On the Universal Approximability and Complexity Bounds of Deep Learning in Hybrid Quantum-Classical Computing

Weiwen Jiang, Yukun Ding, Yiyu Shi

Keywords: deep learning, hybrid quantum-classical computing, universal approximability

Abstract: With the continuously increasing number of quantum bits in quantum computers, there are growing interests in exploring applications that can harvest the power of them. Recently, several attempts were made to implement neural networks, known to be computationally intensive, in hybrid quantum-classical scheme computing. While encouraging results are shown, two fundamental questions need to be answered: (1) whether neural networks in hybrid quantum-classical computing can leverage quantum power and meanwhile approximate any function within a given error bound, i.e., universal approximability; (2) how do these neural networks compare with ones on a classical computer in terms of representation power? This work sheds light on these two questions from a theoretical perspective.

One-sentence Summary: This paper proves the universal approximability of neural networks on a quantum computer for a wide class of functions as well as the associated bounds.

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Reviewed Version (pdf): https://openreview.net/references/pdf?id=J22qDO79rj