Deep neural networks for quantum state characterization, part 2: reconstruction

Quantum state tomography (QST) is a data-intensive task which can be connected to generative modeling problems in machine learning. Generative models based on deep neural networks attempt to learn an underlying distribution for observed data. We connect this task to learning the density matrix of a quantum state from measurement statistics. We go beyond a restricted-Boltzmann-machine approach for QST by combining variational autoencoders (VAEs) and conditional generative adversarial networks (CGANs) into a QST-CGAN architecture. Our method uses standard neural-network architectures and training to learn a quantum state description from measurement data. We compare the QST-CGAN's performance against a standard iterative-maximum-likelihood (iMLE) method for reconstructing optical quantum states. The QST-CGAN method converges faster (almost two orders of magnitude) than iMLE and works well both for pure and mixed quantum states of low rank. We also demonstrate that our QST-CGAN method can be adapted easily to deal with noise and requires much less data (up to two orders of magnitude) than iMLE to reach the same reconstruction fidelity.