 Hidden subgroup problem

The hidden subgroup problem asks for a subgroup $H\le G$ given an oracle $f:G\to X$ that is constant on each left coset of $H$ and takes different values on different cosets. Abelian instances are solved by preparing coset states and applying a group quantum Fourier transform.

The Hidden Subgroup Problem (HSP) is a central problem in the field of computational group theory and quantum computing. It is a generalization of several important problems, including the factoring problem and the discrete logarithm problem, both of which are of significant interest in cryptography.