NMR Realization Of Quantum Computation

The basic aim of research on quantum computation is to construct a new machine which works grounding on quantum mechanics theory and has intense superiority over the classical computer on processing complicated computational problems. Quantum computer can solve some certain problems which are NP ones for their classical counterparts, and Shor's quantum algorithm for prime factorization is a well-known instance. As the experimental implementation of quantum computation need initialization, coherent manipulation,control and read of the fragile quantum system, practically building quantum computers has proved extremely difficult. However, of the extant methods, liquid-state Nuclear Magnetic Resonance (NMR) is the most successful one. Using mature NMR technique, preparing initial states and manipulating quantum gates are both realized. To this day the coherent control of 12 qubits has been implemented. Many quantum algorithms are demonstrated on the level of small numbers of qubits. The experiments have proven the feasibility of quantum computation, which spirits up us to study quantum computation further.In this thesis, we concentrate on some important problems and algorithms concerning robustness against noise in quantum computation.We demonstrate some important quantum protocols in quantum computation use NMR technique. The main research results are as follows. We report the first experimental optimal quantum state-dependent cloner. Besides, we demonstrate an important building block which perform various quantum information processing tasks directly without recourse to quantum tomography, and realize a quantum random walk search algorithm which has a speedup similar to the Grover's quantum search algorithm.To experimental realization of quantum computation, suppressing the noises to an acceptable level is one of the most important problems. Using liquid NMR system, we have studied geometrical quantum computation which is one method to achieve built-in fault tolerant quantum gates with higher fidelities. We have first observed the geometrical phase of the mixed state, implemented high-fidelity unconventional geo- metric quantum gates, and measure the off diagonal geometric phase. Farther, some underway study on solid state system is carried out.This work has given us much practical experience of what it takes to build a quantum computer. The quantum coherence controlling techniques developed for liquid and solid NMR may find use in other, perhaps more scalable quantum computer implementations.