Quantum many-body inspired generative models

Generative models which learn the underlying probability distribution of the unlabeled data and generate new samples accordingly have become one of the cornerstones of probabilistic machine learning. Inspired by the probabilistic nature of quantum mechanics, we employ a generative model, known as the" Born machine" which uses quantum state representation and learns the joint probabilities over such quantum degrees of freedom. Due to many competing degrees of freedom, quantum many-body systems have known to exhibit exotic phases such as many-body localized states (MBL) which manifest peculiar properties in terms of coherence and long-time memories. In this work, we first introduce the MBL-Born machine as a powerful ansatz for the Born machine, and then we investigate the expressibility and trainability of the machine. We show that the MBL-Born machine is able to learn various classical and quantum data set such as MNIST and different phases of quantum many body states.