Learning Global Quantum Properties from Local Measurements with Neural Networks

Characterizing the properties of multiparticle quantum systems is a crucial task for quantum computing and many-body quantum physics. The task, however, becomes extremely challenging when the system size becomes large and when the properties of interest involve global measurements on a large number of sites. Here we develop a multi-task neural network model that can accurately predict global properties of many-body quantum systems, like string order parameters and many-body topological invariants, using only limited measurement data gathered from few neighbouring sites. The model can simultaneously predict multiple quantum properties, including not only expectation values of quantum observables, but also general nonlinear functions of the quantum state, such as entanglement entropies. Remarkably, we find that multi-task training over a given set of quantum properties enables our model to discover new properties outside the original set. Without any labeled data, the model can perform unsupervised classification of quantum phases of matter and uncover unknown boundaries between different phases.