Generalizations of hidden subgroup algorithms

Abstract

In the future, it can be possible to store bit information in atoms. In thatcase, classical mechanics will not be enough to explain the atomic level model. Instead quantum mechanics will have to be used. A quantum bit exists as a superpositionof 0 and 1. Creating superpositions and making parallel computation on them willallow faster solutions than classical computation. The field of quantum computationexamines the possibility of using these physical properties for solving computationalproperties more e±ciently.In this thesis, we consider the problem of generalizing some quantum algorithmsso that they will work on input domains whose cardinality is not necessarily powersof two. When analyzing the algorithms we assume that generating superpositions ofarbitrary subsets of basis states whose cardinalities are not necessarily powers of twoperfectly is possible. We have taken Ballhysa's model as a template and have extendedit to Chi, Kim and Lee's generalization of the Deutsch-Jozsa algorithm and to Simon'salgorithm.