Stochastic Loop Corrections to Belief Propagation for Tensor Network Contraction
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911574200942592 |
|---|---|
| author | Sim, Gi Beom Park, Tae Hyeon Kim, Kwang S. Zang, Yanmei Zou, Xiaorong Kim, Hye Jung Yang, D. ChangMo Willow, Soohaeng Yoo Myung, Chang Woo |
| author_facet | Sim, Gi Beom Park, Tae Hyeon Kim, Kwang S. Zang, Yanmei Zou, Xiaorong Kim, Hye Jung Yang, D. ChangMo Willow, Soohaeng Yoo Myung, Chang Woo |
| contents | Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces systematic errors on graphs with loops. Here, we introduce a hybrid method that achieves accurate results by stochastically sampling loop corrections to BP and showcase our method by applying it to the two-dimensional ferromagnetic Ising model. For any pairwise Markov random field with symmetric edge potentials, our approach exploits an exact factorization of the partition function into the BP contribution and a loop correction factor summing over all valid loop configurations, weighted by edge weights derived directly from the potentials. We sample this sum using Markov chain Monte Carlo with moves that preserve the loop constraint, combined with umbrella sampling to ensure efficient exploration across all correlation strengths. Our stochastic approach provides unbiased estimates with controllable statistical error in any parameter regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08427 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Loop Corrections to Belief Propagation for Tensor Network Contraction Sim, Gi Beom Park, Tae Hyeon Kim, Kwang S. Zang, Yanmei Zou, Xiaorong Kim, Hye Jung Yang, D. ChangMo Willow, Soohaeng Yoo Myung, Chang Woo Strongly Correlated Electrons Statistical Mechanics Quantum Physics Tensor network contraction is a fundamental computational challenge underlying quantum many-body physics, statistical mechanics, and machine learning. Belief propagation (BP) provides an efficient approximate solution, but introduces systematic errors on graphs with loops. Here, we introduce a hybrid method that achieves accurate results by stochastically sampling loop corrections to BP and showcase our method by applying it to the two-dimensional ferromagnetic Ising model. For any pairwise Markov random field with symmetric edge potentials, our approach exploits an exact factorization of the partition function into the BP contribution and a loop correction factor summing over all valid loop configurations, weighted by edge weights derived directly from the potentials. We sample this sum using Markov chain Monte Carlo with moves that preserve the loop constraint, combined with umbrella sampling to ensure efficient exploration across all correlation strengths. Our stochastic approach provides unbiased estimates with controllable statistical error in any parameter regime. |
| title | Stochastic Loop Corrections to Belief Propagation for Tensor Network Contraction |
| topic | Strongly Correlated Electrons Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2603.08427 |