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Paper 1

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

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

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.06730

arXiv

2603.06730

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.

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Paper 2

Overcoming the Trade-Off between Initial Coulombic Efficiency and Rate Performance in Hard Carbon Anodes for Sodium-Ion Storage.

Li Z, Gao Y, Luo W, Xu Z, Wu J, Wang Y, Zhang K, Chen R, Lu Z, Wang HL

Year

2026

Journal

ACS nano

DOI

10.1021/acsnano.5c17936

arXiv

-

Hard carbon (HC) has emerged as a promising anode for sodium-ion batteries owing to its low-voltage plateau and cost-effectiveness. However, HC anodes still suffer from a performance trade-off between the initial Coulombic efficiency (ICE) and rate capability. To address this issue, we propose a scalable synthesis method, the melt-spinning technique (kilogram scale) with a hexamethylenetetramine (HMTA) cross-linking-oxidation strategy, to multidimensionally regulate the structure of phenolic resin-derived hard carbon (CPF-1400) as high-performance anodes. Experimental studies demonstrate that the spatially cross-linked precursor with methylene bridge (-CH-) and rich carbonyl groups (C═O) effectively suppresses excessive graphitization (even at 1400 °C) and enlarges the spacing of carbon interlayers from 0.367 to 0.381 nm. Additionally, it enables the reduction of the specific surface area to merely 1.4 m g and generates abundant and suitable-sized closed pores (0.315 cm g, 1.26 nm) for CPF-1400. Therefore, CPF-1400 delivers an exceptional reversible sodium storage capacity of 431 mAh g with an unprecedentedly high ICE of 95%. Notably, it also retains a rate capability of 308 mAh g at 1 A g, and it achieves a high energy density of 293 Wh kg assembled in full cells. Electrochemical analyses combined with in situ characterizations demonstrate a three-stage sodium storage mechanism in hard carbon and elucidate the correlation between the solid-electrolyte interphase (SEI) and battery performance.

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