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October 9, 2025Open Access

Beyond Belief Propagation: Cluster-Corrected Tensor Network Contraction with Exponential Convergence

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Cluster expansion converges exponentially fast under certain decay conditions, improving approximation accuracy significantly.
Efficacy demonstrated using the two-dimensional Ising model, surpassing belief propagation and existing corrective algorithms.
Developed a systematic framework for better understanding and enhancing belief propagation in tensor networks.
New algorithm allows for computations of cluster expansion to arbitrary order, broadening application possibilities.

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Theoretical framework improves belief propagation accuracy in tensor networks, suggesting new avenues for error correction.

Midha et al. (2025) studied this question.

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