  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 $M$ parameters to a quantum neural network (QNN) with
$O(\text{polylog} (M))$ 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.
