  Chemical compound space (CCS), the set of all theoretically conceivable
combinations of chemical elements and (meta-)stable geometries that make up
matter, is colossal. The first principles based virtual sampling of this space,
for example in search of novel molecules or materials which exhibit desirable
properties, is therefore prohibitive for all but the smallest sub-sets and
simplest properties. We review studies aimed at tackling this challenge using
modern machine learning techniques based on (i) synthetic data, typically
generated using quantum mechanics based methods, and (ii) model architectures
inspired by quantum mechanics. Such Quantum mechanics based Machine Learning
(QML) approaches combine the numerical efficiency of statistical surrogate
models with an {\em ab initio} view on matter. They rigorously reflect the
underlying physics in order to reach universality and transferability across
CCS. While state-of-the-art approximations to quantum problems impose severe
computational bottlenecks, recent QML based developments indicate the
possibility of substantial acceleration without sacrificing the predictive
power of quantum mechanics.
