There go 7 cents out of my 60!...
The case indeed is that if you build a quantum computer by emulating
a Turing-Universal Machine you are a priori circunscribing its own
class of algorithms. That is only natural if that is the largest class of
computable problems you think are worthwhile considering. But it
isn't necessarily the only one. This approach surfaces here and there
in the literature. See for example:

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http://arXiv.org/abs/quant-ph/0205093
Another point worth making is that it seems unlikely that the recourse
to the infinite superposability of quantum states is going to be of any
help in this circunstance. It may be more profitable to look to
entanglement (which incidentaly is the trully novelty that QC brings
to the realm of computation) as the road to a trans-Turing class of
computations.
As to your reference to Penrose, Ben, I should probably add that
his much maligned ideas concerning the possibility of using Quantum
Gravity as a basis for understanding the psychology of mathematical
invention are perhaps worth a second look now that we are learning a
good deal more about quantum information in Black Holes etc...
-Joao Leao
Ben Goertzel wrote:
> > When a finite quantum computer can break the Turing barrier, that will
> > prove something. But when your first step is to prepare an infinite
> > superposition, that has no applicability to the physical universe.
> >
> > Hal Finney
> >
>
> Precisely. Deutsch's arguments make a lot of assumptions about things being
> "finitely given"; Calude's theory makes very different assumptions. If you
> take Calude's assumptions and replace them with finite-precision
> assumptions, the non-Turing stuff goes away.
>
> Less formally: you need to put noncomputable information into QM to get
> noncomputable information out of QM. If you don't explicitly put
> noncomputable information into it, you won't get any out.
>
> ben
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