  We apply deep-neural-network-based techniques to quantum state classification
and reconstruction. We demonstrate high classification accuracies and
reconstruction fidelities, even in the presence of noise and with little data.
Using optical quantum states as examples, we first demonstrate how
convolutional neural networks (CNNs) can successfully classify several types of
states distorted by, e.g., additive Gaussian noise or photon loss. We further
show that a CNN trained on noisy inputs can learn to identify the most
important regions in the data, which potentially can reduce the cost of
tomography by guiding adaptive data collection. Secondly, we demonstrate
reconstruction of quantum-state density matrices using neural networks that
incorporate quantum-physics knowledge. The knowledge is implemented as custom
neural-network layers that convert outputs from standard feedforward neural
networks to valid descriptions of quantum states. Any standard feed-forward
neural-network architecture can be adapted for quantum state tomography (QST)
with our method. We present further demonstrations of our proposed
[arXiv:2008.03240] QST technique with conditional generative adversarial
networks (QST-CGAN). We motivate our choice of a learnable loss function within
an adversarial framework by demonstrating that the QST-CGAN outperforms, across
a range of scenarios, generative networks trained with standard loss functions.
For pure states with additive or convolutional Gaussian noise, the QST-CGAN is
able to adapt to the noise and reconstruct the underlying state. The QST-CGAN
reconstructs states using up to two orders of magnitude fewer iterative steps
than a standard iterative maximum likelihood (iMLE) method. Further, the
QST-CGAN can reconstruct both pure and mixed states from two orders of
magnitude fewer randomly chosen data points than iMLE.
