On the Optimal Linear Contraction Order of Tree Tensor Networks, and Beyond
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913536104464384 |
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| author | Stoian, Mihail Milbradt, Richard Mendl, Christian B. |
| author_facet | Stoian, Mihail Milbradt, Richard Mendl, Christian B. |
| contents | The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a polynomial-time algorithm, by drawing connections to database join ordering. The result relies on the adjacent sequence interchange property of the contraction cost, which enables a global decision of the contraction order based on local comparisons. Based on that, we specify a modified version of the IKKBZ database join ordering algorithm to find the optimal tree tensor network linear contraction order. Finally, we extend our algorithm as a heuristic to general contraction orders and arbitrary tensor network topologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12332 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Optimal Linear Contraction Order of Tree Tensor Networks, and Beyond Stoian, Mihail Milbradt, Richard Mendl, Christian B. Quantum Physics Databases Data Structures and Algorithms The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a polynomial-time algorithm, by drawing connections to database join ordering. The result relies on the adjacent sequence interchange property of the contraction cost, which enables a global decision of the contraction order based on local comparisons. Based on that, we specify a modified version of the IKKBZ database join ordering algorithm to find the optimal tree tensor network linear contraction order. Finally, we extend our algorithm as a heuristic to general contraction orders and arbitrary tensor network topologies. |
| title | On the Optimal Linear Contraction Order of Tree Tensor Networks, and Beyond |
| topic | Quantum Physics Databases Data Structures and Algorithms |
| url | https://arxiv.org/abs/2209.12332 |