Learning Potentials of Quantum Systems using Deep Neural Networks

TL;DR

This paper explores how deep neural networks can be used to approximate quantum system Hamiltonians using limited observational data, bridging machine learning and quantum physics.

Contribution

It introduces an unsupervised method for reconstructing quantum Hamiltonians from probability distributions, leveraging neural networks with inductive biases.

Findings

Neural networks can approximate quantum Hamiltonians from limited data.

The approach provides insights into quantum phenomena using machine learning.

Potential for unsupervised learning in quantum system analysis.

Abstract

Attempts to apply Neural Networks (NN) to a wide range of research problems have been ubiquitous and plentiful in recent literature. Particularly, the use of deep NNs for understanding complex physical and chemical phenomena has opened a new niche of science where the analysis tools from Machine Learning (ML) are combined with the computational concepts of the natural sciences. Reports from this unification of ML have presented evidence that NNs can learn classical Hamiltonian mechanics. This application of NNs to classical physics and its results motivate the following question: Can NNs be endowed with inductive biases through observation as means to provide insights into quantum phenomena? In this work, this question is addressed by investigating possible approximations for reconstructing the Hamiltonian of a quantum system in an unsupervised manner by using only limited information obtained from the system's probability distribution.