发表机构
Centro de Ciências Exatas, Naturais e Tecnológicas - CCENT, Universidade Estadual da Região Tocantina do Maranhão (UEMASUL)（马托格罗索州北部州立大学自然科学与技术科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于Jackson $q$-数的新型$q$-导数算子，保持热力学量一致性，并推导出推广DRAG的脉冲修正以抑制超导量子比特泄漏。
AI 中文摘要
我们提出了一种直接基于Jackson的$q$-数公式构建的新型$q$-导数算子，旨在保持标准微分演算的结构性质的同时纳入变形效应。通过分析$q$-变形的海森堡代数，我们证明了该公式在稀薄气体极限下无需临时链式法则修正即可维持内能、粒子数和比热等热力学量的一致性。此外，我们利用Biedenharn-Macfarlane实现探讨了代数变形的物理意义，展示了$q$-变形如何在量子振子谱中引入内在非谐性，并影响多能级量子系统（$d \ge 3$）。将该代数方案应用于超导transmon量子比特，我们推导出解析脉冲整形修正，推广了绝热门导数移除（DRAG）技术，为超快量子逻辑操作中计算泄漏的抑制提供了一种稳健方法。
英文摘要
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.
Comments23 pages, 3 figures
