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COMPUTATIONAL CHEMISTRY

Accelerating quantum molecular simulations

Nature Computational Science volume 2, pages 292–293 (2022)Cite this article

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Variational Monte Carlo is one of the most accurate methods to solve the many-electron Schrödinger equation, but suffers from high computational cost. A recent study uses a weight-sharing technique to accelerate the neural network-based variational Monte Carlo method, allowing accurate and effective simulations of molecules.

Given a wave function ansatz, VMC optimizes it to minimize the energy of its described quantum system, and drives it towards the ground state. A good ansatz must be as close as possible to the unknown exact solution while satisfying the anti-symmetry requirement. Choosing a good ansatz is therefore a challenge. The traditional choice is the Slater–Jastrow ansatz2, obtained by multiplying the Slater determinant with a (Jastrow) factor. The Slater–Jastrow ansatz, which sometimes undergoes a backflow transformation, determines the accuracy and the computational cost of VMC with respect to other methods, as shown in Fig. 1a. Recently, deep neural networks (DNN) have been used as an ansatz for VMC3,4,5,6,7,8. The main idea is to represent the wave function by a DNN that accepts the atomic configurations as inputs, and outputs the wave function amplitude and phase factor3. Then, the DNN is trained along with the VMC optimizations. In a DNN, weights are the main parameters that specify the strength of the connections among the artificial neurons, visualized as arrows in Fig. 1b. Therefore, the weights of a DNN determine the wave function that is represented throughout the DNN-based VMC approach. Methods of this family yield superior accuracy and computational cost scaling that can be comparable with or better than the highly accurate coupled-cluster singles, doubles and perturbative triples, known as CCSD(T)10. However, as depicted in the inset of Fig. 1a, because the constant prefactor in the scaling is large due to hundreds of thousands of parameters of the DNN, they remain slower than CCSD(T) for small molecular systems. Even the computation of medium-size molecules needs days or weeks of calculations on highly optimized modern hardware, thus the DNN-based VMC approach is generally computationally too expensive for sizes of practical interest.

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Fig. 1: Weight-sharing technique to accelerate DNN-based VMC.

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  1. School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Huan Tran

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Correspondence to Huan Tran.

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Tran, H. Accelerating quantum molecular simulations. Nat Comput Sci 2, 292–293 (2022). https://doi.org/10.1038/s43588-022-00237-w

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