this is really good intro to some of the math of quantum computers and how quantum algorithms work.
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Discussion
Thanks jb
That is interesting. Finally something on quantum that's a little more concrete.
I learned how blockchain work from this youtuber. He is very good at explaining with visuals.
Who is the observer in these models and why should I trust them?
This is good, however there really needs to be one of these videos using our best explanation of quantum computers, which is Everettian or "many worlds".
It is really much easier to understand what is going on in a quantum computer, if you understand that you are dealing with many computers in different universes.
It explains WHY a quantum computer can run a function in parallel: because there actually are many classical computers doing the calculation in different universes.
It explains WHY you only get back probabilities of the outcome: because the only way we can "see into" these different universes is through interference effects where the outputs of all the computers interfere with each other..
So all you have to understand is that you are dealing with many classical computers (which is kinda easy to understand) but that you are limited in how you get to communicate with them.
I have wanted to make a video on this for some time ... someday ... sigh.
because that's not true. there is no evidence for that
That is what interference effects are: evidence of parallel universes.
When you send a single photon through a double slit, there are places on the other side of the slits that the photon will not go.
SOMETHING is interfering with that photon.
That is your evidence.
SOMETHING is keeping the photon from hitting certain places on the screen. What is doing that?
That thing that "bumps up against" or "interferes with" the smallest particles is what we call "other universes."
There is a TON of evidence for other universes.
“the only way we can "see into" these different universes is through interference effects where the outputs of all the computers interfere with each other” <— isn’t the extent to which the parallel worlds interfere with each other also the extent to they are not really parallel worlds?
Yes, that is correct. If the worlds were completely separate, and completely "parallel" then we would have no evidence of their existence, and quantum computers theoretically (and practically) wouldn't work.
Everett's parallel universes don't return information, so you travel to one of them with a one-way ticket. Wolfram has a better idea of branching and merging universe/hypergraph. Check out this: https://www.youtube.com/playlist?list=PLVwcxwu8hWKlx77UMXUYPbWauXlT6g9Xd
They do return information. If they don't then quantum computers wouldn't work.
If they do, then they are not separate universes but parts of a single one
Sure, but we are just getting into semantics.
"There is one Multiverse, make up of separate Universes", would be the way that it is typically described.
I think what I, and others, are having an issue with is the following.
In many worlds, the different branches come about, because after a measurement, the wavefunction is a superposition of different states, each with its own outcome of the measurement, and these states, for all practical purposes, do not talk to each other, because of decoherence. Prior to the measurement, all kinds of interference effects happened, but at that point the wavefunction did not separate into different branches, and there was no meaningful way to talk about different universes or worlds.
Now, for quantum computation, you rely on interference effects. You don't want them to be tiny. So it is precisely what prevents you from talking about separate branches of the wavefunction that is responsible for the speed-up that you want. This is why it seems to me that it is misleading to explain the speed-up of quantum algorithms in terms of parallelism. On the contrary, the speed-up comes from that the wavefunction cannot be separated into different branches.
You are not getting extra compute from different universes. You are getting it because the way the wavefunction evolves mixes everything together in an unseparable way, making use of the whole Hilbert space effectively, rather than dealing with the very specific case of different branches that have decohered. I don't think this is semantics. If you cannot even approximately identify different branches of the wavefunction, while the computation is running, how can you talk about different universes?
Another way to put this is to ask, how is it possible to get an exponential speed-up when comparing a quantum vs classical algorithm? Correct me if I am wrong, but this is what happens with Shor's algorithm. If all it came down to was parallelism, the speed-up would scale with the number of different branches of the wavefunction, would it not?
I still think Wolfram Physics is a more complete theory than Everett's with world histories branching and MERGING.
Imagine trying to debug programs where your output only follows some distribution
Great stuff, thanks. I understood most of it because I took Brilliant course https://brilliant.org/courses/quantum-computing/