  Tensor networks (TN) have found a wide use in machine learning, and in
particular, TN and deep learning bear striking similarities. In this work, we
propose the quantum-classical hybrid tensor networks (HTN) which combine tensor
networks with classical neural networks in a uniform deep learning framework to
overcome the limitations of regular tensor networks in machine learning. We
first analyze the limitations of regular tensor networks in the applications of
machine learning involving the representation power and architecture
scalability. We conclude that in fact the regular tensor networks are not
competent to be the basic building blocks of deep learning. Then, we discuss
the performance of HTN which overcome all the deficiency of regular tensor
networks for machine learning. In this sense, we are able to train HTN in the
deep learning way which is the standard combination of algorithms such as Back
Propagation and Stochastic Gradient Descent. We finally provide two applicable
cases to show the potential applications of HTN, including quantum states
classification and quantum-classical autoencoder. These cases also demonstrate
the great potentiality to design various HTN in deep learning way.
