Robust open-loop stabilization of Fock states by time-varying quantum interactions* *This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Office. The authors were partially supported by the ANR, Projet Blanc EMAQS ANR-2011-BS01-017-01 and Projet C-QUID BLAN-3-139579.