Quantum information processing and quantum control with trapped atomic ions

The role of trapped atomic ions in the field of quantum information processing is briefly reviewed. We discuss some of the historical developments that enabled ions to enter the field and then summarize the basic mechanisms required for logic gates and the use of the gates in demonstrating simple algorithms. We describe potential pathways to reach fault-tolerant error levels and large-scale devices, and highlight some of the main problems that will be faced in achieving these goals. Possible near-term applications in applied and basic science, such as in metrology and quantum simulation, are discussed.