Nuclear Magnetic Resonance Experiment Research On Application Of Quantum Search Algorithm

Quantum information is significant in science and strategy. It is a new interdisci-plinary study of quantum mechanics, information science and computer science. Dur-ing the past two decades, great progress has been made both in the theoretical researchand experimental techniques of quantum computation and quantum communication.As one of the important algorithms in quantum computing, quantum search algorithmcan search the target much faster than the classical algorithm. Because of this, there is awide range of applications in the fields of security and quantum communication. Withthe long decoherence time, nuclear magnetic resonance (NMR) is one of the importantquantum computing implementation strategies, which take the advantage of simplecontrolling operations and the easy sample preparations. So far, NMR has achievedthe largest number of the qubits among various experimental systems in the quantumalgorithm realizations. Furthermore, NMR provides many helpful references and expe-riences for other implementation strategies. Related with NMR quantum computation,this thesis includes such aspects of research works as follows.In the area of pseudopure state initialization, we proposed two di?erent superpo-sition marked protocols. For arbitrary numbers of qubits, we found the proper unitarytransformation operators, and designed the relative quantum circuits, from which thepulse sequences can be constructed easily. We experimentally implemented the formerprotocol in the two-qubit NMR system. Furthermore, both of the two protocols weresimulated by three-qubit NMR simulator.In the field of quantum algorithm application, we proposed a quantum secret-sharing (QSS) protocol based on the four-state Grover algorithm. The loophole of theexisting sixteen-state QSS protocol was discussed, and its solution was given. Ourprotocol was experimentally demonstrated in NMR quantum information processorsuccessfully. We also realized the experimental implementation of a quantum stateprivacy amplification protocol in the two-qubit NMR system. Our experimental results agree with the theory well. Based on the existing duality fixed-point quantum searchalgorithm, we studied its NMR demonstration and verified its process with a three-qubit NMR simulator. In addition, we proposed an improved protocol, in which thee?ciency was promoted 4 times.Moreover, a dynamical decoupling group was given for the ?-type three-levelatom in the field of quantum control method. Our analytical results show that the cor-responding decoupling operations can suppress the decoherence completely in idealconditions. In the realistic situation, the numerical results indicate that the decoher-ence can also be suppressed e?ectively under the condition of finite pulse. At last, wedesigned the corresponding NMR radio-frequency pulse sequences for these decou-pling operations.