Functional Neural Wavefunction Optimization
This work addresses the challenge of designing efficient optimization algorithms for quantum many-body systems, representing an incremental improvement by unifying and extending existing methods with geometric principles.
The authors tackled the problem of optimizing neural network wavefunctions in variational quantum Monte Carlo by developing a geometric framework that translates infinite-dimensional dynamics into tractable algorithms, resulting in accurate ground-state energy estimations for condensed matter models.
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.