  The future development of quantum technologies relies on creating and
manipulating quantum systems of increasing complexity, with key applications in
computation, simulation and sensing. This poses severe challenges in the
efficient control, calibration and validation of quantum states and their
dynamics. Although the full simulation of large-scale quantum systems may only
be possible on a quantum computer, classical characterization and optimization
methods still play an important role. Here, we review different approaches that
use classical post-processing techniques, possibly combined with adaptive
optimization, to learn quantum systems, their correlation properties, dynamics
and interaction with the environment. We discuss theoretical proposals and
successful implementations across different multiple-qubit architectures such
as spin qubits, trapped ions, photonic and atomic systems, and superconducting
circuits. This Review provides a brief background of key concepts recurring
across many of these approaches with special emphasis on the Bayesian formalism
and neural networks.
