> I believe that you missed the real assumption here. The author was NOT
> saying that QM required that 10^500 calculations couldn't be performed in
> a single universe. QM doesn't say anything about that. The assumption
> was that a
> calculation (storage and operations) require the manipulation of physical
> objects. And there are only so many physical objects in the universe.
>
> Now,the way I calculate things, if each particle could be used only once,
> 10^500 calculations requires 10^420 universes. Alternatively, assuming that
> each particle in each universe (of 10^80 particles) can operate at 10^100
> operations per second, then each universe can perform 10^180 operations per
> second. This means you need 10^320 seconds to complete the calculation. The
> 18 billion year old universe is only 10^17 seconds old. Thus you need about
> 10^300 times as long as the current universe has existed to solve the
> problem.
>
> If the quantum computer can solve the problem in 5 minutes, where and how
> did it perform this magic? Once again, the major premise in that author's
> argument was that a calculation required the manipulation of a physical
> object. If this is untrue, then his argument fall flat on its face.
I'll grant that every "calculation" requires a physical operation.
The critical assumption in the Discover article is that 10^500
"calculations" are required to factorize a large number. That is true
when "standard" algorithms are used; it need not be true of other
algorithms.
A digital computer using standard techniques might require 10^12 physical
operations to solve a differential equation, while a properly constructed
analog computer could do it in 10^0 steps. (Well, if you're going to get
technical, it might be more like 10^6.) Approximately 10^15 computational
steps have gone into calculating a precise approximation of the helium atom's
eigenstates. But when two electrons encounter an alpha particle, they
don't perform all those calculations, they "naturally" find the right
eigenstates. In the same way, if someone cleverly constructs an artificial
"atom" in which the quantum eigenstates correspond to the (unknown) factors
of a large number (which is, I believe, what was proposed), the same
principle applies. They're just using a very clever algorithm and a
small number of steps.
Loren Haarsma