Unsupervised Generative Modeling Using Matrix Product States

• Published in: Physical review. X Vol. 8; no. 3; p. 031012
• Main Authors: Han, Zhao-Yu, Wang, Jun, Fan, Heng, Wang, Lei, Zhang, Pan
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 01.07.2018
• Subjects: Algorithms; Allocations; Artificial intelligence; Datasets; Entangled states; Generative adversarial networks; Handwriting; Machine learning; Mathematical models; Modelling; Parameters; Probability distribution; Probability theory; Quantum computing; Quantum phenomena; Quantum physics; Quantum theory; Representations; Samples; Sampling; Standard data; Statistical analysis; Statistical methods; Tensors
• DOI: 10.1103/PhysRevX.8.031012
• ISSN: 2160-3308

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an efficient direct sampling approach for generative tasks. We apply our method to generative modeling of several standard data sets including the Bars and Stripes random binary patterns and the MNIST handwritten digits to illustrate the abilities, features, and drawbacks of our model over popular generative models such as the Hopfield model, Boltzmann machines, and generative adversarial networks. Our work sheds light on many interesting directions of future exploration in the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to realize on quantum devices.