  Neural networks are a promising tool for characterizing intermediate-scale
quantum devices from limited amounts of measurement data. A challenging problem
in this area is to learn the action of an unknown quantum process on an
ensemble of physically relevant input states. To tackle this problem, we
introduce a neural network that emulates the unknown process by constructing an
internal representation of the input ensemble and by mimicking the action of
the process at the state representation level. After being trained with
measurement data from a few pairs of input/output quantum states, the network
becomes able to predict the measurement statistics for all inputs in the
ensemble of interest. We show that our model exhibits high accuracy in
applications to quantum computing, quantum photonics, and quantum many-body
physics.
