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).
Bruno
Brent
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