Re: GUT and P=NP

[jamesd@netcom.com (James A. Donald)]

Ray writes
> 1) By definition, if something can be computed by a turing machine,
> then it is an algorithm (Lewis and Papadimitriou)

Suppose we have a spatial transform performed by light flowing
through a grid.  Is that an algorithm?   Perhaps it is, but I
am about to describe a case that will stretch your definition
of algorithm rather more drastically.


> 2) a quantum computer can be simulated by a TM with exponential 
> slowdown. (claimed by you on the Extropians list, but also
> claimed by Feynmann I believe, not about qm computers, but qm systems
> in general)

True.

> then by (1) and (2), it follows that
> 3) quantum computers are algorithmic (if not, it would contradict
> 2) and possibly 1)

Suppose our quantum system has thirty two bytes.

Then a classical simulation of our quantum system would require
2^257 words of memory

The computer would require more matter than exists in the universe.

Each step of the simulation would require 2^514 steps by the computer,
which even for a computer constructed of very tiny components out
of all the matter in the universe would still require vastly longer
than the entire lifetime of the univers.

> 
>    It doesn't matter how slow the turing machine runs the simulation
> because we allow an arbitrary time along with the infinite tape
> to complete the computation. 
> -Ray

It does not sound like a very useful algorithm, nor is it one
that is easy to describe.

The difference is like the difference in my example of light
flowing through a grid, as against a fourier transform etc,
but the difference is enormously greater.

You say it makes no difference by definition.  I say such
definitions are misleading when we discuss how problems are
to be solved.


-- 
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We have the right to defend ourselves and our
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are.  True law derives from this right, not from
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