Functional Neural Wavefunction Optimization
Abstract
We propose a framework for the design and analysis of optimization algorithms in variational quantum Monte Carlo, drawing on geometric insights into the corresponding function space. The framework translates infinite-dimensional optimization dynamics into tractable parameter-space algorithms through a Galerkin projection onto the tangent space of the variational ansatz. This perspective unifies existing methods such as stochastic reconfiguration and Rayleigh-Gauss-Newton, provides connections to classic function-space algorithms, and motivates the derivation of novel algorithms with geometrically principled hyperparameter choices. We validate our framework with numerical experiments demonstrating its practical relevance through the accurate estimation of ground-state energies for several prototypical models in condensed matter physics modeled with neural network wavefunctions.
Cite
@article{arxiv.2507.10835,
title = {Functional Neural Wavefunction Optimization},
author = {Victor Armegioiu and Juan Carrasquilla and Siddhartha Mishra and Johannes Müller and Jannes Nys and Marius Zeinhofer and Hang Zhang},
journal= {arXiv preprint arXiv:2507.10835},
year = {2025}
}