Beyond the Expressivity-Trainability Paradox: A Dynamical Lie Algebra Perspective on Navigating Barren Plateaus in Quantum Machine Learning
Quantum machine learning confronts a fundamental architectural crisis: the very expressivity that promises quantum advantage simultaneously creates barren plateaus where gradient signals vanish during training. This work reframes the problem through dynamical Lie algebra theory, revealing that quantum underfitting, not overfitting, is the core bottleneck preventing practical QML deployment. The finding inverts classical deep learning intuition and suggests that capacity alone cannot drive quantum advantage without solving trainability constraints first. For AI infrastructure builders, this signals that near-term quantum ML progress depends less on raw qubit count and more on circuit design that balances expressivity with learnable parameter landscapes.62
