Functional Neural Wavefunction Optimization

TL;DR

This paper introduces a geometric framework for optimizing neural network wavefunctions in quantum Monte Carlo, unifying existing methods and deriving new algorithms with improved hyperparameter choices, validated through numerical experiments.

Contribution

It presents a novel geometric perspective that unifies and extends optimization algorithms in variational quantum Monte Carlo using neural network wavefunctions.

Findings

Unified framework for existing algorithms like stochastic reconfiguration

Derived new geometrically motivated optimization algorithms

Accurate estimation of ground-state energies in physics models

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.