  Characterizing multipartite quantum systems is crucial for quantum computing
and many-body physics. The problem, however, becomes challenging when the
system size is large and the properties of interest involve correlations among
a large number of particles. Here we introduce a neural network model that can
predict various quantum properties of many-body quantum states with constant
correlation length, using only measurement data from a small number of
neighboring sites. The model is based on the technique of multi-task learning,
which we show to offer several advantages over traditional single-task
approaches. Through numerical experiments, we show that multi-task learning can
be applied to sufficiently regular states to predict global properties, like
string order parameters, from the observation of short-range correlations, and
to distinguish between quantum phases that cannot be distinguished by
single-task networks. Remarkably, our model appears to be able to transfer
information learnt from lower dimensional quantum systems to higher dimensional
ones, and to make accurate predictions for Hamiltonians that were not seen in
the training.
