On 31 Dec 2013, at 21:19, meekerdb wrote:
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.
Not sure that this makes sense to me. The wave is the"wave of
universe", it evolves in a Hilbert Space, not in any world or branch.
The term "world" is confusing here.
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.
Because we manage to get the result in our quasi-classical world. Yet,
we get an indirect information about what has been computed in the
other branch. We can compute a predicate, which outputs 1 or 0, and
decide, in our branch, to test if all output were identical or not.
Also with Deutsch quantum brain, the observer can know that he has
seen a definite result in each branch, but can't remember which one.
So he can test the presence of the alternate realities, but not much
more (but still more) than with the usual two slits.
Then in arithmetic, the parallel realities existence is an elementary
theorem of RA. So we expect the MW, and are happy that some physicists
already confirm this when abandoning the collapse, ...which is all
absurd by itself, note.
Bruno
http://iridia.ulb.ac.be/~marchal/
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