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Paper 1
High-threshold decoding of non-Pauli codes for 2D universality
Julio C. Magdalena de la Fuente, Noa Feldman, Jens Eisert, Andreas Bauer
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2604.02033
- arXiv
- 2604.02033
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited connectivity. In this work, we explore a non-Pauli stabilizer code that can be used to complete a universal gate set on topological toric and surface codes in strictly two dimensions. Fault-tolerant syndrome extraction for the non-Pauli code requires mid-circuit $X$ corrections, a key difference to conventional Pauli codes. We construct and benchmark a just-in-time (JIT) matching decoder to reliably decide these corrections. Under a phenomenological error model with equally likely physical and measurement errors, we find a high threshold of $\approx 2.5\,\%$, close to the $\approx 2.9\,\%$ of a decoder with access to the full syndrome history. We also perform a finite-size scaling analysis to estimate how the logical error rate scales below threshold and verify an exponential suppression in both physical error rate and in the system size. A second global decoding step for $Z$ errors is required and the non-Clifford gates in the circuit reduce the threshold from $\approx 2.9\,\%$ to $\approx 1.8\,\%$ with a naive decoder. We show how $Z$ decoding can be improved using knowledge of the $X$ corrections, pushing the threshold to $\approx 2.2\,\%$. Our results suggest non-Clifford logic in 2D codes could perform comparably to 2D quantum memory. Our formalism for efficient benchmarking and decoding directly generalizes to a broader family of CSS codes whose $X$ stabilizers are twisted by diagonal Clifford operators, and spacetime versions thereof, defined by CSS-like circuits enriched by $CCZ$, $CS$, and $T$ gates.
Open paperPaper 2
Decoder Dependence in Surface-Code Threshold Estimation with Native Gottesman-Kitaev-Preskill Digitization and Parallelized Sampling
Dennis Delali Kwesi Wayo, Chinonso Onah, Leonardo Goliatt, Sven Groppe
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.25757
- arXiv
- 2603.25757
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 $σ=0.20$, 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 $σ^\star_{3,5}=0.10$ (1911/2000 valid) and $σ^\star_{5,7}=0.1375$ (1941/2000 valid), while other decoders show no valid crossing samples. Dense-window scanning over $σ\in [0.08,0.24]$ 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 ($Δ_{\mathrm{MWPM-UF}}=-0.00383$, 95\% interval $[-0.0104,0.00329]$) across $σ\in [0.05,0.35]$. 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 $|Δ\mathrm{LER}|$ $6.07\times10^{-3}$ 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.
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