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.

9 pages, 6 figures

References in corpus (26)

• Shortcuts to adiabaticity: concepts, methods, and applications
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Quantum Search by Local Adiabatic Evolution
• Quantum Steering
• Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
• Complex weak values in quantum measurement
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Fast atomic transport without vibrational heating
• Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space
• Particle manipulation beyond the diffraction limit using structured super-oscillating light beams
• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• State tomography via weak measurements
• Measurement-induced steering of quantum systems
• Weak-to-strong transition of quantum measurement in a trapped-ion system
• Energetic cost of quantum control protocols
• Breaking the temporal resolution limit by superoscillating optical beats
• Geometric phase in weak measurements
• Topological transition in measurement-induced geometric phases
• Interferences in quantum eraser reveal geometric phases in modular and weak values
• Quantum Rabi dynamics of trapped atoms far in the deep strong coupling regime
• Super-oscillating Electron Wave Functions with Sub-diffraction Spots
• Single atom in a superoscillatory optical trap
• Von Neumann spin measurements with Rashba fields
• Qubit state tomography in superconducting circuit via weak measurements
• Fast and robust particle shuttling for quantum science and technology