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One can get a superposition of all good item using quantum search algorithm in $O$($\sqrt{N}$ ) time, but how one can get all the good items using quantum search algorithm?

I found that all the good items can be found in $O$($\sqrt{Nt}$) time, where t is the number of good items, here, but I couldn't find how.

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What is a "good item"? What is the context for this question? Voting to close. –  Igor Rivin Aug 1 '12 at 19:15
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Eunou, you need to explain your question more. People here are volunteering their time, energy, and expertise, so you need to make it easy for them to help you. As Igor says, you need to define what you mean by a "good item." Also, you link to a paper: is there some specific part of the paper that you don't understand? –  MTS Aug 1 '12 at 19:45
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2 Answers 2

This follows from the fact that if you want to find 1 marked item in set of size N, knowing that there are t marked items, it can be found in $O(\sqrt{n/t})$ queries. Once you find 1 marked item, delete it from your search space and continue searching for the rest. The total complexity is $O(\sqrt{nt})$.

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Sorry guys.... here is a pdf file, and what I said is in p.2.

And for $x\in\{1,2,...,N}$, if $\chi(x)=1$, $x$ is called a good item. The original quantum search algorithm(Grover algorithm) aim to get a superposition of all the good items. But Ambainis above says that it is possible to get the set of all the good items. I'm asking how in this thread.

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When you have more information to add, it's better to edit your question instead of posting an "answer". This will be possible if you "register" and thus don't generate a unique "user" every time you log on. –  John Pardon Aug 2 '12 at 2:52
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