Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914654803984384 |
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| author | Gray, Johnnie Chan, Garnet Kin-Lic |
| author_facet | Gray, Johnnie Chan, Garnet Kin-Lic |
| contents | 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 hyper-optimization over the compression and contraction strategy itself to minimize error and cost. We demonstrate that our protocol outperforms both hand-crafted 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_07044 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Hyper-optimized approximate contraction of tensor networks with arbitrary geometry Gray, Johnnie Chan, Garnet Kin-Lic Quantum Physics Statistical Mechanics Strongly Correlated Electrons 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 hyper-optimization over the compression and contraction strategy itself to minimize error and cost. We demonstrate that our protocol outperforms both hand-crafted 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. |
| title | Hyper-optimized approximate contraction of tensor networks with arbitrary geometry |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2206.07044 |