Many-body physics via machine learning

Louis-François Arsenault, Alejandro López‐Bezanilla, O. Anatole von Lilienfeld +1 more

Filippo Vicentini

Y. G., Long-Gang Pang, Rui Wang +1 more

In recent years, machine learning (ML) techniques have emerged as powerful tools for studying many-body complex systems, and encompassing phase transitions in various domains of physics. This mini review provides a concise yet comprehensive examination of the advancements achieved in applying ML to investigate phase transitions, with a primary focus on those involved in nuclear matter studies.

Roger G. Melko

Ding Liu, Shi-Ju Ran, Peter Wittek +4 more

Abstract The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional TNs in image recognition, showing limited scalability and flexibilities. In this work, we train two-dimensional hierarchical TNs to solve image recognition problems, using a training algorithm derived from the multi-scale entanglement renormalization ansatz. This approach introduces mathematical connections among quantum many-body physics, quantum information theory, and machine learning. While keeping the TN unitary in the training phase, TN states are defined, which encode classes of images into quantum many-body states. We study the quantum features of the TN states, including quantum entanglement and fidelity. We find these quantities could be properties that characterize the image classes, as well as the machine learning tasks.

Giacomo Torlai, Juan Carrasquilla, David J. Schwab +1 more