On 12/31/2013 1:37 AM, Bruno Marchal wrote:

On 30 Dec 2013, at 20:00, meekerdb wrote:

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.

Then you need to add some selection principle to QM. If QC works through QM, the "parallel" computation are done in our quasi-classical world as in any other branch, and this is tested by doing a Fourier Transform which required the computation do be done in some non fictitious way (or you are adding some non linear magic in QM at some place).

I don't understand your comment. It is my point that the computations are done in our world via the interference of wave functions - which have to be in the same world in order to interfere. I take "worlds" to mean quasi-classical worlds and a quasi-classical world may be supported by many different quantum "worlds". But in Deutsch's famous proposed experiment, a quantum AI computer after factoring some prime by Shor's algorithm may not be able to tell us anything more than the factors - because those factors comes out the same in almost all branches and hence correspond to the same quasi-classical world.


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