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Article | Open Access

Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural Networks

Huiping Su1, Hongbo Gao1,2,3( ), Xinmiao Wang1, Xi He1, Da Shen1
Department of Automation, School of Information Science and Technology, University of Science and Technology of China, Hefei 230026, China
Institute of Advanced Technology, University of Science and Technology of China, Hefei 230088, China
School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore
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Abstract

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.

Keywords

deep learningMonte CarloenergySchrödinger equation

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CAAI Artificial Intelligence Research
Volume 3,
2024
Article number: 9150030
DOI: 10.26599/AIR.2024.9150030
Cite this article:
Su H, Gao H, Wang X, et al. Variational Quantum Monte Carlo Solution of the Many-Electron Schrödinger Equation Based on Deep Neural Networks. CAAI Artificial Intelligence Research, 2024, 3: 9150030. https://doi.org/10.26599/AIR.2024.9150030

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Received: 24 April 2023
Revised: 15 December 2023
Accepted: 06 February 2024
Published: 21 June 2024
© The author(s) 2024.

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
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