  An overview of quantum computing and in particular the Hidden Subgroup
Problem are presented from a mathematical viewpoint. Detailed proofs are
supplied for many important results from the literature, and notation is
unified, making it easier to absorb the background necessary to begin research
on the Hidden Subgroup Problem. Proofs are provided which give very concrete
algorithms and bounds for the finite abelian case with little outside
references, and future directions are provided for the nonabelian case. This
summary is current as of October 2004.
