  An isolated system of interacting quantum particles is described by a
Hamiltonian operator. Hamiltonian models underpin the study and analysis of
physical and chemical processes throughout science and industry, so it is
crucial they are faithful to the system they represent. However, formulating
and testing Hamiltonian models of quantum systems from experimental data is
difficult because it is impossible to directly observe which interactions the
quantum system is subject to. Here, we propose and demonstrate an approach to
retrieving a Hamiltonian model from experiments, using unsupervised machine
learning. We test our methods experimentally on an electron spin in a
nitrogen-vacancy interacting with its spin bath environment, and numerically,
finding success rates up to 86%. By building agents capable of learning
science, which recover meaningful representations, we can gain further insight
on the physics of quantum systems.
