Build a toy quantum computer at home(dhruvonmath.com)
dhruvonmath.com
Build a toy quantum computer at home
https://www.dhruvonmath.com/2020/07/19/quantum-computers/#
41 comments
Hi! Author here - If you have any feedback on what can improve please let me know! Thanks for reading and feel free to shoot me a note at [email protected] if you'd like to see something edited.
Those diagrams are scraggly. Don’t change them! Great article and the diagrams are instrumental.
It is a very nice article, and very well articulated.
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.
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.
Hey - this is perfectly reasonable and constructive feedback - thank you! I see your point that the polarization example can be explained using classical approaches. I wanted to explain it in terms of individual photons as I wanted to use this to help provide some visual intuition for qubits. Photon polarization is a nice, visual way of interpreting qubits and as such lent itself well to the task.
EDIT: I've gone ahead and added the footnote. Thanks for the suggestion!
EDIT: I've gone ahead and added the footnote. Thanks for the suggestion!
maybe i'm missing something here, but could we not have just used a stick on the ground and rotated it accordingly, and still end up with the same result - if the stick ends up perpendicular to the plane, i.e. you? Why do we need the light polarization setup?
Hey - you totally could to mock this exact setup like you're suggesting. However, in a real quantum computer setup you would take one qubit and apply either the positive or negative rotation gate to it again and again and rotate the state of that qubit. The "stick" in the quantum computer would be the qubit (or photon in this case). So the post is meant to show what would happen in a real setup. Hope that makes sense.
It's more of a quantum demonstration than a computer, no?
Yes - I used the term computer because it really does allow you to mock this quantum algorithm: https://www.scottaaronson.com/papers/qcoin13.pdf. It's described in Professor Aaronson's lecture notes here: https://www.scottaaronson.com/qclec/5.pdf
It is not even a quantum demonstration.
While this is a nice demonstration of the polarization of light, this is not a demonstration of quantum mechanics, or quantum computing (though it does have pedagogical value, if qualified properly).
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).
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).
> Polarizers essentially just project the electric field of the wave onto some axis
Where goes the energy of the orthogonal component of the field? Absorbed by the polarizer, reflected, ... ?
Where goes the energy of the orthogonal component of the field? Absorbed by the polarizer, reflected, ... ?
Yes, those are both possibilities for building a polarizer [1].
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
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
> 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.
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.
This is incorrect [edit: it isn't] - see the standard "three polarizing filter" experiment [0] which is impossible to explain with classical mechanics [edit: it can actually be explained, see coolgod's comment below]. Polarizing filters don't just zero out the perpendicular component of an electric wave, they measure each individual photon that passes through and either blocks it or permits it to pass with some probability proportional to the angle between the photon's polarization and the filter's polarization.
[0] https://youtu.be/zcqZHYo7ONs
[0] https://youtu.be/zcqZHYo7ONs
Here's how to do the "three polarizing filter" experiment. You can do it at home if you have three pairs of polarized sunglasses.
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.
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.
Thank you for an interesting experiment to try. I’m looking forward to doing it myself.
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?
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?
> Is it correct to call the third filter an obstacle? In the quantum realm, it’s not really an obstacle, is it?
Evidently not!
Evidently not!
The three polarizing filter experiment using common sources of light can be explained perfectly without using quantum mechanics [0]. These effects only need QM to explain in the single photon regime. The polarized light from the LED display is definitely not in the single photon regime thus this experiment does not demonstrate any quantum effects. Without any quantum effects, it is much more difficult to justify the quantumness of this supposed quantum computer.
[0] http://alienryderflex.com/polarizer/
[0] http://alienryderflex.com/polarizer/
I was going to say, this wouldn't explain it because the electric field strength is projected to the polarization axis (with strength 0.707 at 45 degrees) but to match quantum measurement it should be 0.5 strength (0.707 squared). But as the grandparent comment stresses, light intensity is the square of electric field strength... so the measurement matches. Makes sense! I will amend my above comment.
The article/your video make the assumption that light is particle and that those particles are independent and each carry polarization. While we know those assumptions to be true, the classical theory of light is not a theory of particles, but of fields/waves. So when you're asking whether there is a classical explanation that's where you should look. And if you do so, you get something perfectly consistent.
[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.
[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.
Hi - thanks for pointing this out. I've added a note clearing up that as you correctly write the quantum interpretation makes sense at the single photon level. Obviously it's hard to generate and manipulate single photons without the right equipment (especially with a phone like in my case) but I do believe this still provides a nice intuition for what's going on. Thanks for your suggestion!
Not sure what's up, but this website refuses to scroll on any Chrome based browser on my phone. Works fine in Firefox though.
Edit: Weird. Now it works. Though there still some initial "resistance" when I start scrolling...
Edit: Weird. Now it works. Though there still some initial "resistance" when I start scrolling...
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 Thatis.
The 3-polarizer experiment is a very cool way to demonstrate the weirdness of light.
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.)
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.)
Hey, you're right you could use a stick on a piece of paper etc. Totally fair. That being said this is in fact a real application where a qubit can model things a standard bit can't. Professor Aaronson describes it in this paper: https://www.scottaaronson.com/papers/qcoin13.pdf. Additionally, it's described in his lecture notes here: https://www.scottaaronson.com/qclec/5.pdf
Thanks for the links. It doesn't seem like your experiment captures the interesting part, which is that you don't need more qubits to measure a more subtle bias.
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.
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.
Yup. As greek to me as the paper is at least it makes very clear what it sets out to achieve and why (and when) it differs. I suppose it's implicit but I feel article really ought to explain that in the demonstrated case of heavy bias, few attempts and fixed, coarse steps there is of course no advantage - apart from the stick in ground one could also best its resolution off 0b1000000 and ++/--.
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.
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.
This is a real-valued computer, not a quantum computer. In the described algorithm the state is the real-valued angle of the polarizer. One could very well implement this algorithm using the charge on a capacitor. Also the algorithm has bugs, it can overshoot the vertical. The author does acknowledge these shortcomings in the "caveats" section. But with all those caveats, you are not building a quantum computer at home.
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Nice article, but not really a quantum computer or even a system that needs quantum mechanics to explain it. You could do the same calculation with an analog system (e.g. a capacitor that you add/remove charges to/from). The argument from Scott Aaronson about quantum advantage that the author refers to is really not very relevant, as a single qubit doesn't have any information encoding advantage over an analog system. A quantum computer simply cannot produce a speed advantage without relying on entanglement at some point during the quantum computation. So: no entanglement = no speed advantage.
Is it possible / are there virtual or emulated quantum computers?
I read about the Kyndi model but could not find any implementation.
I read about the Kyndi model but could not find any implementation.
Yes, it is possible to emulate a quantum computer, and this is done quite often for research and to try out quantum programs.
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.
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.
I like it.
I liked the article, but this is not a quantum computer. Please do not take away the credibility of what a real quantum computer could achieve. This is at best an algorithm to reveal the angle of polarizer, and also the nature of light.
Although, appreciate the efforts.
Although, appreciate the efforts.