{
  "id": "oai:papers.qnfo.org:code-agnostic-graph-neural-network-decoding-from-detection-error-models-a-reconc",
  "slug": "code-agnostic-graph-neural-network-decoding-from-detection-error-models-a-reconc",
  "title": "Code-Agnostic Graph Neural Network Decoding from Detection Error Models: A Reconciled Quantitative and Structural Assessment",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Graph neural network (GNN) decoders for quantum error correction have traditionally been tied to specific code families through their input representations. The POLYMECHANON decoder [1, 2] proposes a contract in which the sole input is the detection error model (DEM)—a tripartite graph of detectors, error mechanisms, and logical observables—thereby treating the code as data rather than as an architectural choice. This paper provides an independent, arithmetic‑first assessment of that claim. We translate the reported headline percentages into concrete quantities: a 25 % reduction in logical failures versus correlated MWPM on the rotated surface code yields an improvement factor 0.75, which under the standard sub‑threshold scaling ansatz p_L∝(p/p_th)^lceil d/2rceil corresponds to a relative pseudo‑threshold improvement of ≈ 10.06 % at d=5 and ≈ 7.46 % at d=7; a 16 % reduction on the [[130,4,6]] qLDPC code gives a factor 0.84 and an equivalent threshold improvement of ≈ 5.98 %. Assuming “a few ms’’ per shot on a GPU and “a few tens of ms’’ on a CPU, the speedup is bounded in [4×,25×] with a midpoint of ≈ 10×. We derive exact DEM graph sizes for canonical cases (441 detectors, 1 337 mechanisms, 2 681 edges at d=8, R=8), present a cheap non‑isomorphism certificate between surface‑code and qLDPC DEMs, and show that the reported post‑selection result (>10× error reduction at >90 % shot retention) requires discarded shots to fail at ≈ 9.1× the base logical error rate. Size‑generalization, DEM fidelity, and hardware‑asymmetric latency comparison emerge as the principal open risks, each paired with a falsifiable experiment.",
  "abstract_markdown": "Graph neural network (GNN) decoders for quantum error correction have traditionally been tied to specific code families through their input representations. The POLYMECHANON decoder [1, 2] proposes a contract in which the sole input is the detection error model (DEM)—a tripartite graph of detectors, error mechanisms, and logical observables—thereby treating the code as data rather than as an architectural choice. This paper provides an independent, arithmetic‑first assessment of that claim. We translate the reported headline percentages into concrete quantities: a 25 % reduction in logical failures versus correlated MWPM on the rotated surface code yields an improvement factor 0.75, which under the standard sub‑threshold scaling ansatz $p_L\\propto(p/p_{\\mathrm{th}})^{\\lceil d/2\\rceil}$ corresponds to a relative pseudo‑threshold improvement of $\\approx 10.06$ % at $d=5$ and $\\approx 7.46$ % at $d=7$; a 16 % reduction on the $[[130,4,6]]$ qLDPC code gives a factor 0.84 and an equivalent threshold improvement of $\\approx 5.98$ %. Assuming “a few ms’’ per shot on a GPU and “a few tens of ms’’ on a CPU, the speedup is bounded in $[4\\times,25\\times]$ with a midpoint of $\\approx 10$×. We derive exact DEM graph sizes for canonical cases (441 detectors, 1 337 mechanisms, 2 681 edges at $d=8$, $R=8$), present a cheap non‑isomorphism certificate between surface‑code and qLDPC DEMs, and show that the reported post‑selection result (>10× error reduction at >90 % shot retention) requires discarded shots to fail at $\\approx 9.1$× the base logical error rate. Size‑generalization, DEM fidelity, and hardware‑asymmetric latency comparison emerge as the principal open risks, each paired with a falsifiable experiment.",
  "date": "2026-10-04",
  "first_published": "2026-10-04",
  "last_revised": "2026-10-19T12:11:04Z",
  "modified": "2026-10-19T12:11:04Z",
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  "url": "https://papers.qnfo.org/papers/code-agnostic-graph-neural-network-decoding-from-detection-error-models-a-reconc",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "Code-Agnostic Graph Neural Network Decoding from Detection Error Models: A Reconciled Quantitative and Structural Assessment"
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        "description": "Graph neural network (GNN) decoders for quantum error correction have traditionally been tied to specific code families through their input representations. The POLYMECHANON decoder [1, 2] proposes a contract in which the sole input is the detection error model (DEM)—a tripartite graph of detectors, error mechanisms, and logical observables—thereby treating the code as data rather than as an architectural choice. This paper provides an independent, arithmetic‑first assessment of that claim. We translate the reported headline percentages into concrete quantities: a 25 % reduction in logical failures versus correlated MWPM on the rotated surface code yields an improvement factor 0.75, which under the standard sub‑threshold scaling ansatz p_L∝(p/p_th)^lceil d/2rceil corresponds to a relative pseudo‑threshold improvement of ≈ 10.06 % at d=5 and ≈ 7.46 % at d=7; a 16 % reduction on the [[130,4,6]] qLDPC code gives a factor 0.84 and an equivalent threshold improvement of ≈ 5.98 %. Assuming “a few ms’’ per shot on a GPU and “a few tens of ms’’ on a CPU, the speedup is bounded in [4×,25×] with a midpoint of ≈ 10×. We derive exact DEM graph sizes for canonical cases (441 detectors, 1 337 mechanisms, 2 681 edges at d=8, R=8), present a cheap non‑isomorphism certificate between surface‑code and qLDPC DEMs, and show that the reported post‑selection result (>10× error reduction at >90 % shot retention) requires discarded shots to fail at ≈ 9.1× the base logical error rate. Size‑generalization, DEM fidelity, and hardware‑asymmetric latency comparison emerge as the principal open risks, each paired with a falsifiable experiment.",
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