Power and limitations of single-qubit native quantum neural networks. (arXiv:2205.07848v2 [quant-ph] UPDATED)

Quantum neural networks (QNNs) have emerged as a leading strategy to
establish applications in machine learning, chemistry, and optimization. While
the applications of QNN have been widely investigated, its theoretical
foundation remains less understood. In this paper, we formulate a theoretical
framework for the expressive ability of data re-uploading quantum neural
networks that consist of interleaved encoding circuit blocks and trainable
circuit blocks. First, we prove that single-qubit quantum neural networks can
approximate any univariate function by mapping the model …

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