LieTrunc-QNN: Lie Algebra Truncation and Quantum Expressivity Phase Transition from LiePrune to Provably Stable Quantum Neural Networks
Quantum Machine Learning (QML) is fundamentally limited by two challenges: barren plateaus (exponentially vanishing gradients) and the fragility of parameterized quantum circuits under noise. Despite extensive empirical studies, a unified theoretical framework remains lacking. We introduce LieTrunc-QNN, an algebraic-geometric framework that characterizes trainability via Lie-generated dynamics. Parameterized quantum circuits are modeled as Lie subalgebras of u(2^n), whose action induces a Riemannian manifold of reachable quantum states. Expressivity is reinterpreted as intrinsic manifold dimension and geometry. We establish a geometric capacity-plateau principle: increasing effective dime...
| Authors | Haijian Shao, Dalong Zhao, Xing Deng et al. |
|---|---|
| Primary category | cs.LG |
| Published | 3 April 2026 |
| Last updated at source | 3 April 2026 |
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