Re: Quantum chaos in the rat ventral tegmentum?

I wrote
> Even constructing a quantum computer which was just
> designed to show that 15 is equal to 3 times 5 was an
> experimental triumph (L.M.K. Vandersypen, M. Steffen, G.
> Breyta, C.S. Yannoni, M. H. Sherwood, and I.L. Chuang,
> ``Experimental realization of Shor's quantum factoring
> algorithm using nuclear magnetic resonance'', Nature 414,
> 883-887 (20/27 Dec 2001)).

Alfredo Pereira Jr replied
>  Shor's algorithm allows to factorize large prime numbers,
> and therefore it was experimentally demonstrated that
> quantum computers can perform operations that no classical
> computer or even human minds could do. This is much more
> than showing that 3 times 5 equals 15.

By definition, prime numbers (large or small) do not have
(non-trivial) factors.  I assume Pereira meant say that

> Shor's algorithm allows to factorize large numbers

This is correct.  And it is also correct to say that Shor's
algorithm uses a method which is different from any normally
used by classical computers.  Nevertheless, it is possible to
simulate any given finite quantum computation on a classical
computer.  It may be very inefficient but, at least in theory, it
can be done.  The difference between classical and quantum
computers lies not in what they can do in individual instances,
but it how efficiently they can do it.  Efficiency only becomes
important at large scales.  We can all factor small numbers, but
for large (e.g. 20 digit) numbers, the time taken becomes crucial.

If they could be built, large-scale quantum computers would be
able to perform (some) large calculations much more quickly and
efficiently than any classical computer.  But quantum
computers are difficult to build at any scale, and therefore
small-scale quantum computers (however impressive they may
be) are not useful.  As I said, ``A little quantum computation is
just a very expensive ordinary computation.''  This makes
me doubt that biological systems could evolve useful quantum
computation.

I wrote
> quantum computers need very precisely-defined quantum
> states.  Only systems which can be very precisely tuned can
> use such states in the required way.  But evolution does not
> tune something unless it is already producing some sort of
> biological benefit.

Pereira replied
> Artificial quantum computers need very precise (although not
> absolutely precise, given what Heisemberg taught us) states
> because the measurement is made by an external observer. In a
> biological quantum computer, the measurement would be made
> by the computer himself, therefore some kind of fuzzy logic
> may be possible.

Heisenberg taught us that measurements of the position and
momentum of a single particle could not both be completely
precise.

I am talking about a different kind of precision here; about the
precision required in the quantum wavefunctions used within a
quantum computer.  These states can be exactly specified and
need to be to use algorithm's like Shor's.  Biological systems
however do not, in general, control at this level.  Biochemistry
involves ions and atoms and molecules bumping into each other.
It is heat which keeps life moving.  Heat is the enemy in
quantum computation.

The experiments which showed that 15 equals 3 times 5 were
done at room temperature, but they used the quantum states of
nuclear spins of custom-synthesized molecules.  In that
situation, the relative isolation of the nuclear spins from
environmental influences (heat) is essential, but at the same
time that very isolation makes it difficult to manipulate and to
read the states of those spins.  Biological systems may be not
far above room temperature, but they certainly do not contain
11.7 Telsa magnets!

As to the required precise control over the quantum states, in
the experiments considered that was achieved by a whole
variety of precisely tuned radio-frequency pulses.

An explanation of what is needed for the physical
construction of quantum computers is given by David DiVincenzo
in ``The Physical Implementation of Quantum Computation''
quant-ph/0002077

This paper is available from the abstract at

http://arXiv.org/abs/quant-ph/0002077


Matthew Donald ([EMAIL PROTECTED])
web site:
http://www.poco.phy.cam.ac.uk/~mjd1014
``a many-minds interpretation of quantum theory''

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