  Deep learning has deeply changed the paradigms of many research fields. At
the heart of chemical and physical sciences is the accurate ab initio
calculation of many-body wavefunction, which has become one of the most notable
examples to demonstrate the power of deep learning in science. In particular,
the introduction of deep learning into quantum Monte Carlo (QMC) has
significantly advanced the frontier of ab initio calculation, offering a
universal tool to solve the electronic structure of materials and molecules.
Deep learning QMC architectures were initial designed and tested on small
molecules, focusing on comparisons with other state-of-the-art ab initio
methods. Methodological developments, including extensions to real solids and
periodic models, have been rapidly progressing and reported applications are
fast expanding. This review covers the theoretical foundation of deep learning
QMC for solids, the neural network wavefunction ansatz, and various of other
methodological developments. Applications on computing energy, electron
density, electric polarization, force and stress of real solids are also
reviewed. The methods have also been extended to other periodic systems and
finite temperature calculations. The review highlights the potentials and
existing challenges of deep learning QMC in materials chemistry and condensed
matter physics.
