From tensor-network quantum states to tensorial recurrent neural networks
We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to two-dimensional lattices using a multilinear memory update. It supports perfect sampling and wave-function evaluation in poly...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.L032001 |
| _version_ | 1827285174306471936 |
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| author | Dian Wu Riccardo Rossi Filippo Vicentini Giuseppe Carleo |
| author_facet | Dian Wu Riccardo Rossi Filippo Vicentini Giuseppe Carleo |
| author_sort | Dian Wu |
| collection | DOAJ |
| description | We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to two-dimensional lattices using a multilinear memory update. It supports perfect sampling and wave-function evaluation in polynomial time, and can represent an area law of entanglement entropy. Numerical evidence shows that it can encode the wave function using a bond dimension lower by orders of magnitude when compared to MPS, with an accuracy that can be systematically improved by increasing the bond dimension. |
| first_indexed | 2024-04-24T10:10:40Z |
| format | Article |
| id | doaj.art-5b7425be497142cfaea6516702ce83a8 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:10:40Z |
| publishDate | 2023-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-5b7425be497142cfaea6516702ce83a82024-04-12T17:32:14ZengAmerican Physical SocietyPhysical Review Research2643-15642023-07-0153L03200110.1103/PhysRevResearch.5.L032001From tensor-network quantum states to tensorial recurrent neural networksDian WuRiccardo RossiFilippo VicentiniGiuseppe CarleoWe show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to two-dimensional lattices using a multilinear memory update. It supports perfect sampling and wave-function evaluation in polynomial time, and can represent an area law of entanglement entropy. Numerical evidence shows that it can encode the wave function using a bond dimension lower by orders of magnitude when compared to MPS, with an accuracy that can be systematically improved by increasing the bond dimension.http://doi.org/10.1103/PhysRevResearch.5.L032001 |
| spellingShingle | Dian Wu Riccardo Rossi Filippo Vicentini Giuseppe Carleo From tensor-network quantum states to tensorial recurrent neural networks Physical Review Research |
| title | From tensor-network quantum states to tensorial recurrent neural networks |
| title_full | From tensor-network quantum states to tensorial recurrent neural networks |
| title_fullStr | From tensor-network quantum states to tensorial recurrent neural networks |
| title_full_unstemmed | From tensor-network quantum states to tensorial recurrent neural networks |
| title_short | From tensor-network quantum states to tensorial recurrent neural networks |
| title_sort | from tensor network quantum states to tensorial recurrent neural networks |
| url | http://doi.org/10.1103/PhysRevResearch.5.L032001 |
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