  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 datasets 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
Hopfield model, Boltzmann machines and generative adversarial networks. Our
work sheds light on many interesting directions of future exploration on the
development of quantum-inspired algorithms for unsupervised machine learning,
which are promisingly possible to be realized on quantum devices.
