  We review the development of generative modeling techniques in machine
learning for the purpose of reconstructing real, noisy, many-qubit quantum
states. Motivated by its interpretability and utility, we discuss in detail the
theory of the restricted Boltzmann machine. We demonstrate its practical use
for state reconstruction, starting from a classical thermal distribution of
Ising spins, then moving systematically through increasingly complex pure and
mixed quantum states. Intended for use on experimental noisy intermediate-scale
quantum (NISQ) devices, we review recent efforts in reconstruction of a cold
atom wavefunction. Finally, we discuss the outlook for future experimental
state reconstruction using machine learning, in the NISQ era and beyond.
