Generalized belief propagation approximates tensor network contractions via hierarchical region messages and fixed-point solutions, demonstrated on Ising, ice, AKLT, and random tensor networks.
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Numerical examples show that the tensor network loop cluster expansion yields approximately exponential convergence of contraction error with cluster size for ground-state observables in high-bond-dimension tensor networks across 2D/3D spin and fermion systems.
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Contracting Tensor Networks with Generalized Belief Propagation
Generalized belief propagation approximates tensor network contractions via hierarchical region messages and fixed-point solutions, demonstrated on Ising, ice, AKLT, and random tensor networks.
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Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems
Numerical examples show that the tensor network loop cluster expansion yields approximately exponential convergence of contraction error with cluster size for ground-state observables in high-bond-dimension tensor networks across 2D/3D spin and fermion systems.