3blue1brownSo what is a Qubit, anyway?
Audience:
A bit is the smallest unit of information that there is. On or off. A 0 or a 1. Classical computers, like the kind you and I have, can be thought of as machines that manipulate lots of these bits in order to do useful stuff (or, at least stuff that you want it to do - you can be the judge of whether that’s useful or not).
But quantum computers? Well, they’re just cooler, right? I mean, look, it’s got quantum right there in the name. Even their bits are cool. Because quantum bits- wait, no… qubits (yeah, that sounds cool) can even be 0s and 1s at the same time!…I mean, kinda. Sorta. How?
When it comes to quantum computers, there’s a lot of popular science that doesn’t go much beyond this. And, if you do go looking for something more substantial, there’s a decent amount of higher-level, computer science stuff about quantum algorithms, but very little in the quite frankly massive gulf between these two options. So I thought I’d write about the qubit. Just the qubit. What it is and how it works.
I’ll also talk about the Bloch sphere, a way of representing qubit states that gets thrown at you very often very early with no explanation as to why it’s used or why it looks like that. Again, it is difficult to find explanations between the extremes of ‘substitute these trig identities and carry on’ and ‘hope you know your 4D topology’, so I’ve tried to find a kind of “middle-ground” explanation to bridge the gap.
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Really nice write-up! The interactive visualisations are a bit hard to see with the dark grey background, though. And the article just ends abruptly?
Well done! The article gives (almost) everything that it promises, and closes the gap between many popular science and academic level explanations in the quantum computing area. Nicely written, easy to follow, avoid of too complex jargon. The only problem I saw is the article seem to be unfinished, or maybe it’s poorly finished in the middle of something. There is no conclusion part to sum everything up, and the last section seems unfinished. Other than that, I liked it and learnt some new stuff.
A few nitpick comments:
- Interactive demos don’t work on the Chrome browser of my (Android) mobile phone
- The first demo appears twice in the article. The second one is at the beginning of the section “The Bloch Sphere”.
The interactive browser widgets are cool. Your “Explore where different complex numbers lay on the complex plane” has a bug, it doesn’t update from switching one to the other e^(i version) and doesn’t immediately convert unless you wiggle the selector. Again there is a typo in the end paragraph and doesn’t seem to have a conclusion? “We just need to be careful to divide by 2 agian when writing out :”
I feel like this shows a lot of mathematical detail but wasn’t finished out and should have a flashy intro and conclusion about how this is used practically and why it is that this quantum computing could simplify and make obsolete the current ssl, that is a major use case of this quantum computing.
There are good visualizations in here and I like the gradual build up to the complex space once establishing more simple story boards on orthogonality and linear algebra. I think the story seemed a bit incomplete near the end as I was expecting some sort of understanding behind what a qubit is, and it still felt that it could tie up all the threads near the beginning and summarize what a qubit is, and how to visualize it. I think it ended up introducing quite a lot of technical details that we might obfuscate some of the essence of what a qubit is trying to encode.
Thank you i actually learned something My only feedback is that you should be more coherent to your target audience. Quantic physics even basics, implies that people already know complex numbers. I would have skipped the explanation on -1, i rotation
I think that the description of waves isn’t really clear, even after reading the linked article. Some explanation of the physical or mathematical reason behind these waves would help. If I’m not mistaken, the normal explanation of quantum computing is that the waves don’t have a useful physical interpretation and are only used because interference does occur. (I may be wrong - these might be connected to EM waves) Also, if you want to make this article more self-contained, I think describing the functions-as-vectors concept directly using Fourier series might work (just the statement that an infinitely long vector can denote the coefficients for the Fourier series of any function and the definition of a Fourier series (any periodic function can be represented as an infinite sum of waves. Of course, a 2D vector is sufficient in this case) Your explanation of the Bloch sphere is solid, in my opinion. It might also be worth explaining why we don’t go down to a 2dlD representation (the 3D representation is still on a 2D surface, since there are 2 constraints for 4 variables) - but I don’t think it really hurts your article if it’s missing.
I feel like the piece ends somewhat abruptly, I’m left wondering what the representation can be used for. Does is make some operation on qubits more intuitive, does it make the time evolution simpler, why use the sphere? Still, I love the interactive bits on the website, and I particularly like the explanation on why it’s a sphere and not a half sphere.
generally good, but i dont like using the word eigenstates or energy if you’re not talking about a matrix/operator, at the very least i would present a schematic version of the shcrodinger (H\psi = E \psi) equation if you wish to talk about eigen-anything
Hey! It is a great article, thank you.
Math undergrad here and I have seen bloch spheres before, but nothing beyond surface level facts which left it clear as mud still. Eg I had heard “represents 2 complex numbers” and “sums to 1 hence sphere”.
Reading your article has really advanced my knowledge, so thank you again.
I liked the writing style, easy-going and friendly, and the interactive elements are engaging.
On my learning journey through the article, some points I found tricky: I get that the eigenvectors could be functions, I guess it was my first time hearing this so seeing the 2 example functions made me think, why these functions in particular? Where did they come from? Would any functions do? I guess these are the simple & useful forms.
And then the step of “hey these things rotate”, made me ask “why? where did that come from?”. I guess I accept it and the maths falls into place, but it would be really satisfying to know “why”, or perhaps just a comment something like “this is a good model for qubits, and it’s how the universe seems to work, we don’t actually see a physical thing rotate”