  Quantum state tomography is a daunting challenge of experimental quantum
computing even in moderate system size. One way to boost the efficiency of
state tomography is via local measurements on reduced density matrices, but the
reconstruction of the full state thereafter is hard. Here, we present a machine
learning method to recover the full quantum state from its local information,
where a fully-connected neural network is built to fulfill the task with up to
seven qubits. In particular, we test the neural network model with a practical
dataset, that in a 4-qubit nuclear magnetic resonance system our method yields
global states via the 2-local information with high accuracy. Our work paves
the way towards scalable state tomography in large quantum systems.
