Since the first preparation of a single trapped, laser-cooled ion by Neuhauser et al. in 1980, a continuously increasing degree of control over the state of single ions has been achieved, such that what used to be spectroscopy has turned into coherent manipulation of the internal (electronic) state, while laser cooling has evolved into the control of the external degree of freedom, i.e. of the motional quantum state of the ion in the trap.

Based on these developments, Cirac and Zoller proposed in 1995 to use a trapped ion string for processing quantum information, and they described the operations required to realise a universal two-ion quantum logical gate. This seminal proposal sparked intense experimental activities in many groups and has led to spectacular results.

In this lecture, the basic experimental techniques which enable quantum information processing with trapped ions and atoms will be reviewed. In particular, the fundamental concepts of quantum computing, such as quantum bits (qubits), qubit rotations, and quantum gates, translate into experimental procedures in a quantum optics laboratory will be explained.

Furthermore, the recent progress of quantum computing with ions and atoms will be summarised, and some of the new approaches to meet future challenges will be mentioned.

It is intended to provide an intuitive understanding of the matter that should enable the non-specialist student to appreciate the paradigmatic role and the potential of trapped single ions and atoms in the field of quantum computation.