Course 5 Quantum information processing in ion traps I

Abstract

This chapter discusses quantum information processing is discussed using trapped ions with particular emphasis on a realization using trapped Ca + ions where the qubit is encoded in a narrow optical quadrupole transition. The general concept of an ion trap quantum computer is presented. The physics of linear ion traps is described including the behavior of ion strings used to realize a quantum register, the spectroscopy of Ca + -ions as well as laser cooling of ion strings and addressing of individual ions of a string. The basic building blocks for quantum information processing with ions, i.e. the coherent manipulation of the ions' internal and external states, the appearing AC Stark effects and their compensation and basic gate operations are also discussed. Elementary quantum information processing is demonstrated by the operation of the Deutsch-Jozsa algorithm with a single trapped ion. Scaling an ion trap quantum computer requires the realization of 2-qubit operations working on two ions which is discussed in terms of the Cirac-Zoller controlled NOT (CNOT) gate operation described in section 6. Using single and two-qubit operations entanglement of ions is achieved and investigated.