## ABSTRACT

A technology to physically implement quantum computation has many requirements; some conceptual and some technical. In 1995, Cirac and Zoller [13] proposed to implement quantum computation using recently developed experimental techniques [3] which used laser beams to cool atomic ions confined in vacuum inside an ion trap, until they formed a stable linear ion array under the joint forces due to their mutual repulsion and the confining potential gradient. Since each cold ion of the stable array was identifiable, two internal electronic levels of each ion could act as a computational quantum bit, or qubit. A quantum gate, or quantum computational unit, requires a correlated action on at least two qubits. Cold ion internal level qubits have no direct coupling, since the separation of the ions in the linear array is large compared to atomic interaction distances. However, since the minimum of the ion trapping potential is essentially harmonic, the ion array oscillates coherently in the trap at the center of mass (CM) angular

frequency ωCM , which remains the same, regardless of the number of ions. This and other quantized normal modes of oscillation of the ions in the trap can be cooled to their lowest energy state using laser beams, in order to act as a “motional qubit” to couple the ions on demand.