Quantum information processing (QIP) can potentially provide an 
exponential speedup for certain problems over the corresponding (known)  
algorithms on conventional computers. QIP makes use of the 
counter-intuitive properties of quantum mechanics, like entanglement and 
the superposition principle (being in more states than one 
simultaneously). On the way towards a useful QIP device these properties, 
mostly subject of thought experiments so far, will have to become a 
practical reality.

Atomic ions confined in an array of interconnected traps represent a 
potentially scalable approach to QIP.  All basic requirements have been 
experimentally demonstrated in the last few years. The remaining task is 
to scale this approach to a large QIP device while minimizing and 
correcting errors in the system. The talk will give a brief introduction 
to quantum information processing, followed by a survey of recent progress 
in implementing quantum algorithms with up to six ions in trap arrays.  
Efforts towards micro-fabrication and integration of larger trap arrays 
will also be discussed, and the prospects and challenges of this 
particular approach will be summarized.