Physics-informed transformers for electronic quantum states.

Area of Science:

• Quantum mechanics
• Computational physics
• Machine learning

Background:

• Neural-network-based variational quantum states, especially autoregressive models, are used for complex many-body wave functions.
• Current methods face challenges with computational basis selection and lack physical interpretability.

Purpose of the Study:

• To develop a modified variational Monte-Carlo framework that incorporates prior physical information.
• To enhance the interpretability and computational efficiency of neural quantum-state representations.

Main Methods:

• A physics-informed basis is constructed using prior physical knowledge, including a reference state.
• A Transformer model is employed to autoregressively sample corrections to the reference state.
• The approach is demonstrated on a fermionic model exhibiting a metal-insulator transition.

Main Results:

• The Transformer-based approach yields a more interpretable and computationally efficient representation of the ground state.
• The hidden representation of the Transformer captures the energetic ordering of basis states.
• The framework successfully models a fermionic system with a metal-insulator transition.

Conclusions:

• This physics-informed neural quantum state framework offers a path towards more efficient and interpretable quantum many-body calculations.
• Leveraging physical priors improves the performance and understanding of neural network representations of quantum states.