# Could the Hilbert Space Be a Smaller Place? A Neural Network Perspective

## TL;DR

This paper explores using neural networks to efficiently approximate quantum many-body ground states, potentially reducing the exponential complexity traditionally associated with these problems.

## Contribution

It applies neural network-based wave function learning to electron systems, demonstrating a promising approach to simplify complex quantum problems.

## Key findings

- Neural networks can approximate ground states of quantum systems.
- The approach reduces computational complexity compared to traditional methods.
- Initial results show significant simplification of the problem.

## Abstract

In quantum many-body problems, one of the main difficulties comes from the description of non-negligible interactions which require, at least in principle, an exponential amount of information. Recently, in the context of spin glasses and Boltzmann machines, it has been demonstrated that systematic machine learning of the wave function can reduce these issues to a tractable computational problem. In this work, we apply this approach to a different situation, i.e. the problem of finding the ground state of a given quantum system made of electrons, entirely described by its Hamiltonian operator, and by utilizing feedforward neural networks. Although still in the shape of a proof of concept, one can already observe that this seminal idea is able to substantially simplify the complexity of this peculiar, and important, problem.