# Bayesian perspectives for quantum states and application to ab initio quantum chemistry

## TL;DR

This paper reviews recent advances in applying Bayesian machine learning, especially Gaussian Process States, to efficiently represent many-electron wavefunctions for ab initio quantum chemistry, addressing strong correlation challenges.

## Contribution

It introduces the use of Gaussian Process States within a Bayesian framework to improve quantum chemical simulations and unify various machine learning approaches in this domain.

## Key findings

- Gaussian Process States enable efficient wavefunction representation.
- Bayesian models help quantify uncertainty in quantum chemical predictions.
- The approach informs the design of machine learning models for correlation patterns.

## Abstract

The quantum many-electron problem is not just at the heart of condensed matter phenomena, but also essential for first-principles simulation of chemical phenomena. Strong correlation in chemical systems are prevalent and present a formidable challenge in the simulation of these systems, while predictive phenomena in this domain often also requires a demanding level of accuracy to inform chemical behavior. Efficient representations of the many-electron states of chemical systems are therefore also being inspired by machine learning principles to provide an alternative to established approaches. In this chapter, we review recent progress in this endeavor for quantum chemical problems represented in second quantization, and the particular challenges present in this field. In particular, we focus on the application of Gaussian Process States emerging from efficient representations of the many-body wavefunction with rigorous Bayesian modeling frameworks, allowing for the unification of multiple paradigms under a common umbrella. We show how such models (and other representations derived from machine learning) can be used as novel tools to compute ab initio chemical properties, while in turn also informing the design of machine learning models to extract correlation patterns in classical data.