# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics
**Prof. Rainer
Blatt**, Institut f. Experimentalphysik, Universtität Innsbruck,
will give a public talk (followed by a discussion) on **Wed, Jan. 19, 2005**
at **16:00 o'clock** at **HS 2**
on the topic of
"Quantum Computer – Dream and Realization"
. The organziers of the symposium,

Univ.-Prof. Dr. Gerhard Larcher

A.Univ.-Prof. Dr. Jürgen Maaß, and

die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

Series A - General Colloquium:

The intention is to present general information not only to experts, but also to students and guests from outside the mathematical institutes.

### Quantum Computer – Dream and Realization

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. Therefore, there it would be desirable to build a quantum computer. This requires the implementation of quantum bits (qubits), quantum registers and quantum gates and the development of quantum algorithms. In this talk, several techniques for the implementation of a quantum computer will be presented and compared. Special emphasis will be given to the ion storage and laser cooling techniques which are currently investigated for an application with quantum computers. 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. Bell states, and of three particles, i.e. GHZ and W states, were generated using an algorithmic procedure. With a tomographic method, these states were subsequently analysed and the respective entanglement was characterized using various entanglement measures. With Bell states as a resource, entangled states were applied for teleportation and improved precision measurements.