We address the problem of optimal quantum state preparation. We propose a protocol based on a stroboscopic driving of the system in its parameter space combined with repeated measurementlike interactions with an external spectator system. In the limit of infinite-rate interactions, the protocol naturally yields unit fidelity due to the quantum Zeno effect. For realistic finite-rate interactions we show that the fidelity is maximized if the discretized driving trajectory has a minimal geometric length and keeps 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 possible dominance over the coherent driving. Our results can be used in various quantum information applications.

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• Adiabatic quantum optimization
• Measurement-based quantum computing
• Open quantum systems & decoherence
• Quantum Zeno dynamics
• Quantum control
• Quantum protocols
• Geometry