Machine learning quantum states in the NISQ era

We discuss the development of machine learning techniques for the purpose of reconstructing quantum states from projective measurement data. Technology adapted from a branch of unsupervised learning, called generative models, are well-suited for learning representations of quantum states from real experimental data. We discuss quantum state reconstruction with several classes of generative model, and compare in particular the performance of tractable and approximate density models. We demonstrate their practical use for state reconstruction, moving systematically through increasingly complex classes of pure and mixed quantum states. As an example of a use case for a real experimental noisy intermediate-scale quantum (NISQ) device, we review recent efforts in reconstructing a cold atom wavefunction. Finally, we discuss the outlook for scalable experimental state reconstruction using machine learning, in the NISQ era and beyond.