Gauging tensor networks with belief propagation
Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing...
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| Format: | Article |
| Language: | English |
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SciPost
2023-12-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.6.222 |
| _version_ | 1797435137297743872 |
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| author | Joseph Tindall, Matt Fishman |
| author_facet | Joseph Tindall, Matt Fishman |
| author_sort | Joseph Tindall, Matt Fishman |
| collection | DOAJ |
| description | Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm. |
| first_indexed | 2024-03-09T10:42:53Z |
| format | Article |
| id | doaj.art-c2b6bbf52ee4405ca017d991679b9c45 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-09T10:42:53Z |
| publishDate | 2023-12-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-c2b6bbf52ee4405ca017d991679b9c452023-12-01T12:51:24ZengSciPostSciPost Physics2542-46532023-12-0115622210.21468/SciPostPhys.15.6.222Gauging tensor networks with belief propagationJoseph Tindall, Matt FishmanEffectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief propagation, a method that was originally formulated for performing statistical inference on graphical models and has recently found applications in tensor network algorithms. We show that this method is closely related to known tensor network gauging methods. It has the practical advantage, however, that existing belief propagation implementations can be repurposed for tensor network gauging, and that belief propagation is a very simple algorithm based on just tensor contractions so it can be easier to implement, optimize, and generalize. We present numerical evidence and scaling arguments that this algorithm is faster than existing gauging algorithms, demonstrating its usage on structured, unstructured, and infinite tensor networks. Additionally, we apply this method to improve the accuracy of the widely used simple update gate evolution algorithm.https://scipost.org/SciPostPhys.15.6.222 |
| spellingShingle | Joseph Tindall, Matt Fishman Gauging tensor networks with belief propagation SciPost Physics |
| title | Gauging tensor networks with belief propagation |
| title_full | Gauging tensor networks with belief propagation |
| title_fullStr | Gauging tensor networks with belief propagation |
| title_full_unstemmed | Gauging tensor networks with belief propagation |
| title_short | Gauging tensor networks with belief propagation |
| title_sort | gauging tensor networks with belief propagation |
| url | https://scipost.org/SciPostPhys.15.6.222 |
| work_keys_str_mv | AT josephtindallmattfishman gaugingtensornetworkswithbeliefpropagation |