Atomic ions trapped in ultra-high vacuum form an especially well-understood and useful physical system for quantum information processing. They provide excellent shielding of quantum information from environmental noise, while strong, well-controlled laser interactions readily provide quantum logic gates. A number of basic quantum information protocols have been demonstrated with trapped ions. Much current work aims at the construction of large-scale ion-trap quantum computers using complex microfabricated trap arrays. Several groups are also actively pursuing quantum interfacing of trapped ions with photons.Quantum mechanics offers algorithms for efficient factorization of large numbers [1] and efficient searching of large databases [2], two problems that appear insoluble in classical computing. Because much modern cryptography relies on the difficulty of factoring large numbers, a large-scale quantum computer could have a large impact on many areas of technology, Internet commerce being only one example. At the same time, the delicate and demanding nature of quantum information processing (QIP), with every quantum accounted for, requires a more subtle technology than that used to construct a classical computer. The search for physical systems supporting QIP has ranged far and wide, across optics, atomic physics, and condensed-matter physics [3−6]. Several physical implementations, namely linear optics, trapped ions, and superconducting electronic circuits, demonstrate the essential ingredients of QIP, including initialization to a known quantum state, efficient readout of the quantum state, long qubit coherence time, and universal quantum logic. In particular, small quantum computers have already been constructed with trapped ions [7], and a number of basic QIP algorithms [8], quantum memory schemes [9, 10], and communication protocols [11] have been demonstrated. In this review, we discuss the experimental status and prospects of ion-trap QIP, referring to the theory of QIP and to other physical QIP implementations only for context. This is not to underestimate the excellent work in these other areas, but only to keep the review at a manageable length. For a general overview of QIP, the reader is encouraged to consult Nielsen and Chuang's essential text [3], and for a recent review, Ref. [5].Most quantum information processing devices are made up of two-level systems, "qubits", where each qubit is analogous to a single bit in a classical computer. The quantum state of the device encodes information, and an appropriate unitary evolution of the state of the register can perform a computing task. In our case, a qubit corresponds to a trapped ion, with the two qubit states being two electronic energy levels of the ion. Laser cooling of several trapped ions causes the ions to form a Coulomb crystal, in which the ions are held in the equilibrium positions given by the combination of the trap-
