NNQS-AFQMC: Neural network quantum states enhanced fermionic quantum Monte Carlo

TL;DR

This paper presents a novel method combining neural network quantum states with auxiliary-field quantum Monte Carlo to improve the accuracy of ground-state energy calculations in strongly correlated molecules.

Contribution

It introduces a direct integration of neural network quantum states as trial wavefunctions in AFQMC, enhancing accuracy with manageable computational cost.

Findings

Achieved near-exact energies for nitrogen molecule at stretched geometries.

Demonstrated the effectiveness of NNQS as high-quality trial wavefunctions in AFQMC.

Showed potential to overcome challenges in strongly correlated electronic structure calculations.

Abstract

We introduce an efficient approach to implement neural network quantum states (NNQS) as trial wavefunctions in auxiliary-field quantum Monte Carlo (AFQMC). NNQS are a recently developed class of variational ans\"atze capable of flexibly representing many-body wavefunctions, though they often incur a high computational cost during optimization. AFQMC, on the other hand, is a powerful stochastic projector approach for ground-state calculations, but it normally requires an approximate constraint via a trial wavefunction or trial density matrix, whose quality affects the accuracy. Recently it has been shown (Xiao et al, arXiv2505.18519) that a broad class of highly correlated wave-functions can be integrated into AFQMC through stochastic sampling techniques. In this work, we apply this approach and present a direct integration of NNQS with AFQMC, allowing NNQS to serve as high-quality trial wavefunctions for AFQMC with manageable computational cost. We test the NNQS-AFQMC method on the challenging nitrogen molecule (N$_2$) at stretched geometries. Our results demonstrate that AFQMC with an NNQS trial wavefunction can attain near-exact total energies, highlighting the potential of AFQMC with NNQS to overcome longstanding challenges in strongly correlated electronic structure calculations. We also outline future research directions for improving this promising methodology.