Experimental Implementation Of Several Quantum Algorithms And Development Of Novel Techniques In NMR Systems

In recent years quantum information and quantum computing science have been developed rapidly.Quantum information processor is widely used in the fields of quan-tum computation,quantum simulation,quantum metrology and etc.Many new quan-tum algorithms and quantum schemes have been proposed.Thus we need constantly improve the experimental technologies,to implement the algorithms and schemes.As a good quantum experimental testbed,nuclear magnetic resonance(NMR)spin systems provide rich and sophisticated quantum control methods.In recent years a lot of quan-tum experiments have been performed using NMR systems and a series of experimental technologies are developed.Using NMR systems,we experimentally implemented several quantum algorithms and quantum schemes.In order to improve the number of controllable qubits,we stud-ied and improved a series of experimental control technologies and implemented the experiment of 7-qubit pseudo-pure state preparation.Moreover,enhancing the polar-ization of the sample plays an important role in quantum information processing.We did some theoretical research about how to enhance the initial polarization of the sample and proposed a new kind of algorithm cooling.The main contents in my dissertation are as follows:1.In the first chapter,we introduce the background of quantum computation.First-ly we present some basic concepts of quantum computation,such as qubit and quantum gate.Then review some quantum algorithms and introduce several mainstream physical systems for quantum computation.2.In the second chapter,we introduce some basic concepts,model and basic ma-nipulation technologies of quantum computation using NMR systems.3.The third chapter consists of several experimental implementations of quan-tum algorithms using NMR systems.The first one is the experimental implementation of the quantum algorithm of linear system of equations.We solve three 2-dimension linear systems of equations with errors about 7%.The second one is the experimen-tal implementation of the quantum algorithm of the integer square-free decomposition problem.We use it to perform square-free test for the integers 9 and 15.The last one is the experiment of the purification of H-type magic state.4.In the fourth chapter,we discuss the experimental manipulation technologies in multi-qubit experiments using NMR systems.We discuss the difficulties in multi-qubit experiments.Then combining the experiment of 7-qubit pseudo-pure state preparation,we introduce a series of experimental technologies in multi-qubit experiments.5.In the fifth chapter we propose a new heat-bath algorithm cooling scheme.We firstly review the heat-bath algorithm cooling and Overhauser effect.Then using Red-field equation in coherence representation,we analyze the function of cross relaxation.Combining cross relaxation and the decoherence-free subspace we develop a new algo-rithm cooling scheme and further improve the upper bound of the polarization.6.The sixth chapter is my conclusion and perspective.