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arxiv: 2605.17156 · v2 · pith:VJI5DX6Cnew · submitted 2026-05-16 · 🪐 quant-ph · cs.LG

Sparse Mamba Decoder for Quantum Error Correction: Efficient Defect-Centric Processing of Surface Code Syndromes

Samira Sayedsalehi , Nader Bagherzadeh , Maxim Shcherbakov , Jean-Luc Gaudiot This is my paper

Pith reviewed 2026-05-22 09:36 UTC · model grok-4.3

classification 🪐 quant-ph cs.LG
keywords quantum error correctionsurface codesparse decoderMamba modeldefect processingneural decoderfault-tolerant quantum computingsyndrome decoding
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The pith

A sparse Mamba decoder for surface codes processes only active detection events to reach O(k) complexity while cutting logical error rates versus MWPM.

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

The paper introduces the Sparse Mamba Decoder that ignores the vast majority of empty syndrome entries and works only with the small number of active defects. It assigns each defect a fixed 13-dimensional feature vector and feeds the sequence into a Mamba state-space backbone. This yields linear scaling in the number of errors rather than quadratic scaling in the code distance. The approach is shown to improve accuracy over minimum-weight perfect matching on several noise models and to run orders of magnitude faster than existing high-performance decoders while keeping microsecond-scale latency as the distance grows.

Core claim

The Sparse Mamba Decoder processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving O(k) complexity. Across depolarizing, uniform circuit-level, SI1000, and Google Sycamore experimental benchmarks, it reduces the MWPM logical error rate by up to 49% at d ≤ 5 under SI1000 noise, runs 95-467x faster than the Tesseract near-MLD decoder and 232-463x faster than Belief Matching, and maintains nearly constant latency (24-57 us) across d = 3-9 under uniform circuit-level noise.

What carries the argument

Defect-centric processing that encodes each active detection event with a fixed 13-dimensional feature vector and routes the resulting sparse sequence through a Mamba state-space model.

If this is right

  • Reduces logical error rate by up to 49 percent compared with MWPM at small distances under SI1000 noise.
  • Delivers 95-467x speedup over Tesseract and 232-463x speedup over Belief Matching.
  • Keeps latency nearly constant between 24 and 57 microseconds as code distance increases from 3 to 9.
  • Matches or slightly exceeds the accuracy of a dense Mamba decoder on real Sycamore experimental data.
  • Runs on commodity GPUs with only 7.5-16 million parameters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same sparse-event strategy could be applied to larger-distance codes where the fraction of active defects stays small at realistic physical error rates.
  • The method may transfer to other quantum error-correcting codes whose syndrome graphs are also sparse.
  • Hardware implementations could exploit the O(k) scaling to keep decoding latency inside the coherence time of near-term devices.
  • State-space models such as Mamba appear well matched to the sequential, low-density nature of defect streams in quantum error correction.

Load-bearing premise

A fixed 13-dimensional feature representation per defect plus the Mamba backbone captures every relevant spatial and temporal correlation in the full syndrome volume without any loss of decoding accuracy.

What would settle it

A direct comparison at code distances d greater than 9 or under noise models not tested in the paper that shows the Sparse Mamba Decoder's logical error rate rising above a full-syndrome neural decoder or a high-accuracy classical decoder such as Tesseract.

Figures

Figures reproduced from arXiv: 2605.17156 by Jean-Luc Gaudiot, Maxim Shcherbakov, Nader Bagherzadeh, Samira Sayedsalehi.

Figure 1
Figure 1. Figure 1: a) Planar layout of a rotated surface code with code distance [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Sparse Mamba Decoder architecture. (a) Sparse defect extraction from a (d 2−1) × R syndrome volume to k defect tokens d1, . . . , dk (k ≪ d 2R at physically relevant error rates). (b) 13-dimensional feature vector per defect: spatial coordinates (x, y), normalized time t/R, stabilizer type τ , spatial and temporal neighbor flags, boundary distances bZ, bX, and the reconstructed measurement mi,t from cumula… view at source ↗
Figure 3
Figure 3. Figure 3: Logical error rate under depolarizing noise with perfect stabilizer measurements. The [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Logical error rate under uniform circuit-level noise with [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Mean logical error per round on the Google Sycamore experimental dataset at code [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Speed–accuracy Pareto front for MWPM, Belief Matching, Tesseract, and SMD at [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Speed–accuracy Pareto front under uniform circuit-level noise at [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
read the original abstract

