  We show that neural quantum states based on very deep (4--16-layered) neural
networks can outperform state-of-the-art variational approaches on highly
frustrated quantum magnets, including quantum-spin-liquid candidates. We focus
on group convolutional neural networks (GCNNs) that allow us to impose
space-group symmetries on our ans\"atze. We achieve state-of-the-art
ground-state energies for the $J_1-J_2$ Heisenberg models on the square and
triangular lattices, in both ordered and spin-liquid phases, and discuss ways
to access low-lying excited states in nontrivial symmetry sectors. We also
compute spin and dimer correlation functions for the quantum paramagnetic phase
on the triangular lattice, which do not indicate either conventional or
valence-bond ordering.
