Learning Quantum Models from Symmetries

Inverse method algorithms that learn models from data, such as machine learning algorithms, have been successful in solving complicated engineering tasks and are increasingly being applied to study quantum systems. Moreover, inverse methods have the potential to automate the discovery of quantum materials with desired properties. With this goal in mind, we present an inverse method algorithm for learning quantum models, i.e., Hamiltonians, from symmetries or integrals of motion. The forward problem of starting from a given Hamiltonian and finding its symmetries, is generically difficult both analytically and numerically. Yet, despite the difficulty of the forward problem, we show that this method can efficiently solve the inverse problem of starting from a desired set of symmetries and finding Hamiltonians obeying those symmetries. In this talk, we describe this inverse method and give examples of its application.