# Hidden subgroup problem

Let $$H$$ be a hidden subgroup of $$G_1$$ that is indistinguishable from subgroup $$H^{\prime}$$ by quantum Fourier sampling. Now take a larger group $$G_2$$ such that it contains $$G_1$$. Now if I do quantum Fourier sampling over $$G_2$$ instead of $$G_1$$ are they still indistinguishable?

• Have you thought about specific $H$ and $H’$ or $G_1$ or $G_2$, in the context of, say, Shor’s algorithm? Jul 31 '19 at 0:32
• @ Mark S I have a certain wreath product in mind but I intend to ask this in general framework. Partly because I 'think' this should be true in general and mainly because any such examples would be nice.
– Root
Aug 1 '19 at 5:16
• cstheory.stackexchange or mathoverflow may be welcoming to this question, but I would wait a couple of days before cross-posting (and also emphasize that you did ask it here without progress.) Aug 2 '19 at 22:47
• @Mark S I tried to cross-post but couldn't.
– Root
Aug 5 '19 at 12:34
• Hi Root - I think you just ask the same question on one of the other forums, with a beginning comment to the effect of "I have asked this on Quantum Computing Stack Exchange a couple of weeks ago, without any answers... I'm asking here to see if there's any pointers.. Any help here would be appreciated!" Aug 5 '19 at 12:40