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.
Brent
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