Quantum logic with an indium-magnesium ion chain

Summary form only given. A chain of ions in a linear trap is ideally suited to process quantum information. Two long-lived internal states in each ion store the quantum bits, which may be coupled by means of the collective vibrational excitation of the chain. A prerequisite for realizing even the simplest two-bit quantum gate is cooling the vibrational degrees of freedom of the ion crystal to the quantum mechanical ground state. In previous schemes, direct laser cooling of the ions carrying the quantum information was used to this end. Since this inevitably destroys the quantum information, cooling can no longer be applied after the quantum information processing has started. We present a theoretical investigation of the properties of a heterogeneous ion crystal, comparing them with those of a crystal composed of identical ions. In particular, we focus our analysis on the mechanical motion of the ions and the stability of the chain and discuss the possibility oflaser-cooling to the ground state of the collective motion in the confining potential.