Block belief propagation algorithm for two-dimensional tensor networks

Abstract

Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems. Building on a recent connection between the belief propagation algorithm and the problem of tensor network contraction, we propose a block belief propagation algorithm for contracting two-dimensional tensor networks and approximating the ground state of $2D$ systems. The advantages of our method are three-fold: 1) the same algorithm works for both finite and infinite systems; 2) it allows natural and efficient parallelization; 3) given its flexibility it would allow to deal with different unit cells. As applications, we use our algorithm to study the $2D$ Heisenberg and transverse Ising models, and show that the accuracy of the method is on par with state-of-the-art results.

12 pages, 13 figures

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Cited by in corpus (10)

• Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance
• Gauging tensor networks with belief propagation
• Validating quantum-supremacy experiments with exact and fast tensor network contraction
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
• Loop Series Expansions for Tensor Networks
• Nonperturbative decay of bipartite discrete time crystals
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• Nonequilibrium steady-state dynamics of Markov processes on graphs
• Exploring the performance of superposition of product states: from 1D to 3D quantum spin systems