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!
-Bruno >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 >http://www.arxiv.org/abs/quant-ph/0112087. > >>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. > >Hal
