The Laplace–Weierstrass (LW) transform fuses the classical one-sided Laplace transform with Weierstrass Gaussian smoothing, converting linear delay and integro-differential models into algebraic problems in the joint (s, x)-domain while automatically regularizing noise and heterogeneity. Building on the foundational 2013–2014 theory, this paper presents a corrected existence theorem, convolution and fractional-order operational calculus, stable numerical inversion, and a practical hybrid quantum-classical architecture. The framework is applied to lithium-ion battery systems for robust SoC/SoH estimation and thermal dynamics, and to multi-echelon supply chains for inventory recovery and bullwhip-effect mitigation. A major contribution is the seamless coupling of LW dimensionality reduction with quantum annealing for combinatorial subproblems such as unit-load-device (ULD) configuration and disruption re-routing. This hybrid layer is designed to operationalize quantum-logistics and resilience results as constrained interfaces rather than as substitutes for the continuous model. Numerical experiments confirm O(N log N) complexity via FFT methods and demonstrate noise-robust digital-twin components suitable for real-time battery management systems and edge logistics controllers

Keywords— Laplace-Weierstrass transform; quantum annealing; ULD configuration; EV battery SoC/SoH; supply-chain resilience; bullwhip effect; hybrid quantum-classical optimization; digital twins