  Quantum state tomography (QST) is a challenging task in intermediate-scale
quantum devices. Here, we apply conditional generative adversarial networks
(CGANs) to QST. In the CGAN framework, two duelling neural networks, a
generator and a discriminator, learn multi-modal models from data. We augment a
CGAN with custom neural-network layers that enable conversion of output from
any standard neural network into a physical density matrix. To reconstruct the
density matrix, the generator and discriminator networks train each other on
data using standard gradient-based methods. We demonstrate that our QST-CGAN
reconstructs optical quantum states with high fidelity orders of magnitude
faster, and from less data, than a standard maximum-likelihood method. We also
show that the QST-CGAN can reconstruct a quantum state in a single evaluation
of the generator network if it has been pre-trained on similar quantum states.
