For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
Title resolution pending
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
citation-role summary
background 2
citation-polarity summary
roles
background 2polarities
background 2representative citing papers
For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
A stochastic MCMC sampling method with umbrella sampling provides unbiased loop corrections to belief propagation for exact factorization-based tensor network contraction on loopy graphs with symmetric potentials.
Generalized belief propagation approximates tensor network contractions via hierarchical region messages and fixed-point solutions, demonstrated on Ising, ice, AKLT, and random tensor networks.
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
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.
citing papers explorer
-
Algorithmic Locality via Provable Convergence in Quantum Tensor Networks
For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
-
Belief Propagation and Tensor Network Expansions for Many-Body Quantum Systems: Rigorous Results and Fundamental Limits
For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
-
Stochastic Loop Corrections to Belief Propagation for Tensor Network Contraction
A stochastic MCMC sampling method with umbrella sampling provides unbiased loop corrections to belief propagation for exact factorization-based tensor network contraction on loopy graphs with symmetric potentials.
-
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.
-
Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
-
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.