Scott Aaronson, co-author of the comic, is the director of the Quantum Information Center at UT Austin, and has a number of publications about quantum computing. His website has more qualifications: https://www.scottaaronson.com/.

And it's not just the qualifications -- Scott Aaronson is one of the most approachable, honest, and witty science communicators of all time. You almost never see all those traits all together in popsci, even ignoring qualifications.

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.

>You almost never see all those traits all together in popsci

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 :)

His book Quantum Computing Since Democritus is very good too.

Wow. I had no idea, thanks for this!

I don't know what a bunch of words like "event" and "amplitude" (of... what?) mean in context, to the point that I was able to nod along but didn't actually understand any of it.

It's hard to answer your question without giving a course in QM, but this is a good place to share a pet peeve about this. For some deeply unfortunate reason, "amplitude" can refer to:

(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.

[1] http://mathworld.wolfram.com/ComplexArgument.html

If someone refers to phase as amplitude, there is justification in ceasing to read their paper and switching to something else.

Wait, why do they call it amplitude when it's the rotational component? What is the reasoning to call this amplitude?

I don't know, because they hate us?

My knowing-nothing coming in takeaway is that the 'wave' state of QM is more like an ocean wave than the two dimensional wave of a sine wave on a oscilloscope and 'interferes' similar to how wave encountering each other on the ocean might.

Is that at all part of what is trying to be communicated?

This is a bit tricky to explain without more math.

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

An amplitude is kind of like a probability. I guess it's called an amplitude because it's used in complex quantum wave equations. But the rule to get a probability from an amplitude is basically that you square its absolute value, which gives you a positive real number.

This doesn’t really help. How is this amplitude different from traditional probability? How can an event have negative amplitude? What does it even mean?

Amplitudes were needed to easily describe wave-like behavior. To produce an interference pattern, we need something like a probability that can be negative to represent the negative half of a wave.

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.

Isn’t it P(A|C) = P(B|C) = 0 where C is both slits are open? P(A)+P(B) is still > 0. The condition C modifies the marginal probabilities of A and B, does it not?

This was a very effective way to describe it, I've read a great deal about QM and you made it click much better.

Ok, so an "amplitude" is just like a PDF, only that it can also take on negative values and that adding "amplitudes" is a meaningful operation?

Quantum mechanics makes a lot more sense if you don’t care about what it means and just learn the math.

Look at frequency and amplitude in sound, how different sound waves of different amplitudes interfere with each other. That'll help.

Came across this while looking for an example: https://www.youtube.com/watch?v=CAe3lkYNKt8

The traditional probability = amplitude squared. An event can have negative amplitude, but due to the square the probability cannot be negative.

I'm not sure why they don't just say that, it is the most straightforward part of QM.

Amplitudes can be non-real, so simply squaring them doesn't ensure that you have a (non-negative) probability; you have to also take the absolute value. It's still a pretty straightforward process to derive a probability from an amplitude, but fully explaining that process is a bit of a distraction from making the point that amplitudes really aren't probabilities and shouldn't be thought of as equivalent to or even intuitively similar to probabilities.

To be more pedantic, it's actually the product of [amplitude] times [complex conjugate of amplitude][0]. Confusingly, this is sometimes called the "square" of a value - usually in contexts where complex-element vectors and matrices are involved, since most[1] real-element formulas calling for matrix transpose (dot products[2] are a special case of this) actually want conjugate transpose[3] but didn't notice because conjugate is identity on reals.

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...

3: https://en.wikipedia.org/wiki/Conjugate_transpose

I don't think it's important to know how "amplitude" relates to the underlying mathematics. In the context of the comic, it is constrained by the following statements:

* 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.

My takeaway is that amplitude is used because we're thinking about wave patterns and in particular the interference from those waves.

It was indeed a good educational comic, but if you're reading between the lines you're still probably getting things wrong. And there aren't a lot of lines, so if you aren't reading between the lines you aren't getting a lot, period. Probably the best thing to take away is what you don't know.

Scott Aaronson is one of the best in the field, though.

The parallels between Zen Buddhism and quantum anything has been striking to me lately. Not in every way, duh. But mainly "your classical concepts aren't going to work here" and "you nod your head, but you don't really get it yet." But perhaps the biggest parallel is that a lot of people, maybe most, get it way, way wrong starting out.

