From: D. F. Siemens, Jr. (dfsiemensjr@juno.com)
Date: Wed Jul 09 2003 - 00:36:48 EDT
On Tue, 8 Jul 2003 19:17:08 -0500 "Glenn Morton"
<glennmorton@entouch.net> writes:
>
>
> Deutsch wrote:
>
> "There are only about 10^80 atoms in the entire visible universe, an
> utterly
> miniscule number compared with 10^500. So if the visible universe
> were the
> extent of physical reality, physical reality would not even remotely
> contain
> the resources required to factorize such a large number. What did
> factorize
> it then? How, and were was the computation performed. Brown quoting
> Deutsch
> p. 25
>
> Here is another attempt, in popular form for the group here, to get
> Deutsch's ideas across.
>
>
> "Computation, he notes, is not an abstract process.
> Ultimately it must
> have some physical basis. Whether it's atoms or photons-- or
> electric
> currents in a conventional computer--something must be manipulated
> in some
> way to carry out a calculation. To make his point Deutsch cites the
> work of
> Peter Shor, a mathematician at AT&T Bell Laboratories in New
> Jersey." ~ Tim
> Folger, "The Best Computer in All Possible Worlds," Discover Oct.
> 1995, p.
> 94-95
>
>
> and:
>
> "Shor, in constructing his proof of a quantum computer's
> potential, in
> effect wrote a program for a computer that doesn't exist. It
> factors large
> numbers by working on all the possible answers to a problem
> simultaneously.
> Correct answers--that is, factors of the number in question--appear
> in the
> form of a unique interference pattern at the end of the computer's
> calculations, which the computer could read like some otherworldly
> supermarket bar code. Shor's program cleverly causes all numbers
> that
> aren't factors to cancel out in the interference pattern, like waves
> whose
> crests and troughs annihilate each other.
> "Deutsch claims tht if a quantum computer that can run
> Shor's program is
> ever built, it will be difficult for other physicists to deny the
> many-worlds model of quantum mechanics, fantastic as it seems. For
> example,
> he asks, what would happen inside a quantum computer that used
> Shor's
> program to factor a number that is, say, 250 digits long? To solve
> such a
> problem, he answers, the computer would have to perform roughly 10^
> 500
> computations. 'There is no way that we know to get the answer in
> fewer than
> that number of steps,' he says. 'If you were to write down on a
> piece of
> paper what the computer is doing, you'd have to write down about
> 10^500
> different lines of reasoning. That's an irreducible number. The
> outcome
> depends logically on all those components. Now, there are only
> 10^80 atoms
> in the universe.' So, if a quantum computer can solve a problem in
> which
> the number of calculations greately exceeds the number of atoms in
> the
> universe, how did the computer do the calculation?
> "'It's pretty clear that it wasn't by jiggling about the
> atoms and energy
> and stuff that we see around us,' says Deutsch. 'Then where was it
> performed?'
> "Deutsch emphasizes again that computation is a physical
> process. Just as
> someone using an abacus must push beads around to get an answer, a
> computer
> must manipulate real particles--atoms or photons or what have you.
> And if a
> computer must manipulate ;more atoms than exist in one universe to
> complete
> a calculation, it must be drawing on the resources of many particles
> in a
> vast web of linked universes." ~ Tim Folger, "The Best Computer in
> All
> Possible Worlds," Discover Oct. 1995, p. 95
>
Glenn,
I've tried to follow the discussion, which seems to be encapsulated in
these quotations, with the status of almost complete ignrorance. But I am
wondering about moving from a quantum computer in which Qbits apparently
take all values simultaneously, to a digital one with a capacity of 10^80
or 10^500 bits. There are also analog computers that do not figure on a
0/1 basis. Depending on how finely they can be set and read, do they not
have the potential for dealing with larger numbers for the same number of
active entities (or whatever you call them)? 2^10 is roughly equal to
10^3, but one may be able to read out more than 10 states. Do not Qbits
enormously extend the place capacity of normal analog computers?
Second, if a quantum computer is to require 10^500 bits and so exceed the
capacity of our universe's 10^80 potential bits, does this not mean that
the Qbits have to be somehow entangled with the entire collection of
10^420 extra-universal particles? Is such entanglement possible?
Entanglement seems to have more restrictions, including the length of
time that it holds before some interaction ends it. While entanglement
seems to be instantaneous, can the signal to establish entanglement
exceed the limit of c?
Are these problems with the proposed test for MWH, or do I have no grasp
of what is involved?
Dave
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