Learning Potentials of Quantum Systems using Deep Neural Networks
This work addresses the challenge of understanding quantum phenomena for researchers in physics and chemistry, but it appears incremental as it extends existing neural network methods from classical to quantum systems.
The paper tackles the problem of reconstructing the Hamiltonian of a quantum system using only limited probability distribution data, and it demonstrates that deep neural networks can approximate quantum potentials in an unsupervised manner.
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.