Quantum Control In Solid-State Nuclear Magnetic Resonance

In recent years,quantum information science has developed rapidly as an interdis-ciplinary discipline that integrates quantum mechanics,information science,and math-ematics and materials.Due to the unique nature of quantum mechanics,quantum in-formation science has shown superiority over classical information in the processing of certain specific problems.Therefore,quantum information technology has attracted widespread interest and a variety of physical systems are developed to promote the progress of quantum information science.Among them,liquid-state nuclear magnetic system(NMR)is a high-quality platform for studying many quantum information meth-ods due to mature control technology and long decoherence times.However,liquid state NMR is an unlikely candidate for a quantum computer due to the lack of scalability in practice.One way to address this limitation is to extend liquid-state NMR to solid-state NMR,where various dynamical nuclear polarization techniques can be employed and the speed of gate operations can be increased via much larger dipolar couplings.As one of most important technology in quantum information science,quantum control should be improved and developed in solid-state NMR system.During my Ph.D.period,re-search focus on the topics of quantum control in solid-state NMR system.I conducted research from liquid-state systems to solid-state systems as well as from close system control to open system control.This doctor thesis mainly involves the following parts.In chapter 1,I briefly present the background and basic concepts of quantum com-puting and NMR quantum information processing.In chapter 2,I introduce the basic principles of solid-state NMR,including Hamil-tonians,the manipulation techniques commonly used in the field of solid-state NMR,the relaxation theory derived from the master equations,and the average Hamiltonian theory used to design pulse sequences.In chapter 3,I present a comprehensive analysis of the errors arisen in a selective pulse network by using the zeroth and first order average Hamiltonian theory.Effective correction rules are derived for adjusting important pulse parameters such as irradiation frequencies,rotational angles and transmission phases of the selective pulses to increase the control fidelity.Simulations show that applying our compilation procedure for a given circuit is efficient and can greatly reduce the error accumulation.In chapter 4,I construct a reachable set of zero-order average Hamiltonian for multi-pulse sequence of a homonuclear solid-state system by using average Hamiltonian theory.Further,by solving the homonuclear decoupling constraint equations,we design a new homo-nuclear decoupling sequence with controllable scaling factor.The homo-nuclear decoupling sequence was finally shown in a comparative experiment to show the high scaling factor and effective power properties.In chapter 5,I design a novel sequence based on transient nuclear Overhauser ef-fect(NOE)to increase the polarization by using the effect of cross-relaxation on polar-ization in solid-state NMR.Starting from the Solomon equations,I analyze the con-ditions under which the overshoot phenomenon occurs.The relationship between the maximum polarization enhancement and cross-relaxation and the initial values of the I and S nuclear spins is given.A new sequence of enhanced polarization associated with transient NOEs was developed and tested in experiment.Experimental results show that the transient NOE method is more effective than other methods in mobile systems.Chapter 6 is my conclusion and perspective.