On 13/06/2017 9:11 pm, Telmo Menezes wrote:
On Mon, Jun 12, 2017 at 3:43 AM, Bruce Kellett
<bhkell...@optusnet.com.au> wrote:
On 11/06/2017 1:31 am, Telmo Menezes wrote:
I think you built a straw man and now you're attacking it. When I
heard Deutsch make the argument, he was referring explicitly to Shor's
algorithm. This is sufficient to demonstrate an increase in
computational power that would be impossible in the classical world.
No one is denying that Shor's algorithm on a quantum computer would
factorize numbers exponentially faster that a classical Turing machine could
do it. But that does not mean that a quantum computer is just lot of
classical Turing machines acting in parallel.
No, but it does mean that a quantum computer can have the
computational power of a lot of Turing machines acting in parallel,
and it is normal to ask "why?", and be unsatisfied with a theory that
does not answer this question.
I have come across an interesting paper that discusses these questions,
and comes to the conclusion that it is problematic to see quantum
computing as accessing the computing power of other worlds.
Michael Cuffaro, http://arxiv.org/abs/1110.2514v2
The explanation for exponential speedup is:
"On this view, quantum computers are faster than classical computers
because they perform /fewer/, not more, computations. By means of
entanglement, quantum computers make it possible to manipulate the
correlations present between the logical elements of a computation
without representing these elements themselves.....far from computing
all of the values of a function simultaneously, quantum computers are
faster because they avoid the calculation of any values of the function
whatsoever, this time by exploiting the difference between classical and
quantum logic."
I find that to be a quite satisfying explanation of quantum computer
speedup.
I don't see how that could follow. The wave function exists in complex
configuration space -- that is not the "real world".
Well, I'm no sure about that, but classical mechanics exists in R^3
configuration space that is demonstrably not the real world (although
it is the model that most closely matches our day-to-day perception of
reality).
Actually, it is more usual to say that classical physics exists in
6N-dimensional phase space for N particles. But that relates directly to
positions and momenta in ordinary 3-space.
The reason why it would follow is precisely the point of my rhetorical
question above. If you take the wave function seriously, then you take
seriously that qubits really do exist in a superposition of states,
and this explains the exponential increase in computational power as
you add qubits to the systems in certain configurations. I guess you
can accept superposition and deny many worlds, but I would say that it
is quite an awkward move.
Cuffaro argues that many worlds can be a useful heuristic for certain
types of quantum algorithms, but that reifying the elements of
superpositons as defining different 'worlds' runs into difficulty with
the basis problem.
In other posts you alluded to a purely probabilistic interpretation of
quantum mechanics. In that case, I would say that it also becomes
awkward to explain the exponential increase in computational power for
the quantum Fourier transform. These are all just intuitions, of
course. We all have ours.
Not really difficult to explain if you look at in the right way. See above.
Another problem for me with the purely probabilistic interpretation is
that it gives base-level reality to true randomness, and that would
also be quite mysterious in my view. My point being: you argue as if
probabilistic interpretations remove weirdness from the explanation,
but for me true randomness is weirder than many worlds.
Well, we all have our intuitions, as you say. If it is the case that
there is an objective collapse mechanism, as in Bohm's theory, Ghirardi
et al, or Penrose and others, then there is base level randomness and we
just have to get used to it. Intuitions developed in a deterministic
classical world do not necessarily carry across into the quantum realm.
Bruce
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