De Brún Centre for Computational Algebra

National University of Ireland, Galway

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In this course we provide an overview of the most important computational problems in which quantum computers appear to have exponential advantage over classical randomized algorithms. These include the most striking results in the field such as factoring integers, calculating discrete logarithms (Shor's polynomial time methods), computing unit groups and class groups of number fields (Hallgren and independently Schmidt and Vollmer).

We will also discuss some of the most significant open problems in this area, especially the noncommutative case of the Hidden Subgroup Problem (as a possible approach to the Graph Isomorphism problem). We shall also outline the basic used in the existing fast quantum algorithms as well as some promising results including the sources of motivation for the computational algebra problems discussed in the conference talk given by the lecturer.

 

Full information on the course is available here

   Gábor Ivanyos

Gábor Ivanyos

Fast quantum algorithms