Quantum error correction (QEC) is essential for building fault-tolerant quantum computers, requiring decoders that are simultaneously accurate, fast, and scalable. Most state-of-the-art neural decoders achieve high accuracy but process the full dense syndrome array of size $O(d^2 R) $regardless of the actual error rate, where d is the code distance and R is the number of measurement rounds. At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events -- yet existing decoders process the entire syndrome volume. We introduce the Sparse Mamba Decoder (SMD), a defect-centric neural decoder that processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving $O(k)$ complexity. Across depolarizing, uniform circuit-level, SI1000, and Google Sycamore experimental benchmarks, SMD reduces the MWPM logical error rate by up to 49% at $d \le 5$ under SI1000 noise, runs 95-467x faster than the Tesseract near-MLD decoder and 232-463x faster than Belief Matching, and maintains nearly constant latency (24-57 us) across d = 3-9 under uniform circuit-level noise. On the Sycamore experimental dataset, the SMD ensemble matches or slightly surpasses the dense Mamba decoder of Varbanov et al. All results are obtained on commodity NVIDIA GPUs with 7.5-16M parameters, without specialized accelerators.

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 / 3 minor

Summary. The manuscript introduces the Sparse Mamba Decoder (SMD), a neural decoder for surface-code quantum error correction that operates in a defect-centric manner. Instead of processing the full dense syndrome volume of size O(d²R), SMD extracts only the k active detection events, encodes each with a fixed 13-dimensional feature vector (coordinates, timestamp, parity information), and feeds the resulting sequence into a Mamba state-space backbone. The authors report O(k) complexity, up to 49% reduction in logical error rate versus MWPM at d ≤ 5 under SI1000 noise, 95–467× speedups over Tesseract, and nearly constant 24–57 µs latency for d = 3–9. Results are presented on depolarizing, circuit-level, SI1000, and Google Sycamore experimental data, with model sizes of 7.5–16 M parameters.

Significance. If the reported accuracy and scaling hold, the work would constitute a meaningful advance toward real-time, scalable decoders for fault-tolerant quantum computing. The shift from dense to sparse, event-driven processing directly addresses the inefficiency of current neural decoders at low physical error rates, where most syndrome bits are inactive. The application of Mamba to defect sequences is a technically interesting choice that could generalize to other sparse QEC settings. The concrete speed and latency numbers on commodity GPUs strengthen the practical relevance, provided the accuracy claims survive detailed scrutiny of training protocols and feature sufficiency.

major comments (3)
  1. [Abstract and §4.2] Abstract and §4.2: The central claim that a fixed 13-dimensional per-defect feature vector plus Mamba backbone recovers (or exceeds) the accuracy of dense decoders rests on the untested assumption that these 13 dimensions encode all relevant spatial-temporal correlations. No ablation is shown that varies the feature set or compares directly against a dense Mamba baseline at d > 5; if higher-order correlations are lost, the reported 49% logical-error improvement and parity with the dense decoder would not generalize.
  2. [§5.1 and Table 2] §5.1 and Table 2: The training procedure, hyperparameter search, data-split rules, and statistical error bars on the logical-error-rate numbers are not described. Without these details it is impossible to verify that the 49% improvement versus MWPM and the speedups versus Tesseract are reproducible and not artifacts of particular random seeds or benchmark subsets.
  3. [§6.3] §6.3: The latency measurements (24–57 µs) are reported as nearly constant across d = 3–9, yet the paper does not specify whether this includes the full pipeline (defect extraction, feature construction, Mamba inference, and final correction mapping) or only the neural-network forward pass. This distinction is load-bearing for the claimed real-time applicability.
minor comments (3)
  1. [Figure 3] Figure 3: The caption does not state the number of Monte Carlo shots used to generate each data point or whether error bars represent standard error or 95% confidence intervals.
  2. [§3.1] §3.1: The exact definition of the 13-dimensional feature vector is given only in prose; a compact table listing each component and its normalization would improve reproducibility.
  3. [References] References: Several recent works on sparse or event-driven decoders (e.g., recent neural MWPM hybrids) are cited only in passing; a short related-work paragraph would better situate the contribution.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive review of our manuscript. We appreciate the recognition of the potential significance of the Sparse Mamba Decoder for scalable quantum error correction. Below, we provide point-by-point responses to the major comments and indicate the revisions made to address them.

read point-by-point responses

  1. Referee: [Abstract and §4.2] The central claim that a fixed 13-dimensional per-defect feature vector plus Mamba backbone recovers (or exceeds) the accuracy of dense decoders rests on the untested assumption that these 13 dimensions encode all relevant spatial-temporal correlations. No ablation is shown that varies the feature set or compares directly against a dense Mamba baseline at d > 5; if higher-order correlations are lost, the reported 49% logical-error improvement and parity with the dense decoder would not generalize.

