QFlux: Classical Foundations for Quantum Dynamics Simulation. Part I - Building Intuition and Computational Workflows

We introduce QFlux, an open-source Python package for simulating quantum dynamics in chemical systems across multiple levels of theory using a unified classical and quantum computational framework. QFlux integrates deterministic wavefunction propagation, Lindblad master equations, generalized quantum master equations (GQMEs), operator-splitting techniques, and variational quantum algorithms within a modular architecture designed for systematic benchmarking and hybrid classical-quantum execution. The framework supports both closed-and open-system dynamics, including Markovian and non-Markovian regimes, and provides explicit mappings between classical propagators and quantum circuit constructions executable on NISQ hardware. Built atop established scientific and quantum software ecosystems, QFlux emphasizes reproducibility, interoperability, and controlled cross-validation between numerical approximations and hardware-oriented algorithms. Part I in this series of papers presents the theoretical foundations, software design principles, and methodological scope of QFlux, and positions it within the broader landscape of classical, tensor-network, and quantum-circuit-based simulation platforms. The series is designed to serve as a teaching reference for graduate students, a practical guide for researchers implementing custom quantum simulations, and a foundational reference for the broader QFlux ecosystem.