{
  "id": "oai:papers.qnfo.org:the-price-of-the-digital-abstraction-entropy-and-encoding-overhead-when-discrete",
  "slug": "the-price-of-the-digital-abstraction-entropy-and-encoding-overhead-when-discrete",
  "title": "The Price of the Digital Abstraction: Entropy and Encoding Overhead When Discrete Error Models Meet Continuous Quantum Hardware",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Quantum processors built from superconducting transmons operate as anharmonic oscillators with many energy levels, yet fault‑tolerant architectures model each device as a two‑level qubit subject to a discrete Pauli error set. This mismatch forces a continuous bosonic error model into a discrete representation, incurring hidden bookkeeping and physical costs. We analytically quantify four concrete overheads for a single transmon treated as a qudit of dimension d=12: (i) the minimal classical register entropy H_reg=log₂12=3.584963 bits, (ii) the binary‑encoding dimension overhead 4/3 with encoding efficiency η=0.896241, (iii) the entropy distortion introduced by Pauli twirling of an amplitude‑damping channel, Δ H=1.5×10^-3 bits at damping probability γ=10^-3 and the exact law Δ H=(3γ)/(2) for all γ, and (iv) the discarded Hilbert‑space weight for a thermal mode with mean occupation bar n=0.1, p_disc≈3.19×10^-13. These quantities are derived with fully shown arithmetic and no simulation. The results demonstrate that the digital abstraction imposes a measurable bookkeeping burden and a linear entropy excess that scales with physical damping. Designers of large‑scale quantum hardware can use these numbers to assess trade‑offs between radix choice, encoding efficiency, and classical control bandwidth.",
  "abstract_markdown": "Quantum processors built from superconducting transmons operate as anharmonic oscillators with many energy levels, yet fault‑tolerant architectures model each device as a two‑level qubit subject to a discrete Pauli error set. This mismatch forces a continuous bosonic error model into a discrete representation, incurring hidden bookkeeping and physical costs. We analytically quantify four concrete overheads for a single transmon treated as a qudit of dimension $d=12$: (i) the minimal classical register entropy $H_{\\mathrm{reg}}=\\log_{2}12=3.584963$ bits, (ii) the binary‑encoding dimension overhead $4/3$ with encoding efficiency $\\eta=0.896241$, (iii) the entropy distortion introduced by Pauli twirling of an amplitude‑damping channel, $\\Delta H=1.5\\times10^{-3}$ bits at damping probability $\\gamma=10^{-3}$ and the exact law $\\Delta H=\\tfrac{3\\gamma}{2}$ for all $\\gamma$, and (iv) the discarded Hilbert‑space weight for a thermal mode with mean occupation $\\bar n=0.1$, $p_{\\mathrm{disc}}\\approx3.19\\times10^{-13}$. These quantities are derived with fully shown arithmetic and no simulation. The results demonstrate that the digital abstraction imposes a measurable bookkeeping burden and a linear entropy excess that scales with physical damping. Designers of large‑scale quantum hardware can use these numbers to assess trade‑offs between radix choice, encoding efficiency, and classical control bandwidth.",
  "date": "2026-10-11",
  "first_published": "2026-10-11",
  "last_revised": "2026-10-24T17:41:10Z",
  "modified": "2026-10-24T17:41:10Z",
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  "peer_review_status": "Not independently peer-reviewed",
  "resource_type": "ScholarlyArticle",
  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/the-price-of-the-digital-abstraction-entropy-and-encoding-overhead-when-discrete",
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  "sha256": "5a3bfff645e2547d3c75e4ef0851259eca86e4ec2c3e79cf4a1fa93673d00d7c",
  "version_url": "https://papers.qnfo.org/papers/the-price-of-the-digital-abstraction-entropy-and-encoding-overhead-when-discrete/v/1.7.0",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
      {
        "title": "The Price of the Digital Abstraction: Entropy and Encoding Overhead When Discrete Error Models Meet Continuous Quantum Hardware"
      }
    ],
    "publisher": "QNFO",
    "publicationYear": "2026",
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    "dates": [
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        "date": "2026-10-11",
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        "description": "Quantum processors built from superconducting transmons operate as anharmonic oscillators with many energy levels, yet fault‑tolerant architectures model each device as a two‑level qubit subject to a discrete Pauli error set. This mismatch forces a continuous bosonic error model into a discrete representation, incurring hidden bookkeeping and physical costs. We analytically quantify four concrete overheads for a single transmon treated as a qudit of dimension d=12: (i) the minimal classical register entropy H_reg=log₂12=3.584963 bits, (ii) the binary‑encoding dimension overhead 4/3 with encoding efficiency η=0.896241, (iii) the entropy distortion introduced by Pauli twirling of an amplitude‑damping channel, Δ H=1.5×10^-3 bits at damping probability γ=10^-3 and the exact law Δ H=(3γ)/(2) for all γ, and (iv) the discarded Hilbert‑space weight for a thermal mode with mean occupation bar n=0.1, p_disc≈3.19×10^-13. These quantities are derived with fully shown arithmetic and no simulation. The results demonstrate that the digital abstraction imposes a measurable bookkeeping burden and a linear entropy excess that scales with physical damping. Designers of large‑scale quantum hardware can use these numbers to assess trade‑offs between radix choice, encoding efficiency, and classical control bandwidth.",
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