{
  "id": "oai:papers.qnfo.org:parity-protected-superconducting-qubits-at-4-k-a-thermodynamic-error-budget-and-",
  "slug": "parity-protected-superconducting-qubits-at-4-k-a-thermodynamic-error-budget-and-",
  "title": "Parity-Protected Superconducting Qubits at 4 K: A Thermodynamic Error-Budget and Cooling-Crossover Analysis",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Scalable superconducting quantum processors are conventionally operated at millikelvin temperatures, where dilution-refrigerator cooling power is capped near tens of microwatts while every added qubit, cable, and amplifier increases the heat load on a stage that cannot be expanded cheaply. The specific gap addressed here is quantitative: no published analysis relates the cooling-power scaling of cryogenic plants, the heat dissipated per qubit, and the thermally activated error rates of superconducting qubits into a single crossover criterion that says when error-protecting a qubit beats cooling it. We derive such a criterion from the BCS gap-edge Boltzmann factor p_th(T) = e^-Δ/k_BT, the cooling-power law κ(T) = κ₀(T/T₀)^α, and a per-qubit heat-load assumption. For niobium (T_c = 9.2 K, Δ/k_B = 16.192 K) we compute p_th(4 K) = 1.7458 × 10^-2 against 4.78 × 10^-71 at 100 mK, a penalty of 3.65 × 10⁶8; against a target error p_target = 10^-4 this demands a parity-selective suppression factor S ≈ 174.6, and the unsuppressed crossover temperature is T^* ≈ 1.758 K. Aluminum junctions (T_c = 1.2 K) are excluded outright at 4 K (p_th = 0.5897). With the conservative cooling-power ratio 2 × 10⁴ between the 4 K and millikelvin stages and an assumed 10 nW per-qubit load, the permissible qubit budget rises from 5 × 10³ to 10⁸. The result reframes refrigeration roadmaps: the binding design parameter becomes parity-selective suppression, not base temperature.",
  "abstract_markdown": "Scalable superconducting quantum processors are conventionally operated at millikelvin temperatures, where dilution-refrigerator cooling power is capped near tens of microwatts while every added qubit, cable, and amplifier increases the heat load on a stage that cannot be expanded cheaply. The specific gap addressed here is quantitative: no published analysis relates the cooling-power scaling of cryogenic plants, the heat dissipated per qubit, and the thermally activated error rates of superconducting qubits into a single crossover criterion that says when error-protecting a qubit beats cooling it. We derive such a criterion from the BCS gap-edge Boltzmann factor $p_{\\mathrm{th}}(T) = e^{-\\Delta/k_{B}T}$, the cooling-power law $\\kappa(T) = \\kappa_{0}(T/T_{0})^{\\alpha}$, and a per-qubit heat-load assumption. For niobium ($T_{c} = 9.2$ K, $\\Delta/k_{B} = 16.192$ K) we compute $p_{\\mathrm{th}}(4\\ \\mathrm{K}) = 1.7458 \\times 10^{-2}$ against $4.78 \\times 10^{-71}$ at 100 mK, a penalty of $3.65 \\times 10^{68}$; against a target error $p_{\\mathrm{target}} = 10^{-4}$ this demands a parity-selective suppression factor $S \\approx 174.6$, and the unsuppressed crossover temperature is $T^{*} \\approx 1.758$ K. Aluminum junctions ($T_{c} = 1.2$ K) are excluded outright at 4 K ($p_{\\mathrm{th}} = 0.5897$). With the conservative cooling-power ratio $2 \\times 10^{4}$ between the 4 K and millikelvin stages and an assumed 10 nW per-qubit load, the permissible qubit budget rises from $5 \\times 10^{3}$ to $10^{8}$. The result reframes refrigeration roadmaps: the binding design parameter becomes parity-selective suppression, not base temperature.",
  "date": "2026-11-07",
  "first_published": "2026-11-07",
  "last_revised": "2026-11-07T00:00:00Z",
  "modified": "2026-11-07T00:00:00Z",
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  "peer_review_status": "Not independently peer-reviewed",
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  "url": "https://papers.qnfo.org/papers/parity-protected-superconducting-qubits-at-4-k-a-thermodynamic-error-budget-and-",
  "license_url": "https://legal.qnfo.org/",
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  "sha256": "3f68fb37231e96f2b489de5195a6637c7da8bec62fb261af7b852f758a6bdcaa",
  "version_url": "https://papers.qnfo.org/papers/parity-protected-superconducting-qubits-at-4-k-a-thermodynamic-error-budget-and-/v/1.0.0",
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    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Parity-Protected Superconducting Qubits at 4 K: A Thermodynamic Error-Budget and Cooling-Crossover Analysis"
      }
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    "publicationYear": "2026",
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        "date": "2026-11-07",
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        "date": "2026-11-07",
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        "description": "Scalable superconducting quantum processors are conventionally operated at millikelvin temperatures, where dilution-refrigerator cooling power is capped near tens of microwatts while every added qubit, cable, and amplifier increases the heat load on a stage that cannot be expanded cheaply. The specific gap addressed here is quantitative: no published analysis relates the cooling-power scaling of cryogenic plants, the heat dissipated per qubit, and the thermally activated error rates of superconducting qubits into a single crossover criterion that says when error-protecting a qubit beats cooling it. We derive such a criterion from the BCS gap-edge Boltzmann factor p_th(T) = e^-Δ/k_BT, the cooling-power law κ(T) = κ₀(T/T₀)^α, and a per-qubit heat-load assumption. For niobium (T_c = 9.2 K, Δ/k_B = 16.192 K) we compute p_th(4 K) = 1.7458 × 10^-2 against 4.78 × 10^-71 at 100 mK, a penalty of 3.65 × 10⁶8; against a target error p_target = 10^-4 this demands a parity-selective suppression factor S ≈ 174.6, and the unsuppressed crossover temperature is T^* ≈ 1.758 K. Aluminum junctions (T_c = 1.2 K) are excluded outright at 4 K (p_th = 0.5897). With the conservative cooling-power ratio 2 × 10⁴ between the 4 K and millikelvin stages and an assumed 10 nW per-qubit load, the permissible qubit budget rises from 5 × 10³ to 10⁸. The result reframes refrigeration roadmaps: the binding design parameter becomes parity-selective suppression, not base temperature.",
        "descriptionType": "Abstract"
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