Crypto and new computing strategies

[hughes@ah.com (Eric Hughes)]

>I am not shure that it has been demonstrated that a QM mechanis is necessarily
>solely of a Turing architecture. 

The Bekenstein Bound gives limits both on the expected maximum number
of quantum states encodable in a given volume of space and on the
expected maximum number os transitions between these states.  If this
bound holds (and it certainly seems to hold for EM fields), then a
probabilistic Turing machine will be able to simulate it.

>Also there is the potential to use neural networks at these levels (which are
>not necessarily reducable to Turing models, the premise has never been proven)

If you have infinite precision, the statement is unproven.  If you
have finite precision, you get a Turing machine.  You never get
infinite precision in real life, even with quantum superposition.

Steve Smale did some work a few years ago where he made Turing-type
machines out of real numbers, i.e. infinite precision.  P=NP for this
model, and the proof is fairly easy.  From an information-theoretic
point of view, you can encode two real numbers inside of another one
and do computations in that encoded form, because a real number
encodes an infinite amount of information.

If it's finite, it's a Turing machine.  If it's expected finite, it's
a probabilistic Turing machine.  If it's infinite, it cannot be
implemented in hardware.

Eric