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" )
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. 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.
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.
Came across this while looking for an example: https://www.youtube.com/watch?v=CAe3lkYNKt8
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.
* 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.
Tomorrow... will it be string theory? The true secret of the soul is without any doubt hidden in the 13th dimension.
You call this "poking fun", but it's horrifyingly real: https://en.wikipedia.org/wiki/Quantum_mind
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)
> Drawn with great humility and thanks to one of my favorite people. Scott did all of the real work, and I threw in some dirty jokes. So, hey, a pretty good deal all around.
Gee, I wish they'd mentioned that in the literal first panel of the comic.
thank you! I have so much catching up to do :)
If the creator of the comic is here -- please pick a more ethical ad provider.
Really? How recent? All I can find are news articles from December last year saying they were working on it, but I've experienced the problem in the last month or so.
Throwing shade at Roger Penrose there... (I recognized it because that has always been my precise take on all his books.)
The Superman one always gets me:
Do you have any favorites?
This question describes about half the field of quantum computing, so it isn't something I can answer in a post this size.
And yes, a low number of qubits can factor small numbers. https://arxiv.org/abs/1411.6758
Are there some good links out there for someone to understand the concept in a bit more depth.
Please challenge my current assumptions
- Would not be Turing complete
- More qubits are needed for practical applications
- Practical application in cracking crypto
Learning isn't knowing isn't doing isn't engineering. To take a much, much simpler example, just because you very likely know the rules of chess does not make you a grandmaster.
1: Aside from the problem of turbulence.
Some videos used some of the simulators that could simulate a few qbits. I remember that as you added qbits, the amount of ram you needed grew massively (exponentially?). Everything that could be done with a quantum machine could be done with a classical machine, it would just have larger space or time requirements.
I feel like this comic tries to get across a lot of the higher level concepts without using the stupid analogies used in a lot of pop science articles. It's not necessary for understanding the actual maths, but it does help with larger concepts. It's honestly something I'd expect from PhD comics. I stopped reading both SMBC and PhD a while back; need to catch up on my RSS feeds :)
Imagine 2 tennis balls floating in space, each spinning in some direction at some speed.
The quantum amplitude is the extent to which they are matched, or opposed, when you break down the inertia of each into vectors. In fact I'm pretty sure their measurements are very limited in the extent to which they can measure these things to infinite precision. (Duh)
Is this another case of obfuscation by academics? This is truly not complicated. It's even kinda fun. I think we all have a little fear of being mentally outgunned, and fear does what it's always done to creative thought. Dominated it.
My understanding of the spin of a particle is that it turns out, roughly speaking, your spinning tennis ball needs to keep track of a vector along the axis of rotation. This has something to do with the unit vectors in 2D Hilbert space having a correspondence to the group SU(2) (where remembering only the axis is the classical case of SO(3)). Somehow, if you were to take your quantum spinning tennis ball and, by some mechanism (magnetic fields?), slowly rotate its axis by 360 degrees, its spin becomes negative of what it originally was and it can destructively interfere with a tennis ball in the original state. Is this the sort of thing the pair of tennis balls is meant to deal with?
Something I really don't understand is how angular momentum is meant to work... I would have thought it's a Lie algebra thing, but SU(2) and SO(3) have isomorphic Lie algebras.
Disclosure: I don't know any quantum mechanics, just some math.
If I was going to become some kind of researcher in the field, this is still the last thing I would want. Since I'm not a quantum computing researcher, it doesn't matter to me.
Before someone in the thread happily starts on their own condescending lecture, yes, I DO know that IF quantum computing becomes useful that it will massively change computing.
Perhaps if you toss out your bowl of cornflakes and pour it again, that funny taste will go away.