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Solving Quantum Many-Particle Models with Graph Attention Network |
| Qi-Hang Yu1 and Zi-Jing Lin1,2* |
1 Department of Physics, University of Science and Technology of China, Hefei 230026, China
2 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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| Cite this article: |
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Qi-Hang Yu and Zi-Jing Lin 2024 Chin. Phys. Lett. 41 030202 |
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Abstract Deep learning methods have been shown to be effective in representing ground-state wavefunctions of quantum many-body systems, however the existing approaches cannot be easily used for non-square like or large systems. Here, we propose a variational ansatz based on the graph attention network (GAT) which learns distributed latent representations and can be used on non-square lattices. The GAT-based ansatz has a computational complexity that grows linearly with the system size and can be extended to large systems naturally. Numerical results show that our method achieves the state-of-the-art results on spin-1/2 $J_1$–$J_2$ Heisenberg models over the square, honeycomb, triangular, and kagome lattices with different interaction strengths and lattice sizes (up to $24\times 24$ for square lattice). The method also provides excellent results for the ground states of transverse field Ising models on square lattices. The GAT-based techniques are efficient and versatile and hold promise for studying large quantum many-body systems with exponentially sized objects.
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Received: 07 January 2024
Published: 19 March 2024
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| PACS: |
03.67.Lx
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(Quantum computation architectures and implementations)
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03.67.-a
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(Quantum information)
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03.65.Yz
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(Decoherence; open systems; quantum statistical methods)
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03.67.Pp
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(Quantum error correction and other methods for protection against decoherence)
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