A Novel q-Derivative Framework with Applications to q-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits
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 ≥ 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.
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BibTeX
@misc{marinho2026novel,
title = {{A Novel $q$-Derivative Framework with Applications to $q$-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits}},
author = {André A. A. Marinho and Gisele B. Freitas and Clovis A. C. Filho},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30632},
eprint = {2609.30632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30632},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Novel q-Derivative Framework with Applications to q-Deformed Thermodynamics and Leakage Suppression in Superconducting Qubits
AU - André A. A. Marinho
AU - Gisele B. Freitas
AU - Clovis A. C. Filho
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.30632
UR - https://arxiv.org/abs/2609.30632
AB - 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 ≥ 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.
ER -