Realization Of Quantum Computation Using Liquid Nuclear Magnetic Resonance

Quantum computer (QC), based on the principles of quantum mechanics, such as superposition, interference, entanglement, is superior to its classical counterpart for the efficient solution of some problems. The experimental implementation of QC can be divided into three steps: preparation, computation, and readout. However, the special experimental techniques are needed to achieve the above three steps, and what is more, each step is affected by the decoherence. As a consequence, it is rather difficult to implement a QC in a physical system.This dissertation is focused on the development of new methods to prepare the effective pure state for QC, to improve the efficiency of the current QC algorithms, and to demonstrate the algorithms using NMR experiment. The results include:1. Based on the multiple quantum operator algebra theory and the controlled-NOT gates (CNOT) combination theory, we have obtained 2 and 4 quantum bits (qubits) effective pure states for NMR based QC, respectively,2. A novel NMR pulse sequence was proposed to achieve the Grover algorithm of arbitrary qubits. The method was also demonstrated using NMR experiment for a two-qubit Grover algorithm,3. Brüschweiler algorithm was modified to improve the efficiency. The improved Brüschweiler algorithm can search a database of n elements with a n-qubit QC instead of a (n+1)-qubit one. The new method was also realized using a three-qubit NMR experiment.This thesis has covered all three steps of QC implementation, where the aspect (1) corresponds to step 1 (preparation), and either of the aspects (2) and (3) includes the step 2 (computation) and step 3 (readout).