Entanglement-Based Feature Extraction by Tensor Network Machine Learning

Yuhan Liu, Wen-Jun Li, Xiao Zhang, Maciej Lewenstein, Gang Su and Shi-Ju Ran

Front. Appl. Math. Stat., 7, 716044 (2021)-Published 06 August 2021


It is a hot topic how entanglement, a quantity from quantum information theory, can assist machine learning. In this work, we implement numerical experiments to classify patterns/images by representing the classifiers as matrix product states (MPS). We show how entanglement can interpret machine learning by characterizing the importance of data and propose a feature extraction algorithm. We show on the MNIST dataset that when reducing the number of the retained pixels to 1/10 of the original number, the decrease of the ten-class testing accuracy is only O (10–3), which significantly improves the efficiency of the MPS machine learning. Our work improves machine learning’s interpretability and efficiency under the MPS representation by using the properties of MPS representing entanglement.