Quantum computers are expected to enable to solve certain problems that classical computers can hardly do. The extraordinary power of quantum computers comes from the quantum effects such as the superposition of states, entanglement, and measurement. To implement a quantum computer on a specific quantum system, the scalable qubits storing information, the initialization, control and measurement of states of qubits, and the error correction are needed. Among the efforts to realize a quantum computer, only the liquid state nuclear magnetic resonance (NMR) has provided the meaningful demonstrations of its implementation. The implementation of a quantum computer by the NMR requires the profound understanding of not only quantum computation but also multi-spin dynamics quantum-mechanically and is expected to contribute the development of future practical quantum computers on more scalable systems.
In this thesis, the implementation of a quantum computer with the liquid state NMR was studied focusing on the realization of quantum algorithms on a three-qubit system. The refined Deutsch-Jozsa, phase estimation, and quantum counting algorithms were successfully demonstrated along with the improvements of experimental methods related to the determination of the Hamiltonian of a spin system, the preparation of the states of qubits, the optimization of pulse sequences for quantum circuits, and the reconstruction of density operators.
