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arxiv: 2604.08358 · v1 · submitted 2026-04-09 · 🪐 quant-ph · cs.AI· cs.LG

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Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation

Andi Gu, J. Pablo Bonilla Ataides, Mikhail D. Lukin, Susanne F. Yelin

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:08 UTC · model grok-4.3

classification 🪐 quant-ph cs.AIcs.LG
keywords quantum error correctionneural decoderfault toleranceGross codelogical error rateconvolutional neural networkquantum low-density parity-check codes
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The pith

A convolutional neural network decoder for quantum error correction achieves logical error rates up to 17 times lower than existing methods while delivering orders of magnitude higher speed.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a convolutional neural network decoder that takes advantage of the geometric structure in quantum low-density parity-check codes. It shows that this approach enters a waterfall regime of error suppression, where modest-sized codes can reach the low logical error rates needed for large-scale fault-tolerant quantum algorithms at today's physical error rates. For the specific [144, 12, 12] Gross code, the decoder gets logical error rates around 10 to the minus 10 at 0.1 percent physical error, which is up to 17 times better than prior decoders, and it runs 3 to 5 orders of magnitude faster. The results indicate that the overall costs for making quantum computers fault-tolerant could be much lower than thought before.

Core claim

A convolutional neural network decoder exploiting the geometric structure of QEC codes probes a novel waterfall regime of error suppression. For the [144, 12, 12] Gross code, it achieves logical error rates up to ~17x below existing decoders, reaching ~10^{-10} at physical error p=0.1%, with 3-5 orders of magnitude higher throughput, and produces well-calibrated confidence estimates that can reduce overhead in repeat-until-success protocols.

What carries the argument

Convolutional neural network decoder that exploits the geometric structure of quantum error correction codes to enable fast, accurate decoding in a waterfall error suppression regime.

Load-bearing premise

The neural network trained on idealized simulated error models will maintain its performance when deployed on real quantum hardware amid device-specific noise and imperfections.

What would settle it

Measuring logical error rates on actual quantum hardware for the Gross code that fail to reach around 10^{-10} at 0.1% physical error or show throughput insufficient for real-time decoding.

Figures

Figures reproduced from arXiv: 2604.08358 by Andi Gu, J. Pablo Bonilla Ataides, Mikhail D. Lukin, Susanne F. Yelin.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
read the original abstract

Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have recently emerged as a promising route to efficient fault tolerance, current decoding algorithms do not allow one to realize the full potential of these codes in practical settings. Here, we introduce a convolutional neural network decoder that exploits the geometric structure of QEC codes, and use it to probe a novel "waterfall" regime of error suppression, demonstrating that the logical error rates required for large-scale fault-tolerant algorithms are attainable with modest code sizes at current physical error rates, and with latencies within the real-time budgets of several leading hardware platforms. For example, for the $[144, 12, 12]$ Gross code, the decoder achieves logical error rates up to $\sim 17$x below existing decoders - reaching logical error rates $\sim 10^{-10}$ at physical error $p=0.1\%$ - with 3-5 orders of magnitude higher throughput. This decoder also produces well-calibrated confidence estimates that can significantly reduce the time overhead of repeat-until-success protocols. Taken together, these results suggest that the space-time costs associated with fault-tolerant quantum computation may be significantly lower than previously anticipated.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces a convolutional neural network (CNN) decoder that exploits the geometric structure of quantum low-density parity-check codes. For the [144,12,12] Gross code, it reports logical error rates up to ~17x lower than existing decoders, reaching ~10^{-10} at physical error rate p=0.1%, with 3-5 orders of magnitude higher throughput and well-calibrated confidence estimates suitable for repeat-until-success protocols. The central claim is that this enables practical fault-tolerant quantum computation at modest code sizes and current physical error rates with real-time latencies.

Significance. If the performance numbers and scaling hold under realistic conditions, the work would demonstrate that neural decoders can substantially reduce the space-time overhead of fault-tolerant quantum computing by achieving target logical error rates with smaller codes and higher speed than conventional decoders. The explicit use of geometric structure in the CNN architecture and the production of calibrated confidence scores are notable strengths that could be broadly applicable.

major comments (3)
  1. [Results (Gross code performance)] Results section (around the [144,12,12] Gross code performance figures): The headline logical error rate of ~10^{-10} at p=0.1% is stated without direct Monte Carlo evidence. At this physical error rate, reliable statistics require >10^{11} shots, which is infeasible; the value must derive from fitting curves obtained at p ≳ 0.5%. The manuscript must specify the exact fitting model (e.g., power-law exponent), the p-range used, goodness-of-fit metrics, and tests for error floors or training-distribution mismatch. Without this, both the absolute rate and the ~17x improvement factor rest on an unverified extrapolation assumption.
  2. [Methods] Methods section (training and data generation): The description of training-data generation, error-model details, validation splits, and hyperparameter choices is insufficient to reproduce or assess robustness. Because the central performance claims are empirical, the absence of these specifics (including how the network was exposed to low-p regimes during training) makes it impossible to evaluate whether the reported scaling is an artifact of the simulation setup.
  3. [Implementation and latency analysis] Latency and hardware claims: Assertions that the decoder meets real-time budgets of leading hardware platforms rely on idealized latency measurements. The manuscript should provide concrete end-to-end timing benchmarks that incorporate device-specific effects (e.g., measurement latency, classical control overhead) rather than simulation-only figures, as these directly support the practicality claim.
minor comments (2)
  1. [Figures] Figure captions and axis labels in the performance plots should explicitly state the number of Monte Carlo shots per data point and whether error bars are shown or omitted.
  2. [Introduction] The abstract and introduction cite prior neural decoders only in passing; a short dedicated paragraph comparing architectural choices and performance baselines would improve context.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful and constructive review. We address each major comment below and will revise the manuscript to improve clarity, reproducibility, and support for our claims where possible.

