Hidden subgroup problem

The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. The framework captures problems such as factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. This makes it especially important in the theory of quantum computing because Shor's algorithm for factoring in quantum computing is an instance of the hidden subgroup problem for finite abelian groups, while the other problems correspond to finite groups that are not abelian.