On 8/21/2018 7:38 PM, Jason Resch wrote:
On Tue, Aug 21, 2018 at 7:43 PM Brent Meeker <meeke...@verizon.net
<mailto:meeke...@verizon.net>> wrote:
On 8/21/2018 3:37 PM, Jason Resch wrote:
On Tue, Aug 21, 2018 at 5:00 PM Brent Meeker
<meeke...@verizon.net <mailto:meeke...@verizon.net>> wrote:
On 8/21/2018 2:40 PM, agrayson2...@gmail.com
<mailto:agrayson2...@gmail.com> wrote:
If I start a 200 qubit quantum computer at time = 0, and
100 microseconds later it has produced a result that
required going through 2^200 = 1.6 x 10^60 = states
(more states than is possible for 200 things to go
through in 100 microseconds even if they changed their
state every Plank time (5.39121 x 10^-44 seconds), then
physically speaking it **must** have been simultaneous.
I don't see any other way to explain this result. How
can 200 things explore 10^60 states in 10^-4 seconds,
when a Plank time is 5.39 x 10^-44 seconds?
It's no more impressive numerically than an electron wave
function picking out one of 10^30 silver halide molecules on
a photographic plate to interact with (which is also
non-local, aka simultaneous).
Well consider the 1000 qubit quantum computer. This is a 1
followed by 301 zeros.
What is "this". It's the number possible phase relations between
the 1000 qubits. If we send a 1000 electrons toward our
photographic plate through a 1000 holes the Schrodinger wave
function approaching the photographic plate then also has 1e301
different phase relations. The difference is only that we don't
control them so as to cancel out "wrong answers".
The reason I think the quantum computer example is important to
consider is because when we control them to produce a useful result,
it becomes that much harder to deny the reality and significance of
the intermediate states.
Which is why I'm pointing that, while important from our view of it as a
computation, from a physical viewpoint it is nothing unusual. If I poked
a 100 pinholes in a screen and shone my laser pointer on it there would
the same number of "intermediate states" between the screen and a photo
detector.
For instance, we can verify the result of a Shor calculation for the
factorization of a large prime. We can't so easily verify the
statistics of the 1e301 phase relations are what they should be.
This is not only over a googol^2 times the number of silver
halide molecules in your plate, but more than a googol times the
10^80 atoms in the observable universe.
What is it, in your mind, that is able to track and consistently
compute over these 10^301 states, in this system composed of only
1000 atoms?
Are you aware of anything other than many-worlds view that can account
for this?
I don't see anyway a many-worlds view can account for it. All those
qubits have to be entangled and interfere in order to arrive at an
answer. So they all have to be in the same world. Your numerology is
just counting interference relations in this world, they don't imply
some events in other worlds.
Also note that you can only read off 200bits of information
(c.f. Holevo's theorem).
True, but that is irrelevant to the number of intermediate states
necessary for the computation that is performed to arrive at the
final and correct answer.
But you have to put in 2^200 complex numbers to initiate your
qubits. So you're putting in a lot more information than you're
getting out.
You just initialize each of the 200 qubits to be in a superposition.
Those "intermediate states" are just interference patterns in the
computer, not some inter-dimensional information flow.
What is interference, but information flow between different parts of
the wave function: other "branches" of the superposition making their
presence known to us by causing different outcomes to manifest in our
own branch.
Also, many quantum algorithms only give you an answer that is
probably correct. So you have to run it multiple times to have
confidence in the result.
I would say it depends on the algorithm and the precision of the
measurement and construction of the computer. If your algorithm
computes the square of a randomly initialized set of qubits, then the
only answer you should get (assuming perfect construction of the
quantum computer) after measurement will be a perfect square.
Right. There are some quantum algorithms that give probability 1 answer.
Quantum computers will certainly impact cryptography where there's
heavy reliance on factoring primes and discrete logarithms. They
should be able to solve protein folding and similar problems that
are out of reach of classical computers. But they're not a magic
bullet. Most problems will still be solved faster by conventional
von Neumann computers or by specialized neural nets. One reason
is that even though a quantum algorithm is faster in the limit of
large problem size, it may still be slower for the problem size of
interest. It's the same problem that shows up in classical
algorithms; for example the Coppersmith-Winograd algorithm for
matrix multiplication takes O(n^2.375) compared to the Strassen
O(n^2.807) but it is never used because it is only faster for
matrices too large to be processed in existing computers.
So where do you stand concerning the reality of the immense number of
intermediate states the qubits are in before measured?
It's just like flipping two rocks in a pond and being amazed at the
immense number of points at which ripples interfere before they
determine the wave that hits the sand bar.
Brent
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