On 12/30/2013 3:09 AM, Bruno Marchal wrote:
But that's essentially everything, since everything is (presumably) quantum. But
notice the limitation of quantum computers, if it has N qubits it takes 2^N complex
numbers to specify its state, BUT you can only retrieve N bits of information from it
(c.f. Holevo's theorem). So it doesn't really act like 2^N parallel computers.
OK, but nobody pretended the contrary. You can still extract N bits depending on the
2^N results, by doing some Fourier transfrom on all results obtained in "parallel
universes". This means that the 2^N computations have to occur in *some* sense.
But they pretend that the number 2^N is so large that it cannot exist in whole universe,
much less in that little quantum computer and therefore there must be other worlds which
contain these enormous number of bits. What Holevo's theorem shows is the one can regard
all those interference terms as mere calculation fictions in going from N bit inputs to N
bit outputs. It is conceptually no different than doing a calculation in ordinary
probability theory: I start with some initial conditions and I introduce a probability
distribution and compute a probability for some event. In that intermediate step I
introduced a continuous probability distribution which implies an *infinite* number of
bits. Nobody thinks this requires an infinite number of worlds.
Brent
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