder robustness must be reported alongside threshold curves.

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 , MWPM consistently outperforms Union-Find, reducing the mean sampled logical error rate from to , and producing a stable threshold summary with crossing median . In the hybrid fixed-distance run, Union-Find is substantially worse than MWPM (mean LER versus ), while trained neural-guided MWPM tracks MWPM closely (mean LER ). 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 for all decoders. Neural-guided runs also show elevated decoder-failure diagnostics at high noise ( decoder-failure rate at ), 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.
Paper Structure (24 sections, 15 equations, 3 figures, 6 tables, 4 algorithms)

This paper contains 24 sections, 15 equations, 3 figures, 6 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Research Contributions
  3. Background and Related Work
  4. LiDMaS+ as the Experimental Platform
  5. Methodology
  6. Noise Models
  7. Decoders Compared
  8. Threshold Estimation Protocol
  9. Algorithmic Summary
  10. Metrics
  11. Experimental Design
  12. Results
  13. Baseline Decoder Comparison
  14. Distance-Dependent Threshold Trends
  15. Crossing and Threshold Estimates
  16. ...and 9 more sections

Figures (3)

  • Figure 1: Closed-loop LiDMaS+ methodology used in this study. The run branches by noise mode and decoder, recombines for LER estimation and threshold analysis, and then evaluates optimization status. If settings are not optimized, the process loops back to reconfigure and rerun under the same reproducibility controls.
  • Figure 2: Fixed-distance decoder comparison under matched sweep settings. Panel (a) shows a clear MWPM advantage over Union-Find in the Pauli baseline. Panel (b) shows the hybrid $d=5$ comparison with three decoders, where Union-Find is clearly separated from MWPM and trained neural-guided MWPM.
  • Figure 3: Hybrid multi-distance logical-error curves for $d=3,5,7$ (MWPM view). The main effect is the reversal in distance ordering between the low- and high-$\sigma$ regimes; decoder-to-decoder differences are summarized in Table \ref{['tab:hybrid-multidistance-summary']}.