Improved optimization for the neural-network quantum states and tests on the chromium dimer

Area of Science:

• Quantum Chemistry
• Computational Physics
• Machine Learning in Science

Background:

• Neural-network Quantum States (NQS) have emerged as powerful tools for representing wave functions.
• Variational Monte Carlo (VMC) methods are computationally intensive, especially for complex electronic structures.
• Efficient optimization of NQS is crucial for advancing their application in quantum chemistry.

Purpose of the Study:

• To introduce algorithmic enhancements for reducing the computational cost of VMC optimization with NQS.
• To improve the efficiency and robustness of optimizing large-scale restricted Boltzmann machine-based NQS.
• To demonstrate the practical applicability of enhanced NQS in quantum chemistry.

Main Methods:

• Development and implementation of three algorithmic enhancements: adaptive learning rate, constrained optimization, and block optimization.
• Application of the refined VMC-NQS algorithm to multireference bond stretches of H2O and N2 (cc-pVDZ basis set).
• Calculation of the ground-state energy for the strongly correlated chromium dimer (Cr2) (Ahlrichs SV basis set).

Main Results:

• The enhanced VMC-NQS algorithm significantly reduces computational demands.
• Achieved superior accuracy compared to coupled cluster theory for H2O and N2 bond stretches.
• Successfully calculated the ground-state energy of the Cr2 dimer with high accuracy at a modest computational cost.

Conclusions:

• The proposed algorithmic enhancements substantially improve the efficiency and robustness of NQS optimization.
• This work paves the way for more effective optimization of large-scale NQS, particularly restricted Boltzmann machines.
• The findings represent a significant advancement in the practical application of NQS in quantum chemistry.