{
  "id": "oai:papers.qnfo.org:thermodynamic-scaling-limit-of-active-quantum-error-correction",
  "slug": "thermodynamic-scaling-limit-of-active-quantum-error-correction",
  "title": "Thermodynamic Scaling Limit of Active Quantum Error Correction",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Active quantum error correction (QEC) underpins fault‑tolerant quantum computation, yet its control circuitry dissipates heat that must be removed by cryogenic infrastructure. A hard scalability limit arises when the localized power density generated by control pulses exceeds the Kapitza thermal conductance between the qubit substrate and its coolant, causing a runaway temperature rise that destroys coherence. We identify this limit by extending the Caldeira–Leggett model to include a dissipative control term P_rm local=N_q ν_rm cycle ε_q+I²R and the substrate temperature response Δ T_rm local=P_rm local/(A H_K). Using experimentally motivated parameters (ε_q=10^-9J per qubit per cycle, τ_c=10^-6s, qubit pitch a=10^-4m, and a representative Kapitza conductance H_K=10⁴W·m^-2·K^-1), we derive a critical qubit density ρ_rm crit= fracΔ T_rm crit H_Kν_rm cycle ε_q ≈ 3×10⁶ rm qubits m^-2 for a temperature‑rise threshold Δ T_rm crit=0.3K at a base temperature of 0.3K. Above this density the substrate cannot evacuate heat fast enough, leading to a thermal phase transition that overwhelms decoherence suppression. The result predicts a thermodynamic ceiling for gate‑based QEC architectures and motivates a shift toward passive, topologically protected substrates that avoid active control heating.",
  "abstract_markdown": "Active quantum error correction (QEC) underpins fault‑tolerant quantum computation, yet its control circuitry dissipates heat that must be removed by cryogenic infrastructure. A hard scalability limit arises when the localized power density generated by control pulses exceeds the Kapitza thermal conductance between the qubit substrate and its coolant, causing a runaway temperature rise that destroys coherence. We identify this limit by extending the Caldeira–Leggett model to include a dissipative control term $P_{\\rm local}=N_q\\,\\nu_{\\rm cycle}\\,\\varepsilon_q+I^{2}R$ and the substrate temperature response $\\Delta T_{\\rm local}=P_{\\rm local}/(A\\,H_{K})$. Using experimentally motivated parameters ($\\varepsilon_q=10^{-9}\\,$J per qubit per cycle, $\\tau_c=10^{-6}\\,$s, qubit pitch $a=10^{-4}\\,$m, and a representative Kapitza conductance $H_{K}=10^{4}\\,$W·m$^{-2}$·K$^{-1}$), we derive a critical qubit density  \n\\[\n\\rho_{\\rm crit}= \\frac{\\Delta T_{\\rm crit}\\,H_{K}}{\\nu_{\\rm cycle}\\,\\varepsilon_q}\n\\approx 3\\times10^{6}\\ {\\rm qubits\\;m^{-2}}\n\\] \nfor a temperature‑rise threshold $\\Delta T_{\\rm crit}=0.3\\,$K at a base temperature of $0.3\\,$K. Above this density the substrate cannot evacuate heat fast enough, leading to a thermal phase transition that overwhelms decoherence suppression. The result predicts a thermodynamic ceiling for gate‑based QEC architectures and motivates a shift toward passive, topologically protected substrates that avoid active control heating.",
  "date": "2026-10-20",
  "first_published": "2026-10-20",
  "last_revised": "2026-10-20T00:00:00Z",
  "modified": "2026-10-20T00:00:00Z",
  "version": "1.0.0",
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  "language": "en",
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  "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-scaling-limit-of-active-quantum-error-correction",
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  "sha256": "68bfc2df6dd870c0a539fa49ac1e31e9356c1aa82bfee534bb922ae60134021b",
  "version_url": "https://papers.qnfo.org/papers/thermodynamic-scaling-limit-of-active-quantum-error-correction/v/1.0.0",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Thermodynamic Scaling Limit of Active Quantum Error Correction"
      }
    ],
    "publisher": "QNFO",
    "publicationYear": "2026",
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    "dates": [
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        "date": "2026-10-20",
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        "description": "Active quantum error correction (QEC) underpins fault‑tolerant quantum computation, yet its control circuitry dissipates heat that must be removed by cryogenic infrastructure. A hard scalability limit arises when the localized power density generated by control pulses exceeds the Kapitza thermal conductance between the qubit substrate and its coolant, causing a runaway temperature rise that destroys coherence. We identify this limit by extending the Caldeira–Leggett model to include a dissipative control term P_rm local=N_q ν_rm cycle ε_q+I²R and the substrate temperature response Δ T_rm local=P_rm local/(A H_K). Using experimentally motivated parameters (ε_q=10^-9J per qubit per cycle, τ_c=10^-6s, qubit pitch a=10^-4m, and a representative Kapitza conductance H_K=10⁴W·m^-2·K^-1), we derive a critical qubit density ρ_rm crit= fracΔ T_rm crit H_Kν_rm cycle ε_q ≈ 3×10⁶ rm qubits m^-2 for a temperature‑rise threshold Δ T_rm crit=0.3K at a base temperature of 0.3K. Above this density the substrate cannot evacuate heat fast enough, leading to a thermal phase transition that overwhelms decoherence suppression. The result predicts a thermodynamic ceiling for gate‑based QEC architectures and motivates a shift toward passive, topologically protected substrates that avoid active control heating.",
        "descriptionType": "Abstract"
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        "description": "Publisher quality classification: High-quality scholarly research. 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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