  We propose a protocol for transitionless driving of a bound quantum system in
its parameter space using repeated measurement-like interactions with an
external spectator system. As a consequence of the quantum Zeno effect, the
fidelity of the final state preparation is equal to unity in the limit of
infinite-rate interactions. For finite-rate interactions, the maximal fidelity
is achieved for the driving trajectory having a minimal geometric length and
keeping a constant speed with respect to the Provost-Vallee metric in the
parameter space. We numerically test the protocol in an interacting multiqubit
system, demonstrating its dominance over the method of coherent driving.
