Superoscillating Quantum Control Induced By Sequential Selections

Abstract: Superoscillation is a counterintuitive phenomenon for its mathematical feature of ``faster-than-Fourier", which has allowed novel optical imaging beyond the diffraction limit. In this article, we introduce a superoscillating quantum control protocol realized by sequential selections within the framework of weak measurement, which steers the apparatus (target) by repeatedly applying optimal pre- and post-selections to the system (controller). Our protocol accelerates theadiabatic transport of trapped ions and adiabatic quantum search algorithm at a finite energy cost. We demonstrate the accuracy and robustness of the protocol in the presence of decoherence and fluctuating noise, and elucidate the trade-off between fidelity and rounds of selections. Our findings open new avenues for quantum state manipulation and wave-packet control using superoscillation across a range of quantum platforms.