Thanks. I read it quickly. I didn't understand the details.
I have no really opinion. I have been more impressed by Freedman
analogical quantum machine, but Calude suggestion is of the same
type. This could lead to a refutation of comp, not of Church
thesis imo. Those machine does really not compute digitally.
I am open to the idea that we will build them, but not tomorow!
>There was an article recently in New Scientist about a new way to geet
>computing beyond the "Turing barrier". I think it is somewhat similar
>in spirit to the analog machines, in that it uses infinities, but it is
>based on the quantum computing model. The NS article is reprinted at
>http://www.cs.auckland.ac.nz/~cristian/smashandgrab.htm and the original
>paper is available at
>>From the NS article:
> His suggestion is to think bigger: why not create a superposition
> of every conceivable state at once? Something like a hydrogen atom
> has infinitely many possible energy levels. While the levels start
> out well-spaced, they get closer as the energies grow higher, until
> they become almost indistinguishable. In a paper to be published
> in the inaugural edition of MIT's new journal Quantum Information
> Processing, Calude and Pavlov have shown that a superposition of an
> infinite number of energy states would allow a quantum computer to
> do things no classical computer can ever manage-almost like running
> "forever" in a finite time.
> This leap means that a quantum computer can overcome Turing's most
> famous barrier to computing power: the "halting problem".
> Calude is extremely proud of this result: he believes it could be
> implemented on a real-life quantum computer, laying much that is
> "unknowable" open to attack. "Using infinite superpositions is rather
> theoretical, but not necessarily non-practical or non-testable,"
> he says.
>My opinion is that infinite superpositions will never be practical hence
>his machine is of only theoretical interest.