An afternoon in dialogue with quantum machine learning
Markus Heyl & Nicola Pancotti (MPKS, Dresden & Amazon Quantum)

We re-start our series of theory colloquiums with a 90 minutes event on applications of machine learning to many-body physics. We will have two Zoom talks of 35 minutes+10 minutes of questions, each.

Talk 1 (M. Heyl): Quantum many-body dynamics in two dimensions with artificial neural networks

In the last two decades the field of nonequilibrium quantum many-body physics has seen a rapid development driven, in particular, by the remarkable progress in quantum simulators, which today provide access to dynamics in quantum matter with an unprecedented control. However, the efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter still remains a key challenge for current computational methods especially beyond one spatial dimension. In this talk I will present a versatile and efficient machine learning inspired approach. I will first introduce the general idea of encoding quantum many-body wave functions into artificial neural networks. I will then identify and resolve key challenges for the simulation of real-time evolution, which previously imposed significant limitations on the accurate description of large systems and long-time dynamics. As a concrete example, I will consider the dynamics of the paradigmatic two-dimensional transverse field Ising model, where we observe collapse and revival oscillations of ferromagnetic order and demonstrate that the reached time scales are comparable to or exceed the capabilities of state-of-the-art tensor network methods.

Talk 2 (N. Pancotti): Neural Networks Quantum States, Tensor Networks and Machine Learning

Neural Networks Quantum States have been recently introduced as an Ansatz for describing the wave function of quantum many-body systems. In this talk I will give an overview of recent works on Neural Networks Quantum States taking the form of Boltzmann machines. I will explain the motivation for considering Boltzmann machines in machine learning and explain how they can be used to study ground state properties of quantum systems. I will then focus on the expressive power of this class of states and discuss their relationship to Tensor Networks. In particular I will show that restricted Boltzmann machines belong to an exotic class of tensor networks known as String Bond States. This mapping enables us to define generalizations of restricted Boltzmann machines that combine the entanglement structure of tensor networks with the efficiency of Neural Networks Quantum States. This connection sheds light on possible application of tensor networks in machine learning. I will discuss the tight relationship between tensor-network techniques and probabilistic graphical models, an established class of models broadly used in computer science. I finally conclude by presenting possible advantages of using tensor network to tackle machine learning problems.