The Finite Abelian Hidden Subgroup Problem

The hidden subgroup problem has been an active topic of research in quantum
computing for over the past 10 years. Out of all the literature that is out there on this
topic, there are very few survey articles which discuss most or all of the details concerning
the Abelian hidden subgroup problem. As a matter of fact , many articles [17, 26 , 22, 45]
claim that an eff-icient quantum algorithm for the Abelian hidden subgroup problem
is folklore. To quote Jozsa [21]: " ... the detailed description of an efficient quantum
algorithm for the general abelian hidden subgroup problem seems not to have been
described in the literature." Apart from banishing this folklore, the aim of this work is
to serve as a monograph about the Abelian hidden subgroup, discussing many of the finer
points that are ignored in the literature so as to make it accessible and comprehensible
to the mathematically mature reader.