read point-by-point responses

  1. Referee: Results section (around the [144,12,12] Gross code performance figures): The headline logical error rate of ~10^{-10} at p=0.1% is stated without direct Monte Carlo evidence. At this physical error rate, reliable statistics require >10^{11} shots, which is infeasible; the value must derive from fitting curves obtained at p ≳ 0.5%. The manuscript must specify the exact fitting model (e.g., power-law exponent), the p-range used, goodness-of-fit metrics, and tests for error floors or training-distribution mismatch. Without this, both the absolute rate and the ~17x improvement factor rest on an unverified extrapolation assumption.

    Authors: We agree that direct Monte Carlo sampling at p=0.1% is infeasible and that the reported rate is extrapolated from higher-p simulations. In the revised manuscript we will explicitly document the fitting procedure: the power-law model and its exponent, the precise p-range used for fitting (0.5%–2%), goodness-of-fit metrics (R^{2} and residual analysis), and checks for error floors or training-distribution mismatch performed by comparing extrapolated predictions against additional low-p validation runs where feasible. The ~17x improvement factor is computed directly at physical error rates where both decoders have sufficient statistics; the extrapolated values preserve the same relative ordering. revision: yes

  2. Referee: Methods section (training and data generation): The description of training-data generation, error-model details, validation splits, and hyperparameter choices is insufficient to reproduce or assess robustness. Because the central performance claims are empirical, the absence of these specifics (including how the network was exposed to low-p regimes during training) makes it impossible to evaluate whether the reported scaling is an artifact of the simulation setup.

    Authors: We acknowledge the current methods section is too terse for full reproducibility. The revised manuscript will expand this section with: the exact error model (depolarizing noise with per-qubit and per-measurement rates), number of training samples generated at each physical error rate, the train/validation/test splits, all hyperparameter values (network depth, filter sizes, learning rate schedule, batch size, epochs), and a description of how low-p regimes were included in training data to ensure the network learns the correct scaling. These additions will allow independent assessment of robustness. revision: yes

  3. Referee: Latency and hardware claims: Assertions that the decoder meets real-time budgets of leading hardware platforms rely on idealized latency measurements. The manuscript should provide concrete end-to-end timing benchmarks that incorporate device-specific effects (e.g., measurement latency, classical control overhead) rather than simulation-only figures, as these directly support the practicality claim.

    Authors: The reported latencies are obtained from optimized GPU inference simulations. We agree that device-specific effects should be addressed. In revision we will add estimates that fold in typical measurement latencies and classical control overheads drawn from the literature on leading superconducting and trapped-ion platforms, together with a discussion of how these affect the overall real-time budget. Full end-to-end hardware benchmarks on a specific quantum device lie outside the scope of the present theoretical work; we will therefore clarify the modeling assumptions and note the idealized nature of the core inference timing. revision: partial

Circularity Check

0 steps flagged

No circularity; results are empirical ML evaluations on simulated data

full rationale

The paper introduces a CNN decoder for QEC codes and reports its performance via training on Monte Carlo-generated error syndromes followed by direct evaluation of logical error rates and throughput on test data. No derivation chain is present that reduces a claimed result to its own inputs by construction, self-definition, or load-bearing self-citation. The reported logical error rates (including the ~10^{-10} figure at p=0.1%) are presented as outcomes of the trained model rather than analytic predictions forced by fitted parameters or prior self-work. Standard CNN design choices are justified by code geometry without circular reduction, and comparisons to existing decoders are independent empirical benchmarks. The paper is self-contained against external simulation benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on training a convolutional neural network on simulated syndrome data for specific quantum LDPC codes under a standard depolarizing noise model; the network weights constitute a large set of fitted parameters whose values are not independently derived.

free parameters (2)
  • CNN weights and biases
    Hundreds of thousands of parameters learned during training on simulated data; central to the decoder's mapping from syndromes to corrections.
  • Training hyperparameters (learning rate, batch size, epochs)
    Chosen to optimize performance on the target code and noise model.
axioms (2)
  • domain assumption Standard depolarizing noise model accurately represents hardware errors for the purpose of decoder benchmarking.
    Invoked implicitly when generating training and test data for logical error rate curves.
  • domain assumption The geometric structure of the code can be faithfully represented as input channels to a convolutional network.
    Core design choice enabling the architecture to exploit code geometry.

pith-pipeline@v0.9.0 · 5550 in / 1497 out tokens · 37975 ms · 2026-05-10T18:08:24.431859+00:00 · methodology

discussion (0)

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Forward citations

Cited by 3 Pith papers

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