A Deterministic Framework for Neural Network Quantum States in Quantum Chemistry

TL;DR

This paper introduces a deterministic optimization framework for Neural Network Quantum States that avoids sampling issues, enabling efficient and accurate calculations of strongly correlated quantum systems.

Contribution

A novel deterministic method for optimizing Neural Network Quantum States using a projection and perturbative correction, improving stability and scalability.

Findings

Achieves sub-linear wall-time scaling with respect to subspace size.

Enables calculations on systems with Hilbert spaces of 10^23 configurations.

Provides stable convergence with accuracy comparable to reference methods.

Abstract

We present a deterministic optimization framework for Neural Network Quantum States (NQS) designed to bypass the sampling variance and slow mixing issues inherent in stochastic optimization. By projecting a neural backflow ansatz onto dynamically evolving configuration subspaces and applying a post-hoc second-order perturbative correction, our method provides a systematic route for optimizing the selected variational component of the wavefunction and estimating residual correlation through a post-hoc perturbative correction. The implementation utilizes a hybrid CPU-GPU architecture that shows empirical sub-linear wall-time scaling with respect to the subspace size over the tested range, enabling the calculation of strongly correlated systems, such as the chromium dimer, within Hilbert spaces of $10^{23}$ configurations. Benchmarks on molecular bond dissociations demonstrate that this deterministic approach yields stable convergence and accuracies comparable to selected reference methods in the tested systems.