Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural Networks
The solution of Schrödinger equation generates the quantisation properties of the system, which can completely describe the quantum behaviour of microscopic particles in a physical system. However, solving the Schrödinger equation is a non-deterministic polynomial time (NP)-hard problem. Numerical m...
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2024-02-01
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| Series: | CAAI Artificial Intelligence Research |
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| Online Access: | https://www.sciopen.com/article/10.26599/AIR.2024.9150030 |
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| author | Huiping Su Hongbo Gao Xinmiao Wang Xi He Da Shen |
| author_facet | Huiping Su Hongbo Gao Xinmiao Wang Xi He Da Shen |
| author_sort | Huiping Su |
| collection | DOAJ |
| description | The solution of Schrödinger equation generates the quantisation properties of the system, which can completely describe the quantum behaviour of microscopic particles in a physical system. However, solving the Schrödinger equation is a non-deterministic polynomial time (NP)-hard problem. Numerical methods for solving the Schrödinger equation require careful selection of basis configurations, and the complete basis set has high accuracy but its complexity increases exponentially in the number of particles. Therefore, it is crucial to find an effective numerical method. To solve this problem, this paper present a deep learning architecture, VMCNet, using the powerful computational efficiency of neural networks to improve the speed of numerical computation. Moreover, this paper proposes a suitable wavefunction ansatz, witch determines the accuracy of neural networks, that achieves more accurate energy solutions of the many-electron Schrödinger equation compared to the conventional single-determinant variational molecular Monte Carlo. We introduce non-local and local blocks to represent quantum mechanical interactions, which contain more physical information about the particle system. The experimental results show that VMCNet can cover more than 93% of the correlation energy of the main group elements (Be–Ne) for the monoatomic system and more than 90% of the correlation energy for the diatomic system. |
| format | Article |
| id | doaj-art-6fd875b7b3fb47f289d2758974eebab6 |
| institution | Kabale University |
| issn | 2097-194X 2097-3691 |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | CAAI Artificial Intelligence Research |
| spelling | doaj-art-6fd875b7b3fb47f289d2758974eebab62025-01-10T06:44:32ZengTsinghua University PressCAAI Artificial Intelligence Research2097-194X2097-36912024-02-013915003010.26599/AIR.2024.9150030Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural NetworksHuiping Su0Hongbo Gao1Xinmiao Wang2Xi He3Da Shen4Department of Automation, School of Information Science and Technology, University of Science and Technology of China, Hefei 230026, ChinaDepartment of Automation, School of Information Science and Technology, University of Science and Technology of China, Hefei 230026, ChinaDepartment of Automation, School of Information Science and Technology, University of Science and Technology of China, Hefei 230026, ChinaDepartment of Automation, School of Information Science and Technology, University of Science and Technology of China, Hefei 230026, ChinaDepartment of Automation, School of Information Science and Technology, University of Science and Technology of China, Hefei 230026, ChinaThe solution of Schrödinger equation generates the quantisation properties of the system, which can completely describe the quantum behaviour of microscopic particles in a physical system. However, solving the Schrödinger equation is a non-deterministic polynomial time (NP)-hard problem. Numerical methods for solving the Schrödinger equation require careful selection of basis configurations, and the complete basis set has high accuracy but its complexity increases exponentially in the number of particles. Therefore, it is crucial to find an effective numerical method. To solve this problem, this paper present a deep learning architecture, VMCNet, using the powerful computational efficiency of neural networks to improve the speed of numerical computation. Moreover, this paper proposes a suitable wavefunction ansatz, witch determines the accuracy of neural networks, that achieves more accurate energy solutions of the many-electron Schrödinger equation compared to the conventional single-determinant variational molecular Monte Carlo. We introduce non-local and local blocks to represent quantum mechanical interactions, which contain more physical information about the particle system. The experimental results show that VMCNet can cover more than 93% of the correlation energy of the main group elements (Be–Ne) for the monoatomic system and more than 90% of the correlation energy for the diatomic system.https://www.sciopen.com/article/10.26599/AIR.2024.9150030schrödinger equationdeep learningenergymonte carlo |
| spellingShingle | Huiping Su Hongbo Gao Xinmiao Wang Xi He Da Shen Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural Networks CAAI Artificial Intelligence Research schrödinger equation deep learning energy monte carlo |
| title | Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural Networks |
| title_full | Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural Networks |
| title_fullStr | Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural Networks |
| title_full_unstemmed | Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural Networks |
| title_short | Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural Networks |
| title_sort | variational quantum monte carlo solution of the many electron schrodinger equation based on deep neural networks |
| topic | schrödinger equation deep learning energy monte carlo |
| url | https://www.sciopen.com/article/10.26599/AIR.2024.9150030 |
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