Beyond the Expressivity-Trainability Paradox: A Dynamical Lie Algebra Perspective on Navigating Barren Plateaus in Quantum Machine Learning

As Quantum Machine Learning (QML) transitions toward practical implementation, the field faces a critical architectural bottleneck that challenges the fundamental assumptions of classical statistical learning theory. In classical deep learning, increasing model capacity typically risks overfitting. However, this study advances a counter-intuitive paradigm: unstructured contemporary QML architectures suffer from a profound state of quantum underfitting, driven by the "expressivity-trainability paradox." We demonstrate that the vast Hilbert space capacity of Parameterized Quantum Circuits (PQCs)