  We investigate the ground state properties of quantum skyrmions in a
ferromagnet using variational Monte Carlo with the neural network quantum state
as variational ansatz. We study the ground states of a two-dimensional quantum
Heisenberg model in the presence of the Dzyaloshinskii-Moriya interaction
(DMI). We show that the ground state accommodates a quantum skyrmion for a
large range of parameters, especially at large DMI. The spins in these quantum
skyrmions are weakly entangled, and the entanglement increases with decreasing
DMI. We also find that the central spin is completely disentangled from the
rest of the lattice, establishing a non-destructive way of detecting this type
of skyrmion by local magnetization measurements. While neural networks are well
suited to detect weakly entangled skyrmions with large DMI, they struggle to
describe skyrmions in the small DMI regime due to nearly degenerate ground
states and strong entanglement. In this paper, we propose a method to identify
this regime and a technique to alleviate the problem. Finally, we analyze the
workings of the neural network and explore its limits by pruning. Our work
shows that neural network quantum states can be efficiently used to describe
the quantum magnetism of large systems exceeding the size manageable in exact
diagonalization by far.
