On 8/21/2018 9:01 PM, Jason Resch wrote:
On Tue, Aug 21, 2018 at 10:50 PM Brent Meeker <meeke...@verizon.net
<mailto:meeke...@verizon.net>> wrote:
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.
Okay. But this example tends to ignore the intermediate steps of the
computation, in a way that is easier to look over.
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.
Where are these interference relations existing? We've already
established there are not enough atoms to account for all the states
That's because the states aren't things, they are entanglements, i.e.
relations between things. That's why the numbers are in exponential in
the number of things. They are not things themselves, so it's specious
to compare them to atoms.
in the whole observable universe (one world), nor are there enough
Plank times to account for iterating over every possible state
involved in the computation in (one world). So where are all of these
states existing and being processed?
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.
Except there are more ripples than bits in the Hubble volume, and more
state transitions than there have been Plank times in the age of the
universe.
Not ripples, the analogy is intersection of ripples. The huge numbers
are combinatorics. They are abstract "states" only in the sense that
the /*relation*/ of two different atoms in a ripple is a state.
Brent
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