Tensor networks and the Belief Propagation algorithm
November 19, 2024 3:30 PM Singapore (Registration starts at 3:20 PM)
Abstract
A major challenge in using tensor-networks methods is the problem of tensor-network contraction, which can be exponentially hard for general tensor networks. Building on recent works that related tensor-networks to graphical models, and neural networks in general, I will present a belief-propagation (BP) algorithm for the contraction of tensor networks. BP is a well-known message-passing algorithm from the world of classical physics and machine learning. It can be used to approximate the local marginals on multivariate probability distributions that are described by graphical models. Like the classical BP algorithm, our algorithm is exact on tree TNs, and often gives surprisingly good results on loopy graphs. I will also discuss a generalization of this algorithm, called blockBP, which is designed to be more accurate for 2D tensor networks with many loops, and show how it can lead to state-of-the-art results in simulations of many-body quantum systems.
PAPERS
1) Tensor networks contraction and the belief propagation algorithm, R. Alkabetz and I. Arad. Phys. Rev. Research 3, 023073
2) Block belief propagation algorithm for two-dimensional tensor networks, Chu Guo, Dario Poletti, and Itai Arad, Phys. Rev. B 108, 125111
About the Speaker
Itai Arad is a Research Associate Professor at the Centre of Quantum Computation (CQT). After a PhD on the subject of theoretical turbulence, he started his academic career in the subject quantum information as a postdoc of Dorit Aharonov and later of Umesh Vazirani. After 4 years as a senior researcher at the CQT, he spent 7 years as an assistant Professor at the faculty of Physics at the Technion, Israel. His main research interests lie in the intersection of quantum information, machine learning, complexity theory and many-body quantum theory. In particular, he is interested in questions about tensor-networks, the entanglement structure of many-body quantum states, as well as rigorous and heuristic methods for simulating these systems.
For more information about the ESD Seminar, please email esd_invite@sutd.edu.sg