Learning and Discovering Quantum Properties with Multi-Task Neural Networks

Deep neural networks are a powerful tool for predicting properties of quantum states from limited measurement data. Here we develop a network model that can simultaneously predict multiple quantum properties, including not only expectation values of quantum observables, but also general nonlinear functions of the quantum state, like entanglement entropies and many-body topological invariants. Remarkably, we find that a model trained on a given set of properties can also discover new properties outside that set. Multi-purpose training also enables the model to infer global properties of many-body quantum systems from local measurements, to classify symmetry protected topological phases of matter, and to discover unknown boundaries between different phases.