Unsupervised Generative Modeling Using Matrix Product States

TL;DR

This paper introduces a quantum physics-inspired generative model using matrix product states, enabling efficient learning and sampling for datasets like MNIST, with potential for quantum device implementation.

Contribution

It presents a novel unsupervised generative modeling approach based on tensor networks, bridging quantum physics concepts with machine learning.

Findings

Effective modeling of binary datasets like Bars and Stripes

Comparable performance to classical generative models on MNIST

Potential for quantum hardware implementation

Abstract

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.