Hidden Subgroup Zoo

Hidden Subgroup Problem (HSP)

Given: <math>f</math>, a function from a group <math>G</math> to a set <math>S</math>, <math>f:G \rightarrow S</math> which is promised to be constant and distinct on different left cosets of an unknown subgroup <math>H</math>:

<math>f(g_1)=f(g_2)~{\rm iff}~g_1H = g_2H</math>

Problem: Find the hidden subgroup problem <math>H</math> by returning a set of generators for <math>H</math>