Bridging the Gap between Transformer-Based Neural Networks and Tensor Networks for Quantum Chemistry

The neural network quantum state (NNQS) method has demonstrated promising results in <i>ab initio</i> quantum chemistry, achieving remarkable accuracy in molecular systems. However, efficient calculation of systems with large active spaces remains challenging. This study introduces a novel approach that bridges tensor network states with the transformer-based NNQS-Transformer (QiankunNet) to enhance accuracy and convergence for systems with relatively large active spaces. By transforming tensor network states into active space configuration interaction type wave functions, QiankunNet achieves accuracy surpassing both the pretraining density matrix renormalization group (DMRG) results and traditional coupled cluster methods, particularly in strongly correlated regimes. We investigate two configuration transformation methods: the sweep-based direct conversion (Conv.) method and the entanglement-driven genetic algorithm (EDGA) method, with Conv. showing superior efficiency. The effectiveness of this approach is validated on H₂O with a large active space (10e, 24o) in the cc-pVDZ basis set, demonstrating an efficient routine between DMRG and QiankunNet and also offering a promising direction for advancing quantum state representation in complex molecular systems.