A Novel $q$-Derivative Framework with Applications to $q$-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits

Quantum Physics arXiv:2609.30632 (quant-ph) [Submitted on 24 Sep 2026] Title:A Novel $q$-Derivative Framework with Applications to $q$-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits Authors:André A. A. Marinho, Gisele B. Freitas, Clovis A. C. Filho View a PDF of the paper titled A Novel $q$-Derivative Framework with Applications to $q$-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits, by Andr\'e A. A. Marinho and 1 other authors View PDF HTML (experimental) 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. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2609.30632 [quant-ph] (or arXiv:2609.30632v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.30632 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: André Marinho [view email] [v1] Thu, 24 Sep 2026 23:36:57 UTC (2,730 KB) Full-text links: Access Paper: View a PDF of the paper titled A Novel $q$-Derivative Framework with Applications to $q$-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits, by Andr\'e A. A. Marinho and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)