  Skyrmions in condensed matter physics appear as classical topological spin
structures. This nontrivial state can be obtained solving the corresponding
micromagnetic model, where the magnetization is treated as a continuous
classical vector field. Here, we introduce a new concept of quantum skyrmions
of a nanoscale size. This distinct magnetic state can be formed in spin-1/2 low
dimensional magnets characterized by a strong Dzyaloshinskii-Moriya
interaction. This concept can also be applied to usual spin systems
characterized by a nonzero exchange interaction if the quantum solution of the
problem is accessible. To perform a complete characterization of such a quantum
nanoskyrmion state, we analyze basis functions giving the largest contribution
to the ground state at different values of external magnetic field and
temperature. We observe that the quantum skyrmionic state is stabilized even
when the corresponding classical skyrmionic solution has already undergone a
phase transition towards the polarized ferromagnetic state.
