Training Classical Neural Networks by Quantum Machine Learning

In recent years, advanced deep neural networks have required a large number of parameters for training. Therefore, finding a method to reduce the number of parameters has become crucial for achieving efficient training. This work proposes a training scheme for classical neural networks (NNs) that utilizes the exponentially large Hilbert space of a quantum system. By mapping a classical NN with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> parameters to a quantum neural network (QNN) with O(polylog(M)) rotational gate angles, we can significantly reduce the number of parameters. These gate angles can be updated to train the classical NN. Unlike existing quantum machine learning (QML) methods, the results obtained from quantum computers using our approach can be directly used on classical computers. Numerical results on the MNIST and Iris datasets are presented to demonstrate the effectiveness of our approach. Additionally, we investigate the effects of deeper QNNs and the number of measurement shots for the QNN, followed by the theoretical perspective of the proposed method. This work opens a new branch of QML and offers a practical tool that can greatly enhance the influence of QML, as the trained QML results can benefit classical computing in our daily lives.