Theoretical And Experimental Study On Quantum Control Based On Zero-to Ultralow-field Nuclear Magnetic Resonance

With a deeper understanding of quantum mechanics,people are not just satisfied with applying it to describe and understand natural phenomena.They are looking for-ward to utilizing quantum properties in practical applications.Quantum control is the bridge between knowledge of quantum properties and practical applications.The study of quantum control is crucial to the development of quantum information,quantum com-puting,quantum sensing and other quantum technologies.Because of its long coherence time and established control techniques,nuclear magnetic resonance(NMR)provides a suitable experimental platform for studies on quantum control.In recent years,the newly developed zero-to ultralow-field NMR is considered a supplement to the conven-tional high-field NMR.It promises to find applications in fundamental physics,chem-istry,biology and medicine.However,there is a lack of quantum control protocols in zero-to ultralow-field NMR.The study on quantum control in this research field is thus urgently needed.The research topic of this dissertation is spin-based quantum control.NMR is the subject of study and provides an experimental platform.Theoretical and experimental studies on quantum control in zero-to ultralow-field NMR are performed.The main contents of this dissertation are as follows:1.A universal quantum control scheme is theoretically proposed in zero-field NMR for the first time.This scheme enriches the quantum control methods in zero-field NMR.It is expected to play a vital role in practical applications based on zero-field NMR.2.Based on the Pontryagin's maximum principle and a newly developed symmetry reduction technique,the time-optimal control scheme for arbitrary single-qubit gates in an independent two-qubit system under global control in zero-field NMR is obtained for the first time.The control scheme is realized in a zero-field NMR experiment for the first time.The experimental fidelity is around 0.99,and the time cost is only 20%?30%of the traditional composite-pulse scheme.This method is expected to contribute to practical applications based on zero-field NMR and other similar quantum systems.3.The relationship between global phases and optimal times of quantum oper-ations is studied.It is experimentally demonstrated in an NMR experiment by NMR interferometry.4.An extended Kalman filter is designed to realize the real-time estimation of de-caying sinusoidal signals with unknown and time-varying frequencies.The filter is im-plemented in an ultralow-field NMR experiment,preliminary results indicate the ability to achieve real-time estimation of the NMR signal with time-varying frequencies.The implementation of the above Kalman filter is a first step towards further studies on NMR quantum feedback control.