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 |
| Summary: | 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. |
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| ISSN: | 2643-1564 |