  We investigate the transport properties of a thin superconducting Al layer
covering a square array of magnetic dots with out-of-plane magnetization. A
thorough characterization of the magnetic properties of the dots allowed us to
fine-tune their magnetic state at will, hereby changing the influence of the
dots on the superconductor in a continuous way. We show that even though the
number of vortex-antivortex pairs discretely increases with increasing the
magnetization of the dots, no corresponding discontinuity is observed in the
resistance of the sample. The evolution of the superconducting phase boundary
as the magnetic state of the dots is swept permits one to devise a fully
controllable and erasable field induced superconductor.
