If there was a Scott Aaronson tier communicator for every subfield of science, the world would be a much better place. I also wouldn't have to type nearly as many comments.
Hold on a second. Scott Aaronson is popsci, as in popular science.
As for what you refer to, see the name of the journal the boy is reading in the first panel :)
(1) The (complex) coefficient of a component of a state vector.
(2) If we treat that number c as re^(iθ), then r is sometimes called c's "amplitude" (though it's more often called the "norm" or the "modulus").
(3) Some authors even use it to refer to θ ("The argument is sometimes also known as the phase or, more rarely and more confusingly, the amplitude" [1])
Luckily, in quantum mechanics, they almost always mean (1). That's the usage here.
Is that at all part of what is trying to be communicated?
The sine wave is 1-dimensional and the ocean wave is 2-dimensional, but both have the property that the amplitude at a point (say, f(x) or f(x, y)) is a real number. In QM, to describe position, we have a 3-d wave whose amplitude is complex. This is obviously hard to visualize.
But consider for a moment a particle confined to one dimension. Its wave function is a function f(x). This function can also be thought of as a vector in an infinite-dimensional Hilbert space called the L^2 function space[1]. In quantum computing, we generally deal with two-dimensional Hilbert spaces (and their tensor products), which you can sort of think of as discrete waves with only two points. This is because, while a particle can take on an infinite number of positions, there are only two possible spins (for example). If you follow Prof. Aaronson's lectures, these are the sorts of "waves" that matter.
Leaving that aside, you could imagine two 1-D sine waves (with different speeds and/or phases) interfering, just as you could two ocean waves. The difference in QM is that you're summing complex numbers.
[1] https://en.wikipedia.org/wiki/Square-integrable_function
I'm not sure why they don't just say that, it is the most straightforward part of QM.
0: zz* = (z)·(z*) = (a+bi)·(a-bi)
1: Possibly all - I have yet to happen across a counterexample.
2: https://en.wikipedia.org/wiki/Dot_product#Algebraic_definiti...
Came across this while looking for an example: https://www.youtube.com/watch?v=CAe3lkYNKt8
Amplitudes are like probabilities that can destructively interfere when added. With traditional probabilities, if P(A) > 0 and P(B) > 0 the sum of the probabilities P(A)+P(B) cannot be zero. However, we needed to model observations like the two slit experiment where we observed that a location on the target that had positive probability of being hit by a photon in the two single-slit-only situations, that became zero when both slits were open.
* A qubit is special because it's a superposition of "0" and "1"
* A superposition isn't described by being "both" of them, or "maybe one or the other in weird ways"; it's "a complex combination" that's also a "unit vector"
* Quantum mechanics is a generalization of probability
* (Not in comic, but common knowledge) Any "event" has a certain "probability" that it will occur
* Classical probability can only range from 0 to 1, along a straight 1D line
* Quantum events are determined by the 2D probability "amplitude", where this word describes the superposition of "0" and "1" of the qubit above
* (Common knowledge) Taking a measurement of a qubit or any other quantum system collapses the superposition
* When you measure a qubit, there is a rule that converts the "amplitude" into a classical probability. In the case of a qubit, the "event" is whether it will be a "0" or a "1"
* Because amplitudes are actually 2D (while the qubit is in superposition), the rules for adding two amplitudes are different than for adding two 1D probabilities. In particular, they can "interfere" and cancel out. Think of two vectors that point in opposite directions, or (1 + 0i) + (-1 + 0i) = (0 + 0i)
Some of the above is probably cheating, since I read the other replies to this comment before rereading the comic. However, I think if you move even further away from the detailed math, the usage of "amplitude" is pretty clear. Non-quantum bits would have a "probability" of being measured as "0" or "1". A qubit in superposition has a certain "amplitude" that is analogous to probability, determining whether it will be measured as "0" or "1". Quantum computing exploits the special probabilities of this "amplitude" to do calculations you can't normally do, for very specific problems. It's very hard to keep even a few small qubits in the state of "superposition", which is required to exploit these properties.
Scott Aaronson is one of the best in the field, though.
You call this "poking fun", but it's horrifyingly real: https://en.wikipedia.org/wiki/Quantum_mind
Tomorrow... will it be string theory? The true secret of the soul is without any doubt hidden in the 13th dimension.
Now it's starting to sound a bit like learning a new language, too. Stuff that tries to make it easy and approachable and bite-size like Duolingo just never seems to do the job; the success stories I know of (including my own) always involve accepting that it's going to be unpleasant and confusing for a while, keeping your nose against that grindstone, and giving your brain some time to rewire itself.
That said, knowing physics, someone out there has already read this and interpreted it in some Chopraesque way that I can't even anticipate, and someone else is probably getting ready to downvote in reaction to some other Chopraesque interpretation I failed to read into my own words, so I probably should keep my mouth shut instead of posting. People get (understandably) twitchy about this topic.
But, effit, I'm going to anyway. The only practical characteristic of HN karma is its combustibility.
OK, now I must ask forgiveness for using monads in an analogy.
The other important thing to know is that our brains are subject to the same complex probability amplitudes as qbits- That's why things seem weird when we magnify quantum phenomena via experiments and try to explain what's happening: Our brains get entangled with the experiment and the "slice" of the world that we're experiencing varies depending on the results of the experiment. Quantum phenomena seem a lot less "weird" once you get comfortable with this fact: i.e. that our brains are just physical objects prone to the exact same physical laws as elementary particles, and that the organ we're using to reason about the experiment with is entangled with the experiment itself.
(Disclaimer: I'm only an armchair enthusiast)
https://www.microsoft.com/en-us/research/video/quantum-compu...