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