The comic kind of pokes fun at such parallels, especially in the final panel ("Quantum computing and consciousness are both weird and therefore equivalent,") but I think it's a common experience, and quantum physics in general becomes the canonical example because everybody has the same experience with it. Whereas with many other examples, two people might find different things intuitive or counter-intuitive, depending on their path to the subject. I've even seen a professor confuse an entire classroom by describing something as "counterintuitive" when it was completely straightforward from the perspective they had been taught the previous semester. Quantum mechanics can serve as the byword for needing to absorb an entirely new and counterintuitive set of concepts because everyone experiences it that way.

Many years ago, people believed that "magnetism" is the answer for mysteries of life and soul. These days, magnets are considered boring, so people updated to "quantum".

Tomorrow... will it be string theory? The true secret of the soul is without any doubt hidden in the 13th dimension.

> "Quantum computing and consciousness are both weird and therefore equivalent,"

You call this "poking fun", but it's horrifyingly real: https://en.wikipedia.org/wiki/Quantum_mind

Hmm. I'm no physicist, but I'm a (lapsed) member of a Soto community, and once upon a time my best friend was working on a quantum computing project and occasionally tried to explain his work to me over cocktails. I think I see where you're going there - any attempt at a popular explanation seems doomed to failure. There's no real Cliff's Notes version, you just need to keep grinding through the work (staring at a wall on the one hand, staring at a chalkboard hanging from a wall on the other), and eventually it starts to make intuitive sense just through repeated exposure.

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.

What's a Soto community? No luck googling.

Soto is one of the major sects of Zen.

Sounds like you’re describing a cult! Haha.

First, do a couple of problems in elementary quantum mechanics. Then, see if still “strikes you lately.”

That's unlikely to happen. Was there a point you were driving at?

Your comment seems like the kind of problem the comic is arguing against. To paraphrase the final panel: "Quantum computing and Zen Buddhism are easy to get completely wrong and therefore equivalent."

Umm, no, that's not where I was going at all. But I guess I could see how it might be taken that way with a little squinting.

Quantum mechanics is just math, and it’s possible to work the equations and get valid results even if you haven’t the slightest understanding of what any of it means. There’s no such parallel with Buddhism.

It was accurate and hilarious. I don't know how useful it is if you don't already know quantum mechanics. (Note: that's not the idiom of "I don't know" = "I doubt it". It's actually "I don't know." One thing I have learned over the years is that once you've rewired your brain for this stuff, you have no intuition for what exposition will actually work for someone who hasn't.)

It's like coming up with a metaphor for monads once you understand monads.

OK, now I must ask forgiveness for using monads in an analogy.

I did not know until today that I needed an emoji that was both lol and angry.

It's actually educational and was cowritten by Scott Aaronson, who has a great lecture that explains the idea of "quantum mechanics as complex probabilities": https://www.scottaaronson.com/democritus/lec9.html

I've been recently exposed to dual and split-complex number systems. Is there any place for probability theories based on those "sibling" number systems?

As someone who used to think all the "wrong" things, and then actually sat down and read what quantum computing actually is (thanks Wikipedia!) and realized that the popular depiction is, in fact, wrong, yes, this comic repeatedly hits all the right points.

It's much better than most other brief explanations I've read. One thing I wish it would hit more strongly is that the "actual world" is bigger than what we can interact with, we only experience a "slice" of this larger world under almost all circumstances- The complex amplitudes of qbits hint at this fact, and quantum computers essentially take advantage of this "extra stuff in the world" to do calculations, though in a completely different manner than mere "parallel computation". What we don't yet know is if this "extra stuff" is really big (i.e. represents parallel universes) or is just some kind of more restricted phenomenon.

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)

I'm not an expert, but I think this comic does a decent job of breaking down a few of the easy, popular misconceptions, provided you don't get completely lost. You're not going to gain any real understanding from this comic, it's not intended for that. Unfortunately, I don't think it's possible to have any deep understanding of quantum computing without sticking your head in the numbers.

My coworker gave this talk on quantum computing for computer scientists that I found extremely helpful. It just requires basic knowledge of linear algebra and classical computer architecture.

https://www.microsoft.com/en-us/research/video/quantum-compu...