Dear Andrei and Jonathan, and colleagues
As an outsider in the theme, let me make a couple of light observations.
First about the curious problem of very few Q. algorithms:
In quantum computing there were created a few quantum algorithms and
developed devices, "quantum pre-computers", with a few quantum registers.
However, difficulties could not be more ignored. By some reason it was
impossible to create numerous quantum algorithms which could be applied to
various problems. Up to now the whole project is based on 2-3 algorithms
and among them the only one, namely, the algorithms for finding prime
factors, can be interesting for real applications. There is a general
tendency to consider this situation with quantum algorithms as an
occasional difficulty. But as years pass, one might start to think that
there is something fundamentally wrong.
It reminds a problem I mentioned on biological information months ago. In
purity, no such thing as "biological information processing" can be
accessed, rather the living cell is always engaged in the advancement of
its own life cycle, and therein some ad hoc "processual" activities may be
superimposed... "nested processing" might be called too. Therefore, the
algorithmic decomposability in Boolean streams mandated by Turing schemes
(see Jonathan, below), may occur only as an exception in some brief
biological windows, and perhaps as I see in Quantum Information it would be
similar. Somehow the quantum existentiality is also engaged in the
informational advancement of its cycle/phase in connection with an
open-ended environment. Let me then conclude this comment with a dictum by
Michael Conrad (1996): "when we look at a biological system we are looking
at the face of the underlying physics of the universe."
Turing machines provide a good formal model for classical digital
computers. Is there an equally good formal model for quantum computation?
Can the output from a physically feasible quantum computer ever be more
than a single classical bit --a single yes or no answer?
More generally: What exactly is computable with quantum computation? (For
comparison, Church's Thesis says that Turing machines compute recursive
functions.)
Sometimes it is claimed that the human brain displays certain aspects of
quantum computation. Is this analogy helpful? How far does it go?
A related claim recently made by some parties, some of them in this list
(Hans), takes a further step: information as the ultimate stuff of the
universe (Wheeler, Zeilinger, Smolin... ); but maybe this direction is a
little premature, right now at the beginning of our discussion.
best regards
Pedro
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