  We consider a superconductor proximity coupled to a two-dimensional
ferromagnetic film with a skyrmion texture. Using the T-matrix calculations and
numerical modeling we calculate the spin-polarized local density of states in
the superconductor in the vicinity of the skyrmion. We predict the skyrmion
bound states (SBS) that are induced in the superconductor, similar to the
well-known Yu-Shiba-Rusinov (YSR) states. The SBS wavefunctions have spatial
power law decay. Presence of the SBS suggests the mechanism by which
superconductivity could facilitate an effective long-range interaction between
skyrmions when their SBS wavefunctions overlap.
