Quantum-Classical Machine learning by Hybrid Tensor Networks

TL;DR

This paper introduces hybrid tensor networks combining quantum and classical methods to enhance deep learning capabilities, addressing limitations of traditional tensor networks in representation power and scalability.

Contribution

The paper proposes a novel hybrid tensor network framework that integrates quantum and classical neural networks, enabling deep learning training methods for tensor networks.

Findings

HTN overcomes regular tensor network limitations

HTN can be trained with standard deep learning algorithms

Demonstrated applications include quantum state classification and autoencoders

Abstract

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.