  Quantum state tomography aiming at reconstructing the density matrix of a
quantum state plays an important role in various emerging quantum technologies.
Inspired by the intuition that machine learning has favorable robustness and
generalization, we propose a deep neural networks based quantum state
tomography (DNN-QST) approach, which are applied to three
measurement-constrained cases, including few measurement copies and incomplete
measurements as well as noisy measurements. Numerical results demonstrate that
DNN-QST exhibits a great potential to achieve high fidelity for quantum state
tomography with limited measurement resources and can achieve improved
estimation when tomographic measurements suffer from noise. In addition, the
results for 2-qubit states from quantum optical devices demonstrate the
generalization of DNN-QST and its robustness against possible error in the
experimental devices.
