Learning models of quantum systems from experiments

As Hamiltonian models underpin the study and analysis of physical and chemical processes, it is crucial that they are faithful to the system they represent. However, formulating and testing candidate Hamiltonians for quantum systems from experimental data is difficult, because one cannot directly observe which interactions are present. Here we propose and demonstrate an automated protocol to overcome this challenge by designing an agent that exploits unsupervised machine learning. We first show the capabilities of our approach to infer the correct Hamiltonian when studying a nitrogen-vacancy centre set-up. In preliminary simulations, the exact model is known and is correctly inferred with success rates up to 59%. When using experimental data, 74% of protocol instances retrieve models that are deemed plausible. Simulated multi-spin systems, characterized by a space of 1010 possible models, are also investigated by incorporating a genetic algorithm in our protocol, which identifies the target model in 85% of instances. The development of automated agents, capable of formulating and testing modelling hypotheses from limited prior assumptions, represents a fundamental step towards the characterization of large quantum systems. Quantum systems make it challenging to determine candidate Hamiltonians from experimental data. An automated protocol is presented and its capabilities to infer the correct Hamiltonian are demonstrated in a nitrogen-vacancy centre set-up.