Decoder Dependence in Surface-Code Threshold Estimation with Native Gottesman-Kitaev-Preskill Digitization and Parallelized Sampling

Quantum Physics [Submitted on 25 Mar 2026] Decoder Dependence in Surface-Code Threshold Estimation with Native Gottesman-Kitaev-Preskill Digitization and Parallelized Sampling Dennis Delali Kwesi Wayo, Chinonso Onah, Vladimir Milchakov, Leonardo Goliatt, Sven Groppe We quantify decoder dependence in surface-code threshold studies under two matched regimes: Pauli noise and native GKP-style Gaussian displacement digitization. Using LiDMaS+ v1.1.0, we benchmark MWPM, Union-Find (UF), Belief Propagation (BP), and neural-guided MWPM with fixed seeds, identical sweep grids, and unified reporting across runs 06--14. At d=5 and \sigma=0.20, MWPM and UF define the Pareto frontier, with (runtime, LER) = (1.341 s, 0.2273) and (1.332 s, 0.2303); neural-guided MWPM is slower and less accurate (1.396 s, 0.3730), and BP is dominated (7.640 s, 0.6107). Crossing-bootstrap diagnostics are stable only for MWPM, with median \sigma^\star_{3,5}=0.10 (1911/2000 valid) and \sigma^\star_{5,7}=0.1375 (1941/2000 valid), while other decoders show no valid crossing samples. Dense-window scanning over \sigma \in [0.08,0.24] returns NaN crossings for all decoders, confirming estimator- and window-sensitive threshold localization. Rank-stability and effect-size bootstrap analyses reinforce ordering robustness: BP remains rank 4, neural-guided MWPM rank 3, and MWPM-UF differences are small (\Delta_{\mathrm{MWPM-UF}}=-0.00383, 95\% interval [-0.0104,0.00329]) across \sigma \in [0.05,0.35]. Threaded execution preserves statistical fidelity while improving throughput: 1.34\times speedup in Pauli mode and 1.94\times in native GKP mode, with mean |\Delta\mathrm{LER}| 6.07\times10^{-3} and 5.20\times10^{-3}, respectively. We therefore recommend estimator-conditional threshold reporting coupled to runtime-fidelity checks for reproducible hardware-facing practical future decoder benchmarking workflows. Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2603.25757 [quant-ph]   (or arXiv:2603.25757v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.25757 Focus to learn more Submission history From: Dennis Wayo [view email] [v1] Wed, 25 Mar 2026 18:07:04 UTC (82 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.IT math math.IT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)