Improved Optimization for the Neural-network Quantum States and Tests on the Chromium Dimer

The advent of Neural-network Quantum States (NQS) has significantly advanced wave function ansatz research, sparking a resurgence in orbital space variational Monte Carlo (VMC) exploration. This work introduces three algorithmic enhancements to reduce computational demands of VMC optimization using NQS: an adaptive learning rate algorithm, constrained optimization, and block optimization. We evaluate the refined algorithm on complex multireference bond stretches of H₂O and N₂ within the cc-pVDZ basis set and calculate the ground-state energy of the strongly correlated chromium dimer (Cr₂) in the Ahlrichs SV basis set. Our results achieve superior accuracy compared to coupled cluster theory at a relatively modest CPU cost. This work demonstrates how to enhance optimization efficiency and robustness using these strategies, opening a new path to optimize large-scale Restricted Boltzmann Machine (RBM) -based NQS more effectively and marking a substantial advancement in NQS's practical quantum chemistry applications.