**Quantum computers – dream and realization **

*Rainer Blatt*

*Institute
for Experimental Physics,*

*University** of **Innsbruck**, Technikerstrasse 25,
A-6020 **Innsbruck**, **Austria*

Rainer.Blatt@uibk.ac.at, http://heart-c704.uibk.ac.at

*and*

*Institute
for Quantum Optics and Quantum Information,*

*Austrian** **Academy** of Sciences, Technikerstrasse
25, A-6020 **Innsbruck**, **Austria*

Rainer.Blatt@oeaw.ac.at, http://www.oeaw.ac.at/

Computational operations always rely
on real physical processes, which are data input, data representation in a
memory, data manipulation using algorithms and finally, the data output. With
conventional computers all the processes are classical processes and can be
described accordingly. Theoretically, it is known for several years now that
certain computations could be processed much more efficiently using quantum
mechanical operations. This requires the implementation of quantum bits
(qubits), quantum registers and quantum gates and the development of quantum
algorithms. Several approaches for the implementation of quantum computers will
be presented, with special emphasis on the ion storage techniques. Experimental
realizations of quantum registers and quantum gate operations using strings of
trapped ions in a linear Paul trap will be discussed.

With a small ion-trap quantum
computer based on two and three trapped Ca^{+ }ions as qubits we have
generated in a pre-programmed way specific quantum states. In particular,
entangled states of two particles, i.e.