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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A hybrid method uses fixed quantum annealing states as boundary resources for classical MERA tensor networks to improve ground-state approximations without deeper quantum circuits.
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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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Combining non-parametric quantum states and MERA tensor networks for ground-state optimization
A hybrid method uses fixed quantum annealing states as boundary resources for classical MERA tensor networks to improve ground-state approximations without deeper quantum circuits.