{
  "id": "oai:papers.qnfo.org:thermodynamic-feedback-limits-on-the-scalability-of-surface-code-quantum-error-c",
  "slug": "thermodynamic-feedback-limits-on-the-scalability-of-surface-code-quantum-error-c",
  "title": "Thermodynamic Feedback Limits on the Scalability of Surface‑Code Quantum Error Correction",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Quantum error correction (QEC) is essential for fault‑tolerant quantum computation, yet the control electronics, wiring, and cryogenic heat load required for each correction cycle generate heat that raises the qubit temperature and thereby increases the intrinsic physical error rate. This creates a positive feedback loop—an error‑correction chasm—that can preclude scalable fault tolerance. We couple a standard surface‑code threshold model to a thermodynamic budget by (i) expressing the logical error probability p_L as a function of the physical error probability p, (ii) relating p to the qubit temperature T through an Arrhenius‑type law, and (iii) linking T to the dissipated power per qubit via a thermal resistance and, alternatively, via a heat‑capacity model. Solving the resulting fixed‑point equations yields two quantitative scenarios. In a realistic low‑power scenario (per‑qubit power P_q=10^-6 W, thermal resistance R_th=5 mathrmK W^-1) the critical temperature rise is Δ T_crit≈23.0 K and the maximum qubit count is N_max=10⁶. In a heat‑capacity‑limited scenario (per‑cycle heat q_tot=1.5×10^-12 J, volumetric heat capacity c=2×10^-3 mathrmJ K^-1 cm^-3, qubit volume v=10^-12 mathrmcm³) the temperature rise per cycle is Δ T≈7.5×10² K, driving the physical error probability to p≈1.25×10^-2 and rendering the feedback loop unstable. The analysis shows that, under current hardware assumptions, thermodynamic feedback imposes a hard ceiling on scalable QEC. The result guides hardware architects toward ultra‑low‑power designs and motivates experimental validation of the temperature‑error feedback loop.",
  "abstract_markdown": "Quantum error correction (QEC) is essential for fault‑tolerant quantum computation, yet the control electronics, wiring, and cryogenic heat load required for each correction cycle generate heat that raises the qubit temperature and thereby increases the intrinsic physical error rate. This creates a positive feedback loop—an *error‑correction chasm*—that can preclude scalable fault tolerance. We couple a standard surface‑code threshold model to a thermodynamic budget by (i) expressing the logical error probability \\(p_{\\mathrm{L}}\\) as a function of the physical error probability \\(p\\), (ii) relating \\(p\\) to the qubit temperature \\(T\\) through an Arrhenius‑type law, and (iii) linking \\(T\\) to the dissipated power per qubit via a thermal resistance and, alternatively, via a heat‑capacity model. Solving the resulting fixed‑point equations yields two quantitative scenarios. In a realistic low‑power scenario (per‑qubit power \\(P_{\\mathrm{q}}=10^{-6}\\,\\mathrm{W}\\), thermal resistance \\(R_{\\mathrm{th}}=5\\,\\mathrm{K\\,W^{-1}}\\)) the critical temperature rise is \\(\\Delta T_{\\mathrm{crit}}\\approx23.0\\,\\mathrm{K}\\) and the maximum qubit count is \\(N_{\\max}=10^{6}\\). In a heat‑capacity‑limited scenario (per‑cycle heat \\(q_{\\text{tot}}=1.5\\times10^{-12}\\,\\mathrm{J}\\), volumetric heat capacity \\(c=2\\times10^{-3}\\,\\mathrm{J\\,K^{-1}\\,cm^{-3}}\\), qubit volume \\(v=10^{-12}\\,\\mathrm{cm^{3}}\\)) the temperature rise per cycle is \\(\\Delta T\\approx7.5\\times10^{2}\\,\\mathrm{K}\\), driving the physical error probability to \\(p\\approx1.25\\times10^{-2}\\) and rendering the feedback loop unstable. The analysis shows that, under current hardware assumptions, thermodynamic feedback imposes a hard ceiling on scalable QEC. The result guides hardware architects toward ultra‑low‑power designs and motivates experimental validation of the temperature‑error feedback loop.",
  "date": "2026-10-26",
  "first_published": "2026-10-26",
  "last_revised": "2026-10-26T00:00:00Z",
  "modified": "2026-10-26T00:00:00Z",
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  "language": "en",
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    "High-quality scholarly research",
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  "quality_label": "High-quality scholarly research",
  "quality_basis": "QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
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  "peer_review_status": "Not independently peer-reviewed",
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  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/thermodynamic-feedback-limits-on-the-scalability-of-surface-code-quantum-error-c",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
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        "identifier": "https://papers.qnfo.org/papers/thermodynamic-feedback-limits-on-the-scalability-of-surface-code-quantum-error-c",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Thermodynamic Feedback Limits on the Scalability of Surface‑Code Quantum Error Correction"
      }
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    "publicationYear": "2026",
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    "dates": [
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        "date": "2026-10-26",
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        "date": "2026-10-26",
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        "description": "Quantum error correction (QEC) is essential for fault‑tolerant quantum computation, yet the control electronics, wiring, and cryogenic heat load required for each correction cycle generate heat that raises the qubit temperature and thereby increases the intrinsic physical error rate. This creates a positive feedback loop—an error‑correction chasm—that can preclude scalable fault tolerance. We couple a standard surface‑code threshold model to a thermodynamic budget by (i) expressing the logical error probability p_L as a function of the physical error probability p, (ii) relating p to the qubit temperature T through an Arrhenius‑type law, and (iii) linking T to the dissipated power per qubit via a thermal resistance and, alternatively, via a heat‑capacity model. Solving the resulting fixed‑point equations yields two quantitative scenarios. In a realistic low‑power scenario (per‑qubit power P_q=10^-6 W, thermal resistance R_th=5 mathrmK W^-1) the critical temperature rise is Δ T_crit≈23.0 K and the maximum qubit count is N_max=10⁶. In a heat‑capacity‑limited scenario (per‑cycle heat q_tot=1.5×10^-12 J, volumetric heat capacity c=2×10^-3 mathrmJ K^-1 cm^-3, qubit volume v=10^-12 mathrmcm³) the temperature rise per cycle is Δ T≈7.5×10² K, driving the physical error probability to p≈1.25×10^-2 and rendering the feedback loop unstable. The analysis shows that, under current hardware assumptions, thermodynamic feedback imposes a hard ceiling on scalable QEC. The result guides hardware architects toward ultra‑low‑power designs and motivates experimental validation of the temperature‑error feedback loop.",
        "descriptionType": "Abstract"
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