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  "slug": "parity-protected-superconducting-qubits-at-4-k-a-reconciled-thermodynamic-error-",
  "title": "Parity-Protected Superconducting Qubits at 4 K: A Reconciled Thermodynamic Error-Budget Analysis",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Scalable superconducting quantum computing is conventionally operated at millikelvin temperatures, where the cooling power available from dilution refrigerators is severely limited. This paper tests the conjecture that a thermodynamic bottleneck at millikelvin temperatures could be relieved by operating parity-protected superconducting qubits at 4 K, where closed-cycle refrigeration supplies roughly 2×10⁴ times more cooling power. We construct an explicit thermal error budget with fully shown arithmetic: the thermal energy scale at 4 K is k_BT/h ≈ 83.3465 GHz; against the niobium gap 2Δ_Nb/h ≈ 700 GHz this yields a Boltzmann quasiparticle factor e^-Δ/k_BT ≈ 1.5006×10^-2, compared with ≈ 1.12×10^-73 at 100 mK — a penalty factor of order 10⁷1.13. Aluminum (T_c=1.2 K) is shown to be thermodynamically excluded as a junction material at 4 K. Against a stated fault-tolerance target of p_target=10^-4, an unprotected niobium qubit requires a suppression factor S=150 on thermally activated quasiparticle errors and meets the target only below T^*≈ 1.82 K. [...]",
  "abstract_markdown": "Scalable superconducting quantum computing is conventionally operated at millikelvin temperatures, where the cooling power available from dilution refrigerators is severely limited. This paper tests the conjecture that a thermodynamic bottleneck at millikelvin temperatures could be relieved by operating parity-protected superconducting qubits at 4 K, where closed-cycle refrigeration supplies roughly $2\\times10^{4}$ times more cooling power. We construct an explicit thermal error budget with fully shown arithmetic: the thermal energy scale at 4 K is $k_{B}T/h \\approx 83.3465$ GHz; against the niobium gap $2\\Delta_{\\mathrm{Nb}}/h \\approx 700$ GHz this yields a Boltzmann quasiparticle factor $e^{-\\Delta/k_{B}T} \\approx 1.5006\\times10^{-2}$, compared with $\\approx 1.12\\times10^{-73}$ at 100 mK — a penalty factor of order $10^{71.13}$. Aluminum ($T_{c}=1.2$ K) is shown to be thermodynamically excluded as a junction material at 4 K. Against a stated fault-tolerance target of $p_{\\mathrm{target}}=10^{-4}$, an unprotected niobium qubit requires a suppression factor $S=150$ on thermally activated quasiparticle errors and meets the target only below $T^{*}\\approx 1.82$ K. [...]",
  "date": "2026-10-10",
  "first_published": "2026-10-10",
  "last_revised": "2026-10-10T00:00:00Z",
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  "url": "https://papers.qnfo.org/papers/parity-protected-superconducting-qubits-at-4-k-a-reconciled-thermodynamic-error-",
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  "version_url": "https://papers.qnfo.org/papers/parity-protected-superconducting-qubits-at-4-k-a-reconciled-thermodynamic-error-/v/1.0.0",
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    "titles": [
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        "title": "Parity-Protected Superconducting Qubits at 4 K: A Reconciled Thermodynamic Error-Budget Analysis"
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        "description": "Scalable superconducting quantum computing is conventionally operated at millikelvin temperatures, where the cooling power available from dilution refrigerators is severely limited. This paper tests the conjecture that a thermodynamic bottleneck at millikelvin temperatures could be relieved by operating parity-protected superconducting qubits at 4 K, where closed-cycle refrigeration supplies roughly 2×10⁴ times more cooling power. We construct an explicit thermal error budget with fully shown arithmetic: the thermal energy scale at 4 K is k_BT/h ≈ 83.3465 GHz; against the niobium gap 2Δ_Nb/h ≈ 700 GHz this yields a Boltzmann quasiparticle factor e^-Δ/k_BT ≈ 1.5006×10^-2, compared with ≈ 1.12×10^-73 at 100 mK — a penalty factor of order 10⁷1.13. Aluminum (T_c=1.2 K) is shown to be thermodynamically excluded as a junction material at 4 K. Against a stated fault-tolerance target of p_target=10^-4, an unprotected niobium qubit requires a suppression factor S=150 on thermally activated quasiparticle errors and meets the target only below T^*≈ 1.82 K. [...]",
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