Implementation of two-qubit and three-qubit quantum computers using liquid-state nuclear magnetic resonance

The field of quantum computing has grown rapidly in the last years. Most realizations of quantum computers were done on liquid-state NMR quantum computers so far. We present in a didactic approach how to build small NMR quantum computers with two and three qubits. The two-qubit quantum computer was implemented on α-D-methylglucose using ¹³C spins, whereas the three-qubit quantum computer was implemented on 4-bromo-1,1,2-trifluoro-1-butene using ¹⁹F spins. We describe in detail how to initialize these systems by generating pseudo-pure states. For initialization, we used the spatial averaging method, which has the advantage that it can be easily understood by product operators. Furthermore, the implementation of quantum logic gate operations will be presented.