  Magnetic skyrmions are vortex-like quasiparticles characterized by long
lifetime and remarkable topological properties. That makes them a promising
candidate for the role of information carriers in magnetic information storage
and processing devices. Although considerable progress has been made in
studying skyrmions in classical systems, little is known about the quantum
case: quantum skyrmions cannot be directly observed by probing the local
magnetization of the system, and the notion of topological protection is
elusive in the quantum realm. Here, we explore the potential robustness of
quantum skyrmions in comparison to their classical counterparts. We
theoretically analyze the dynamics of a quantum skyrmion subject to local
projective measurements and demonstrate that the properties of the skyrmionic
quantum state change very little upon external perturbations. We further show
that by performing repetitive measurements on a quantum skyrmion, it can be
completely stabilized through an analog of the quantum Zeno effect.
