Decomposing finite Abelian groups
Ka Chun Cheung, Michele Mosca · Quantum Information and Computation · 2001
This paper describes a quantum algorithm for efficiently decomposing finite Abelian groups into a product of cyclic groups. Such a decomposition is needed in order to apply the Abelian hidden subgroup algorithm. Such a decomposition (assuming the Generalized Riemann Hypothesis) also leads to an efficient algorithm for computing class numbers (known to be at least as difficult as factoring).