Cohen, O. (2006). Classical teleportation of classical states. Fluctuation and Noise Letters, 6(02), C1-C8. ]]>

> You mean, your algorithm is slower when the number of marked items is unknown, right?

I’m not sure I understand your question. Our algorithm does not rely on “knowing the *number* of marked items”. We use other assumptions (see Table 1 in our paper) that are very similar though. What I mean is that we don’t get a quadratic speed-up over the classical algorithm in the case when there is more than one marked item. The run-time of our algorithm decreases when the number of marked elements is increased, but we would like it to decrease faster.

> If you know you have two marked items, then you define a new oracle which, if given as input a marked item, declares “marked” with probability 1/2.

Our oracle is *not* probabilistic — it will always tell you with certainty whether an element is marked or not (it does not matter whether there is only one such element or more). We do, however, make the *walk* “lazy” in the sense that with probability 1/2 it does nothing and with probability 1/2 is proceeds as usual. This is for technical reasons and affects the run-time only by a factor of 2.

> Do you know any expression for the hitting time involving the eigenvectors of P (not P’).

By definition, the hitting time is the expected time it takes to *find* a marked item (starting from some initial distribution). Thus, different sets of marked elements will result in different hitting times. However, P does not encode what the set of marked elements is whereas P’ does. For this reason I don’t see how one would be able to express the hitting time using P. Note that even if your graph has lots of symmetries, the set of marked elements can be arbitrary and thus not obey those symmetries.

Do you know any expression for the hitting time involving the eigenvectors of P (not P’). I mean, I give you a nice graph, with a lot of symmetry, I know its spectrum and I ask you “what is the hitting time?” And you reply: “Sorry, I don’t care about the symmetries, I don’t care that you know the eigenvectors of the graph, I can tell you the hitting time if you give me the eigenvectors of P’, which doesn’t have any symmetries.” By symmetries I mean regular, translation-invariant graph. The hypercube for instance.

Thanks!

]]>Have you heard of Ludovico Einaudi? I discovered his music recently. It’s not polyrhythm (I think, or my ears are bad), but it is in some way similar. My favourite so far: http://www.youtube.com/watch?v=ImzB5L3p-bY ]]>

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