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About this paper
Jialiang Tang, Jialin Zhang, Xiaoming Sun
A constructive quantum neural network (SAQNN) is introduced, proven to universally approximate square-integrable functions, and quantifiably shown to achieve optimal parameter complexity and polynomial scaling in high dimensions for Sobolev function approximation, mitigating the curse of dimensionality compared to classical models.
Key insights
- Pure quantum neural networks can constructively realize the Universal Approximation Property for arbitrary square-integrable functions.
- SAQNN achieves asymptotically optimal parameter complexity for approximating Sobolev functions under the L2 norm, matching theoretical lower bounds.
- Quantum neural networks can offer asymptotic advantages over classical ReLU Feed-Forward Neural Networks in high-dimensional scenarios, exhibiting polynomial scaling with input dimension 'd'.
Summary by alphaXiv.
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