Magnetic vortices form the ground state in micron and submicron ferromagnetic disks. By inserting artificial defects (antidots) into a submicron ferromagnetic disk, magnetic vortices can be pinned controllably thus enabling a different way for magnetic switching. We show that by inserting n antidots into a disk magnetization reversal takes place via n-1 jumps of the vortex core between neighboring antidots. This cannot only be used to establish stable two-state switching for n=2, but also to realize a multilevel remanent state with low switching fields. (C) 2004 American Institute of Physics.