On Tue, Aug 21, 2018 at 7:43 PM Brent Meeker <[email protected]> wrote:
> > > On 8/21/2018 3:37 PM, Jason Resch wrote: > > > > On Tue, Aug 21, 2018 at 5:00 PM Brent Meeker <[email protected]> wrote: > >> >> >> On 8/21/2018 2:40 PM, [email protected] 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. 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? > > >> 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. > > 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? Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
