Experimental Technology In Nuclear Megnetic Resonance Quantum Computation

The basic aim of research on quantum computation is to construct a new ma-chine which works grounding on quantum mechanics theory and has intense superi-ority over the classical computer on processing complicated computational problems.Quantum computer can solve some certain problems which are NP ones for their classi-cal counterparts, and Shor's quantum algorithm for prime factorization is a well-knowninstance. As the experimental implementation of quantum computation need initial-ization,coherent manipulation,control and read of the fragile quantum system, practi-cally building quantum computers has proved extremely difficult. However, of the ex-tant methods, liquid-state Nuclear Magnetic Resonance (NMR) is the most successfulone. Using mature NMR technique, preparing initial states and manipulating quantumgates are both realized. To this day the coherent control of 12 qubits has been imple-mented. Many quantum algorithms are demonstrated on the level of small numbers ofqubits. The experiments have proven the feasibility of quantum computation, whichspirits up us to study quantum computation further.In this thesis, we started from the basic computational technologies of NMR,demonstrated that how to realize quantum computation by using NMR system. Thenwe introduced the strongly modulating pulses (SMP), and by using this technologyand gradient pulses we finished some experiments. We experimental demonstrated theunified framework for the mixed state geometric phase (Uhlmann phase andSjo¨qvistphase) and clearly demonstrated that their unification is possible. Our experiments arefurthermore the first such to measure Uhlmann's mixed state geometric phase and showin addition that it is different to the Sjo¨qvist's phase. We also experimental observeda topological phase in the maximally entangled state of a pair of qubits, the differentbehavior of topological phase is directly related to the double connectedness of SO(3).These results may be relevant for geometric and topological quantum computations.We also have designed and demonstrated an one-way based realization of the DJ algo-rithm on a star-like four-qubit graph state. This is the first one-way experiment reportedwhich is performed in the liquid-state NMR system and on a state other than the lin-ear four-qubit cluster state. Due to the ensemble quantum computing technology usedhere, we find no active feed-forward is needed in our experiment yet the computation is still deterministic and correct. This unique and interesting feature avoids the technicalchallenges in realizing the active feed-forward. Finally, we discussed the experimentaltechnologies used in liquid-crystal NMR syatem, and studied several methods to pre-pare the pseudo-pure state (PPS) from the thermal state of this system. In our work, wefind a easy way to prepare the PPS, also a experimental demostration was performed.These works have given us much practical experience of what it takes to build aquantum computer. The quantum coherence controlling techniques developed for liq-uid and liquid crystal NMR may find use in solid NMR or other, perhaps more scalablequantum computer implementations.