    Authors: We acknowledge that an explicit ablation study on the feature set would provide additional validation. The 13 features were selected based on standard QEC literature to capture position, time, parity, and local syndrome information necessary for decoding. On the Google Sycamore experimental dataset, our model matches or exceeds the performance of the dense Mamba decoder from Varbanov et al., suggesting that the sparse representation retains the essential correlations. However, we agree that a direct comparison at larger d is valuable and have added a limited ablation study in the revised §4.2 comparing subsets of features. A full dense Mamba baseline at d>5 was not feasible due to memory constraints, but we discuss this limitation and provide scaling arguments in the updated manuscript. revision: partial

  2. Referee: [§5.1 and Table 2] The training procedure, hyperparameter search, data-split rules, and statistical error bars on the logical-error-rate numbers are not described. Without these details it is impossible to verify that the 49% improvement versus MWPM and the speedups versus Tesseract are reproducible and not artifacts of particular random seeds or benchmark subsets.

    Authors: We thank the referee for pointing this out. In the revised manuscript, we have expanded §5.1 to fully describe the training procedure, including the hyperparameter search method (grid search over learning rate, batch size, and model dimensions), data-split rules (80/10/10 train/validation/test with no overlap in error configurations), and added statistical error bars to Table 2 based on 10 independent training runs with different random seeds. These details ensure reproducibility of the reported improvements. revision: yes

  3. Referee: [§6.3] The latency measurements (24–57 µs) are reported as nearly constant across d = 3–9, yet the paper does not specify whether this includes the full pipeline (defect extraction, feature construction, Mamba inference, and final correction mapping) or only the neural-network forward pass. This distinction is load-bearing for the claimed real-time applicability.

    Authors: We apologize for the ambiguity. The reported latency figures include the complete end-to-end pipeline: defect extraction from the syndrome, construction of the 13-feature vectors, Mamba model inference, and mapping to the final correction. We have clarified this explicitly in the revised §6.3, including a breakdown of the time contributions from each stage to demonstrate that the neural inference dominates but the overall latency remains suitable for real-time decoding. revision: yes

Circularity Check

0 steps flagged

No circularity in Sparse Mamba Decoder claims; performance is empirically benchmarked

full rationale

The paper introduces an architectural design that processes only active detection events via a fixed 13-dimensional per-defect feature vector and Mamba backbone to achieve O(k) complexity. This is a direct consequence of the input representation choice rather than a derived prediction that reduces to fitted quantities by construction. All reported gains (up to 49% logical error reduction vs MWPM, 95-467x speedup vs Tesseract) are external empirical measurements on depolarizing, SI1000, circuit-level, and Sycamore experimental data, compared against independent baselines. No equations, self-citations, or uniqueness theorems are invoked to force the results; the 13-dim features and accuracy claims remain testable assumptions validated outside the model's own definitions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on trained neural-network weights and the modeling assumption that sparse local features suffice for global decoding accuracy.

free parameters (1)
  • Neural network weights
    7.5-16 million parameters fitted during training on syndrome data.
axioms (1)
  • domain assumption A 13-dimensional feature vector per defect is informationally sufficient for accurate decoding.
    Invoked by the choice of sparse input representation in the decoder design.

pith-pipeline@v0.9.0 · 5834 in / 1301 out tokens · 47264 ms · 2026-05-22T09:36:52.919421+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We introduce the Sparse Mamba Decoder (SMD), a defect-centric neural decoder that processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving O(k) complexity.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Each active detection event is represented by a 13-dimensional feature vector encoding spatial coordinates on the rotated lattice, stabilizer type (X or Z), spatial and temporal neighborhood connectivity flags, normalized distances to the logical boundaries, and a reconstructed stabilizer measurement computed via cumulative XOR.

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The paper appears to rely on the theorem as machinery.
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unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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