Jesse & Stephen:
About quantum computing getting around the limitations of Turing machines:
you don't have to cite Feynman, this matter was settled fairly clearly in
David Deutsch's classic work on quantum computation. He showed that the
only quantum-computable functions are Turing-computable functions. Quantum
computers may be able to compute some things *faster* than classical
computers (in the average case), but this is a different story.

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In his book Shadows of the Mind, Penrose reacts to this result with
disappointment, and with an expression of hope that "quantum gravity
computers" will be able to compute non-Turing-computable functions. But so
far neither he nor anyone else has offered much more than hope and
speculation in this direction. My own opinion is that this is probably a
pipe dream, and we must make do with Turing-computable functions, but I'm of
course open to new ideas and new information...
-- Ben Goertzel
> -----Original Message-----
> From: Jesse Mazer [mailto:[EMAIL PROTECTED]]
> Sent: Monday, December 30, 2002 11:41 AM
> To: [EMAIL PROTECTED]
> Subject: Re: Quantum Probability and Decision Theory
>
>
> Stephen Paul King wrote:
>
> >
> >Dear Jesse,
> >
> > Please read the below referenced paper. It shows that QM
> comp *CAN* "
> >"solve an undecidable problem"
> > (relative to a classical computer)."
>
> Where does it say that?
>
> >I do not see how I misread Feynman's
> >claim
>
> Again, the paper says:
>
> "Is there any hope for quantum computing to challenge the Turing barrier,
> i.e., to solve an undecidable problem, to compute an uncomputable
> function?
> According to Feynman's argument ... the answer is negative."
>
> That seems pretty clear to me--if the answer is negative, that
> means there
> is *not* "any hope for quantum computing to challenge the Turing
> barrier".
> Do you understand "negative" to mean something different?
>
> Jesse
>
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