Differentiable Programming of Isometric Tensor Networks
| Title: | Differentiable Programming of Isometric Tensor Networks |
|---|---|
| Authors: | Geng, Chenhua, Hu, Hong-Ye, Zou, Yijian |
| Source: | Mach. Learn.: Sci. Technol. 3 015020 (2022) |
| Publication Year: | 2021 |
| Collection: | Computer Science Condensed Matter Quantum Physics |
| Subject Terms: | Quantum Physics, Condensed Matter - Strongly Correlated Electrons, Computer Science - Machine Learning |
| More Details: | Differentiable programming is a new programming paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has also been generalized to tensor network optimizations. Here, we extend the differentiable programming to tensor networks with isometric constraints with applications to multiscale entanglement renormalization ansatz (MERA) and tensor network renormalization (TNR). By introducing several gradient-based optimization methods for the isometric tensor network and comparing with Evenbly-Vidal method, we show that auto-differentiation has a better performance for both stability and accuracy. We numerically tested our methods on 1D critical quantum Ising spin chain and 2D classical Ising model. We calculate the ground state energy for the 1D quantum model and internal energy for the classical model, and scaling dimensions of scaling operators and find they all agree with the theory well. Comment: 17 pages, 22 figures |
| Document Type: | Working Paper |
| DOI: | 10.1088/2632-2153/ac48a2 |
| Access URL: | http://arxiv.org/abs/2110.03898 |
| Accession Number: | edsarx.2110.03898 |
| Database: | arXiv |
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| Items | – Name: Title Label: Title Group: Ti Data: Differentiable Programming of Isometric Tensor Networks – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Geng%2C+Chenhua%22">Geng, Chenhua</searchLink><br /><searchLink fieldCode="AR" term="%22Hu%2C+Hong-Ye%22">Hu, Hong-Ye</searchLink><br /><searchLink fieldCode="AR" term="%22Zou%2C+Yijian%22">Zou, Yijian</searchLink> – Name: TitleSource Label: Source Group: Src Data: Mach. Learn.: Sci. Technol. 3 015020 (2022) – Name: DatePubCY Label: Publication Year Group: Date Data: 2021 – Name: Subset Label: Collection Group: HoldingsInfo Data: Computer Science<br />Condensed Matter<br />Quantum Physics – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Quantum+Physics%22">Quantum Physics</searchLink><br /><searchLink fieldCode="DE" term="%22Condensed+Matter+-+Strongly+Correlated+Electrons%22">Condensed Matter - Strongly Correlated Electrons</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Science+-+Machine+Learning%22">Computer Science - Machine Learning</searchLink> – Name: Abstract Label: Description Group: Ab Data: Differentiable programming is a new programming paradigm which enables large scale optimization through automatic calculation of gradients also known as auto-differentiation. This concept emerges from deep learning, and has also been generalized to tensor network optimizations. Here, we extend the differentiable programming to tensor networks with isometric constraints with applications to multiscale entanglement renormalization ansatz (MERA) and tensor network renormalization (TNR). By introducing several gradient-based optimization methods for the isometric tensor network and comparing with Evenbly-Vidal method, we show that auto-differentiation has a better performance for both stability and accuracy. We numerically tested our methods on 1D critical quantum Ising spin chain and 2D classical Ising model. We calculate the ground state energy for the 1D quantum model and internal energy for the classical model, and scaling dimensions of scaling operators and find they all agree with the theory well.<br />Comment: 17 pages, 22 figures – Name: TypeDocument Label: Document Type Group: TypDoc Data: Working Paper – Name: DOI Label: DOI Group: ID Data: 10.1088/2632-2153/ac48a2 – Name: URL Label: Access URL Group: URL Data: <link linkTarget="URL" linkTerm="http://arxiv.org/abs/2110.03898" linkWindow="_blank">http://arxiv.org/abs/2110.03898</link> – Name: AN Label: Accession Number Group: ID Data: edsarx.2110.03898 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/2632-2153/ac48a2 Subjects: – SubjectFull: Quantum Physics Type: general – SubjectFull: Condensed Matter - Strongly Correlated Electrons Type: general – SubjectFull: Computer Science - Machine Learning Type: general Titles: – TitleFull: Differentiable Programming of Isometric Tensor Networks Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Geng, Chenhua – PersonEntity: Name: NameFull: Hu, Hong-Ye – PersonEntity: Name: NameFull: Zou, Yijian IsPartOfRelationships: – BibEntity: Dates: – D: 08 M: 10 Type: published Y: 2021 |
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