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Theoretish-Physikalishes Seminar
QuantenComputer WS 2007/2008
Prof. Dr.
Heiko Rieger mit Dr. Yu-Cheng Lin
Elementare Quantenalgorithmen
Manuel Noll
In order to explain quantum omputation, it is the easiest to investigate it
via its realisation as algorithms. There the enormous power of these mahines
omes apparent. Therefore we have to take a loser look at omputational
omplexity theory and its notion, the Landau notation. With this in bakhand we are able to analyse the great advantages that quantum mahines have
over lassial omputer devies. Sine quantum mahines are probabilisti in
their inner nature, quantum algorithms have to be so too. Therefore these
algorithms have resemblane to randomized algorithms whih we will disuss
briey. But sine randomized algorithms are just a sublass of lassial omplexity lasses we onsider quantum omplexity lasses and lassial omplexity
lasses in the following. Thus quantum mahines dier by their nature from
lassial ones, it is neessary to explore the realisation of bits, registers and
gates on this new kind of mahines. In this ontext we lear the import role
of unitary matries and their meaning in quantum algorithmi design. Having
now all tools together we start to address the quantum algorithms, beginning
with an easy example, the Deutsh's problem, giving us a shortly introdution
in to the usage of the introdued notations. Being familiar with the elementary
realisation of an quantum algorithm we are able to deepen our understand of
quantum algorithms by Simon's problem of determining whether a funtion is
periodi or bijetive. At the end we will fous on Grover's searh algorithm,
performing searhes on databases. That algorithm is indeed better than its
lassial equivalents, though not exponentially better. We lose this disussion
with an outline of quantum networks as an possible way to implement quantum
algorithm and quantum omputers respetively.
Mi, 30.Jan.2008, 16-18 Uhr
E2.6 Seminarraum 4.18