A framework for efficient ab initio electronic structure with Gaussian Process States

TL;DR

This paper introduces a flexible framework using Gaussian Process States for efficient ab initio electronic structure calculations, demonstrating competitive accuracy and scalability for complex fermionic systems.

Contribution

It develops a novel approach combining Gaussian Process States with local Fock space representations, improving scalability and accuracy in quantum many-body simulations.

Findings

Achieved accurate results for systems with up to 64 electrons.

Demonstrated a simplified ab initio model of the Mott transition.

Showed improved scalability over previous machine learning inspired methods.

Abstract

We present a general framework for the efficient simulation of realistic fermionic systems with modern machine learning inspired representations of quantum many-body states, towards a universal tool for ab initio electronic structure. These machine learning inspired ansatzes have recently come to the fore in both a (first quantized) continuum and discrete Fock space representations, where however the inherent scaling of the latter approach for realistic interactions has so far limited practical applications. With application to the 'Gaussian Process State', a recently introduced ansatz inspired by systematically improvable kernel models in machine learning, we discuss different choices to define the representation of the computational Fock space. We show how local representations are particularly suited for stochastic sampling of expectation values, while also indicating a route to overcome the discrepancy in the scaling compared to continuum formulated models. We are able to show competitive accuracy for systems with up to 64 electrons, including a simplified (yet fully ab initio) model of the Mott transition in three-dimensional hydrogen, indicating a significant improvement over similar approaches, even for moderate numbers of configurational samples.