From Reachability to Learnability: Geometric Design Principles for Quantum Neural Networks
Classical deep networks are effective because depth enables adaptive geometric deformation of data representations. In quantum neural networks (QNNs), however, depth or state reachability alone does not guarantee this feature-learning capability. We study this question in the pure-state setting by viewing encoded data as an embedded manifold in $\mathbb{C}P^{2^n-1}$ and analysing infinitesimal unitary actions through Lie-algebra directions. We introduce Classical-to-Lie-algebra (CLA) maps and the criterion of almost Complete Local Selectivity (aCLS), which combines directional completeness with data-dependent local selectivity. Within this framework, we show that data-independent trainabl...
| Authors | Vishal S. Ngairangbam, Michael Spannowsky |
|---|---|
| Primary category | quant-ph |
| Published | 3 March 2026 |
| Last updated at source | 25 March 2026 |
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