{
  "abstract": "We propose a new $q$-derivative operator built directly from Jackson's $q$-number formulation, designed to preserve the structural properties of standard differential calculus while incorporating deformation effects. By analyzing $q$-deformed Heisenberg algebras, we demonstrate that this formulation maintains the consistency of thermodynamic quantities-such as internal energy, particle number, and specific heat-in dilute gas limits without requiring ad-hoc chain-rule modifications. Furthermore, we explore the physical implications of algebraic deformation using the Biedenharn-Macfarlane realization, showing how $q$-deformation induces intrinsic anharmonicity in quantum oscillator spectra and affects multi-level quantum systems ($d \\ge 3$). Applying this algebraic scheme to superconducting transmon qubits, we derive analytical pulse-shaping corrections that generalize the Derivative Removal by Adiabatic Gate (DRAG) technique, offering a robust method to suppress computational leakage in ultra-fast quantum logic operations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30632",
  "author_total": 3,
  "authors": [
    {
      "name": "André A. A. Marinho"
    },
    {
      "name": "Gisele B. Freitas"
    },
    {
      "name": "Clovis A. C. Filho"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/282x5vjgckvg5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30632",
  "fulltext_url": null,
  "id": "282x5vjgckvg5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30632",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3109|Noncommutative and Quantum Gravity Theories"
    ]
  ],
  "openalex": "W7214618866",
  "pdf_url": "https://arxiv.org/pdf/2609.30632",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/282x5vjgckvg5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.30632",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30632"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A Novel $q$-Derivative Framework with Applications to $q$-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits",
  "title_text": "A Novel q-Derivative Framework with Applications to q-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/282x5vjgckvg5",
  "venue": "arXiv",
  "versions": []
}