Quantum Neural Networks as Universal Function Approximators: Theory and Implementation

Quantum neural networks combine the principles of neural networks and quantum computing, aiming to solve conventional computing problems with the special advantages of quantum computing. Although it has shown potential in some specific scenarios, its applicability to more general problems and the efficient encoding of classical data into quantum systems are still challenges. This paper proposes a hybrid classical-quantum neural network model based on end-to-end encoding method, which can approximate any continuous function and is also available in experiment. The universality of proposed model is rigorously proved. This model can also achieve an accuracy of over 95% on the mini-batch MNIST dataset through numerical simulation. These results not only validate the effectiveness of quantum neural networks in addressing classical problems but also contribute to further exploration of the potential advantages of quantum neural networks.