Crypto and new computing strategies
Eric Hughes
hughes at ah.com
Wed Mar 30 12:23:42 PST 1994
>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
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