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.
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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.
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
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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.
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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.
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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 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.
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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.