Deep-neural-network solution of the electronic Schrödinger equation

Area of Science:

• Quantum chemistry
• Computational physics
• Deep learning applications

Background:

• Solving the electronic Schrödinger equation analytically is limited to simple systems like the hydrogen atom.
• Exact numerical methods, such as full configuration-interaction, are computationally prohibitive for larger molecules due to exponential scaling with electron number.
• Quantum Monte Carlo (QMC) methods offer a scalable alternative for large molecular systems, but their accuracy is often constrained by the flexibility of the chosen wavefunction ansatz.

Purpose of the Study:

• To introduce PauliNet, a novel deep-learning wavefunction ansatz designed to overcome the limitations of existing methods.
• To achieve nearly exact solutions for the electronic Schrödinger equation in molecules with up to 30 electrons.
• To enhance the accuracy and efficiency of quantum Monte Carlo simulations.

Main Methods:

• Development of PauliNet, a deep-learning wavefunction ansatz incorporating a multireference Hartree-Fock baseline.
• Integration of physical constraints for valid wavefunctions within the PauliNet architecture.
• Training of PauliNet using the variational quantum Monte Carlo (VQC) framework.

Main Results:

• PauliNet demonstrated superior performance compared to state-of-the-art variational ansatzes for atoms and diatomic molecules.
• The method achieved high accuracy on a strongly correlated linear H10 system.
• PauliNet matched the accuracy of specialized quantum chemistry methods for the transition-state energy of cyclobutadiene, with improved computational efficiency.

Conclusions:

• PauliNet represents a significant advancement in computational quantum chemistry, enabling accurate electronic structure calculations for moderately sized molecules.
• The deep-learning approach combined with VMC offers a computationally efficient and accurate alternative to traditional methods.
• This work paves the way for applying advanced deep learning techniques to complex chemical and physical problems.