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  "id": "oai:papers.qnfo.org:planck-fidelity-fundamental-leakage-cost-of-binary-truncation-of-bosonic-ladders",
  "slug": "planck-fidelity-fundamental-leakage-cost-of-binary-truncation-of-bosonic-ladders",
  "title": "Planck Fidelity: Fundamental Leakage Cost of Binary Truncation of Bosonic Ladders",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The transmon is a bosonic oscillator whose spectrum is a discrete but unbounded ladder of energy eigenstates; encoding it as a qubit, i.e. restricting the computational space to n ∈ \\0,1\\, is a radix choice rather than a physical necessity. We formalize the conjecture, originating in the QNFO \"Rosetta\" corpus, that any finite-time gate driven through the raising operator a^† on such a ladder incurs a strictly positive \"Planck Loss\" L_P = 1 - Tr(P_qubit |ψ⟩⟨ψ|), a leakage floor independent of materials and control engineering. We give two complementary derivations: an exact detuned-Rabi solution in the three-level truncation, and a first-order perturbative bound L₂ = 8(Ω/|α|)² sin²(α T_g/2). Under explicitly labeled illustrative parameters (f_Ω = 20 MHz, f_α = 200 MHz), a single π pulse carries coherent leakage ≈ 4.76 × 10^-4 and a 1000-gate sequence retains only ≈ 62\\% subspace population absent leakage return. [...]",
  "abstract_markdown": "The transmon is a bosonic oscillator whose spectrum is a discrete but unbounded ladder of energy eigenstates; encoding it as a qubit, i.e. restricting the computational space to $n \\in \\{0,1\\}$, is a radix choice rather than a physical necessity. We formalize the conjecture, originating in the QNFO \"Rosetta\" corpus, that any finite-time gate driven through the raising operator $a^\\dagger$ on such a ladder incurs a strictly positive \"Planck Loss\" $L_P = 1 - \\mathrm{Tr}(P_{\\mathrm{qubit}}\\,|\\psi\\rangle\\langle\\psi|)$, a leakage floor independent of materials and control engineering. We give two complementary derivations: an exact detuned-Rabi solution in the three-level truncation, and a first-order perturbative bound $L_2 = 8(\\Omega/|\\alpha|)^2 \\sin^2(\\alpha T_g/2)$. Under explicitly labeled illustrative parameters ($f_\\Omega = 20\\,\\mathrm{MHz}$, $f_\\alpha = 200\\,\\mathrm{MHz}$), a single $\\pi$ pulse carries coherent leakage $\\approx 4.76 \\times 10^{-4}$ and a 1000-gate sequence retains only $\\approx 62\\%$ subspace population absent leakage return. [...]",
  "date": "2026-10-10",
  "first_published": "2026-10-10",
  "last_revised": "2026-10-10T00:00:00Z",
  "modified": "2026-10-10T00:00:00Z",
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  "doi": null,
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  "url": "https://papers.qnfo.org/papers/planck-fidelity-fundamental-leakage-cost-of-binary-truncation-of-bosonic-ladders",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "Planck Fidelity: Fundamental Leakage Cost of Binary Truncation of Bosonic Ladders"
      }
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    "publisher": "QNFO",
    "publicationYear": "2026",
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        "description": "The transmon is a bosonic oscillator whose spectrum is a discrete but unbounded ladder of energy eigenstates; encoding it as a qubit, i.e. restricting the computational space to n ∈ \\0,1\\, is a radix choice rather than a physical necessity. We formalize the conjecture, originating in the QNFO \"Rosetta\" corpus, that any finite-time gate driven through the raising operator a^† on such a ladder incurs a strictly positive \"Planck Loss\" L_P = 1 - Tr(P_qubit |ψ⟩⟨ψ|), a leakage floor independent of materials and control engineering. We give two complementary derivations: an exact detuned-Rabi solution in the three-level truncation, and a first-order perturbative bound L₂ = 8(Ω/|α|)² sin²(α T_g/2). Under explicitly labeled illustrative parameters (f_Ω = 20 MHz, f_α = 200 MHz), a single π pulse carries coherent leakage ≈ 4.76 × 10^-4 and a 1000-gate sequence retains only ≈ 62\\% subspace population absent leakage return. [...]",
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