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, 451 claim that an efficient quantum algorithm for the Abelian hidden subgroup problem is folklore. To quote Jozsa [211: "...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.
0599: Quantum physics
0984: Computer science