Build a toy quantum computer at home
dhruvonmath.com
dhruvonmath.com
Polarizers essentially just project the electric field of the wave onto some axis, zeroing out the perpendicular component. Keeping in mind that light intensity is the square of the electric field strength, all of this can be explained through straightforward classical electrodynamics.
An analogous statement would be that interference of light (say through a pair of slits) is also quantum mechanical in nature. This isn't strictly wrong (since basically everything is quantum mechanical in nature when you get down to it) but is a misleading way to present something that can (and was) understood perfectly well before quantum mechanics came along.
Note: These kind of experiments for a single particle (e.g. photons, electrons, etc) are a different story and do provide a demonstration of quantum mechanics (and the combination of wave-like and particle-like properties intrinsic to it).
1. Take two of the lenses, hold them an inch apart, and shine a light so that it goes through both. The amount of light that goes through depends on their relative angle; at the right angle (90 degrees difference), no light will pass through. Hold them like this, so that no light gets through.
2. Insert a third polarizing filter between the two at a 45 degree angle. Amazingly, some light will now get through. You added an obstacle, and more light passes through.
I want to ask, though. Is it correct to call the third filter an obstacle? In the quantum realm, it’s not really an obstacle, is it?
Evidently not!
[I.e. if you assumed quantum mechanics didn't exist and that Maxwell's equations were the ground truth, you could explain this behaviour without any issue (with some leeway to define a polarizer)].
I think if you try and use that line of thought strictly (only call an explanation "classical" if you can explain with discrete photon particles), you'd probably have to argue that basically all of electromagnetism is fundamentally quantum mechanical. Again, while not strictly wrong (given our present knowledge), this goes too far for me (and I'd imagine most people).
Also: The "three-polarizer" experiment from your quoted video has a perfectly simple explanation in terms of electromagnetic waves. You use a polarizer to get light polarized along say "y" == (0,1). If you put another polarizer in front of it along "x" == (1,0) then the projection is of the E-field is zero and no light passes through. Now add another polarizer at 45 deg between the two: it then projects the E-field onto its axis, mapping it from (0,E) to (E/2,E/2) (magnitude is 1/sqrt(2)). The E-field now has a non-zero component along "x". So light comes out the final polarizer.
Where goes the energy of the orthogonal component of the field? Absorbed by the polarizer, reflected, ... ?
It depends on the type of polariser.
The type used in LCD displays and 3D cinema glasses absorbs, that's why everything looks darker through them but they don't look like mirrors.
A polarising beam splitter reflects one mode and passes the other. It looks like a half-mirror.
For example, a simple polarizer could be a grid of thin metal wires whose spacing is smaller than the wave-length of the incoming light. For the component of the E-field parallel to the wires currents can be induced freely along their length, and so the grid behaves much like a solid metal plate and reflects that part of the wave. For the component of the E-field perpendicular to the wires, significant currents can't be generated (since the wires are thin) and that part of the wave passes through.
[1] https://en.wikipedia.org/wiki/Polarizer
[2] https://en.wikipedia.org/wiki/Polarizer#Wire-grid_polarizers
However, this article falls into a pet peeve of mine which is that the behavior exhibited here can also be completely explained classically -- this is also a standard demo when explaining how polarization works classically. I feel that it is worth it to at least include a footnote to that effect. The reason that I bring it up is that I (as someone who first learned classical optics, but is now learning quantum optics) personally suffered from some deep rooted misunderstandings about quantum mechanics due to having seen so many of these simplified demos which do not actually capture the quantum nature of light.
The way this article is presented it implies that one can also model quantum phenomenon using maxwells equations -- which is obviously not true. In this specific case you get the same answer, but as soon as you start looking at the individual photon statistics your answers will start to diverge. This is where the actually quantum things like Bells inequality and the Hong–Ou–Mandel effect come into play. If people had just been up front with their descriptions 'oh by the way, when you look at the aggregate behavior of photons they look perfectly classical, it is only when you look at the statistics do they behave any different' it would have saved me a lot of soul searching and misguided contempt for the quantum community.
EDIT: I've gone ahead and added the footnote. Thanks for the suggestion!
And the idea of using sequential rotation to keep track of cumulative bias in coin flips is an interesting concept.
But ultimately I think neither one of those concepts really depends on the other in this experiment. Checking for light through polarizers is neat, but keeping track of any other rotating macro-scale object would work just as well. You can do the same thing by rotating a stick on a piece of graph paper. If it goes beyond your pre-determined test angle, you declare a bias.
As I understand it, the crazy thing about quantum computing is that you don't need to go sequentially; you can simultaneously compute every test flip in one step with qubits. That's why quantum computing could speed up certain calculations. (Note: please don't ask me to explain how.)
As I understand the experiment now, it seems like the more subtle the bias in the coin, the more times you would need to rotate the polarizer to detect the bias.
If there is something about using the polarizing filters to keep track of tries that is more efficient than using something like a stick, then I would emphasize that in your write-up.
It's a nice explainer on polarization but tries to be more than that and doesn't achieve it - but with further work (not in form of added caveats but rather a new approach to tying the two concepts together) I'm sure it could.
I read about the Kyndi model but could not find any implementation.
The problem is it takes O(2^n) classical computer resources to emulate a general purpose n-qubit quantum computer. In other words, exponential time or size.
(We can simulate some larger quantum chemistry systems on a classical computer, but those aren't general purpose. The simulations are quite restricted in what they can measure, and there's still a significant practical size limit.)
So we can only emulate very small general purpose quantum computers or other quantum systems. For larger quantum computers, in principle those can be emulated too, except you would need an impossibly fast and large classical computer to do it. So we can't do so in practice.
This is actually the motivation for building real quantum computers of significant capacity.
If a real quantum computer can be built with a large number of high quality, fully coherent qubits, it will be able to do calculations that can't be emulated on any classical computer we can actually build and run, just because of the O(2^n) practical limit.
Right now, there are no quantum computers like that. There are some dubious marketing claims around, and there are also some genuine, but smaller, devices.
Because we can't even simulate a large quantum computer, we don't know for certain whether such a device can even be built in the physical world. The abstracted maths of quantum mechanics, which has proven to be extremely accurate and correct for everything it's been used on, says it can (subject to practical engineering details), but the physical world may have a subtle limitation which we can't detect in smaller systems, that only happens with larger quantum computers and prevents it from being possible. The maths itself might even have a subtle reason (such as stability or entropy) why the system cannot work, but no such reason is known at the moment. We can't "run" the maths to find out its behaviour on a large system, for the same reason we can't simulate a large quantum computer without a large quantum computer in the first place. We can only reason about it in the abstract.
Although, appreciate the efforts.
Edit: Weird. Now it works. Though there still some initial "resistance" when I start scrolling...