Structured Quantum Baths with Memory: A QuTiP Framework for Spectral Diagnostics and Machine Learning Inference

We introduce a compact simulation framework for modeling open quantum systems coupled to structured, memory-retaining baths using QuTiP. Our method models the bath as a finite set of layered qubits with adjustable connections, interpreted either as a physical realization or as a conceptual representation, rather than as a continuum. This explicit modeling enables direct control over non-Markovian dynamics and allows spectral diagnostics via Fast Fourier Transform (FFT) of system observables. Using a triangle-based bath motif and its extension to a six-qubit anisotropic fractal-like architecture, we demonstrate how spectral fingerprints encode bath topology and memory depth. Standard machine learning tools such as Principal Component Analysis (PCA) and gradient boosting can then be employed to infer bath parameters and estimate proximity to exceptional points (EPs). The results suggest that spectral analysis can serve as a unifying, quantum-platform agnostic tool across theory, simulation, and experiment, offering both a student-accessible and experimentally relevant approach to understanding coherence loss and memory flow in quantum hardware. Rather than treating noise as an adversary to be eliminated, our approach views structured baths as collaborative partners, enabling controlled memory and delocalized memory and information flow for engineered quantum dynamics. In addition to its diagnostic power, the framework offers a modular and reproducible platform for teaching open quantum systems. Ultimately, we frame this as a pedagogical tool: students can pair FFT-based spectral features with lightweight ML (e.g., PCA and gradient boosting) to extract data-rich, interpretable signatures of open-system and non-Hermitian dynamics.