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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?

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  • $\begingroup$ Have you thought about specific $H$ and $H’$ or $G_1$ or $G_2$, in the context of, say, Shor’s algorithm? $\endgroup$
    – Mark S
    Jul 31 '19 at 0:32
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    $\begingroup$ @ 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. $\endgroup$
    – Root
    Aug 1 '19 at 5:16
  • $\begingroup$ 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.) $\endgroup$
    – Mark S
    Aug 2 '19 at 22:47
  • $\begingroup$ @Mark S I tried to cross-post but couldn't. $\endgroup$
    – Root
    Aug 5 '19 at 12:34
  • $\begingroup$ 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!" $\endgroup$
    – Mark S
    Aug 5 '19 at 12:40

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