Experimental Research Of Quanutm Computation Based On Quadrupolar NMR System

Nuclear magnetic resonance(NMR)is one of the most well-developed platform to implement quantum computation experiment.People have initialized quantum state and realized the quantum logical gates of the largest qubits number in NMR system,besides,plenty of quantum algorithm and quantum simulation experiments have been carried out with NMR.However,most of these work were done with a spin-1/2 nuclear system containing isotopes such as13C,1H and 19F.There are several reasons for this:on the one hand,these nucleus have been widely studied in traditional NMR spectroscopy,which results in abundant research achievements and experience,what is more,the nucleus such as 13C,1H tend to form small organic molecules,supplying kinds of multi-qubit samples for NMR quantum computation;on the other hand,the two-level qubit system supported by a spin-1/2 nuclei corresponds well to the conception of bit in the classical computer;at last,the NMR information can be completely revealed with the method of liquid NMR,of which the liquid sample is much easier to be obtained,the liquid NMR technique is much easier too.Although spin-1/2 NMR system have so many advantages mentioned above,nu-cleus with spin>1/2 which constitute approximately 75%of the NMR-activate iso-topes in the periodic table,have attracted interest of researchers in the field of quantum computation gradually for several reasons in recent years.Spin>1/2 nucleus exhibits electrical quadrupolar moment because of the non-spherical symmetric distribution of the electric charge,so it was named as "quadrupolar nucleus",we can also call it "high spin".My research subject during my phD period is quantum computation with quadrupo-lar NMR system,the obtained achievement laid a solid foundation for the further study on the topic,the dissertation is planned as follows:Chapter 1 is the preface.Chapter 2,we introduced the basic knowlodge of quantum computation with quadrupo-lar NMR system,including a brief introduction to quadrupolar nuclei,quadrupolar N-MR samples,the spin operators of high spins,the Hamiltonian of quadrupolar NMR system,pulse operation,quantum state initialization and quantum state tomography.Among which we introduced the GRAPE algorithm to quadrupolar system for the first time,and prepared initial states in spin-3/2 and spin-7/2 with relatively high fidelities.And in the section of tomography,we have improved the former method based on line-selective pulse by reducing the number of pulse and the times of the experiments.Chapter 3,after a introduction of the relaxation in quadrupolar NMR,we provided the explicit master equations of quadrupolar nuclei systems with different spin number given pure quadrupolar relaxation mechanism,and the Lindblad operators were also presented.After that,we solved the master equation analytically in the case of T1>>T2,the transverse relaxation time is measured in the NaN03 single crystal.At last we put forward a proposal to measure the relaxation parameters in a even higher spin system,I-7/2.Chapter 4,we implemented a quantum simulation experiment,a two-site Bose-Hubbard model was simulated using a spin-3/2 quadrupolar nucleus in NaN03,and the interesting phenomenon of interaction blockade and the single-atom tunneling was ob-served.It is the first adiabatic quantum simulation experiment in the quadrupolar NMR system as far as we know,our work exhibits the potential of quadrupolar NMR system in the field of quantum simulation.As an example,we briefly explained how to simu-late a quantum chaotic model in the quadrupolar system,and the expected experiment result is also presented.Chapter 5 was a discussion on quantum metrology study using quadrupolar NMR system.Firstly,we introduced the basic conception of quantum metrology,and then the realization of NOON state and spin squeezed state in quadrupolar NMR system was talked.Secondly,we carried out a quantum metrology experiment to estimate the quadrupolar coupling in the quadrupolar NMR system based on the Mach-Zenhder in-terference.At last,we analysed the effect of the imperfections of the initial states and unitary control in practical experiment in the language of quantum Fisher information,the effect of relaxation was highlighted.Chapter 6 was the conclusion and the outlook.