# Quantum-Classical Machine learning by Hybrid Tensor Networks

arXiv: https://arxiv.org/abs/2005.09428 · HTML: https://mlsanity.com/paper/2005.09428/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 May 2020.

## Built on by (most cited first, 3 of 3)

- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [Fast Kernel Density Estimation with Density Matrices and Random Fourier Features](https://mlsanity.com/paper/2208.01206/) (2022)

## Abstract (arXiv)

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.