Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a hyperoptimization over the compression and contraction strategy...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-01-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.14.011009 |
| _version_ | 1827372731675443200 |
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| author | Johnnie Gray Garnet Kin-Lic Chan |
| author_facet | Johnnie Gray Garnet Kin-Lic Chan |
| author_sort | Johnnie Gray |
| collection | DOAJ |
| description | Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a hyperoptimization over the compression and contraction strategy itself to minimize error and cost. We demonstrate that our protocol outperforms both handcrafted contraction strategies in the literature as well as recently proposed general contraction algorithms on a variety of synthetic and physical problems on regular lattices and random regular graphs. We further showcase the power of the approach by demonstrating approximate contraction of tensor networks for frustrated three-dimensional lattice partition functions, dimer counting on random regular graphs, and to access the hardness transition of random tensor network models, in graphs with many thousands of tensors. |
| first_indexed | 2024-03-08T11:05:17Z |
| format | Article |
| id | doaj.art-68d645ff95a4490983952339ce8e83c5 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-03-08T11:05:17Z |
| publishDate | 2024-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-68d645ff95a4490983952339ce8e83c52024-01-26T15:05:23ZengAmerican Physical SocietyPhysical Review X2160-33082024-01-0114101100910.1103/PhysRevX.14.011009Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary GeometryJohnnie GrayGarnet Kin-Lic ChanTensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a hyperoptimization over the compression and contraction strategy itself to minimize error and cost. We demonstrate that our protocol outperforms both handcrafted contraction strategies in the literature as well as recently proposed general contraction algorithms on a variety of synthetic and physical problems on regular lattices and random regular graphs. We further showcase the power of the approach by demonstrating approximate contraction of tensor networks for frustrated three-dimensional lattice partition functions, dimer counting on random regular graphs, and to access the hardness transition of random tensor network models, in graphs with many thousands of tensors.http://doi.org/10.1103/PhysRevX.14.011009 |
| spellingShingle | Johnnie Gray Garnet Kin-Lic Chan Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry Physical Review X |
| title | Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry |
| title_full | Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry |
| title_fullStr | Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry |
| title_full_unstemmed | Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry |
| title_short | Hyperoptimized Approximate Contraction of Tensor Networks with Arbitrary Geometry |
| title_sort | hyperoptimized approximate contraction of tensor networks with arbitrary geometry |
| url | http://doi.org/10.1103/PhysRevX.14.011009 |
| work_keys_str_mv | AT johnniegray hyperoptimizedapproximatecontractionoftensornetworkswitharbitrarygeometry AT garnetkinlicchan hyperoptimizedapproximatecontractionoftensornetworkswitharbitrarygeometry |