So, I have a question. I found the 'article'... well comic, surprisingly easy to read and I think I learned something. However, my knowledge of quantum computing has mostly been based on articles that the comic was poking fun at. I've not had any formal education. So my question is, was this indeed a good educational comic, or does it just have a different set of problems from other articles on quantum computing?
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.
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.
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.
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?
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.
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.
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.
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.
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."
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 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.
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.
Apparently this was a collaboration with Scott Aaronson:
> 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.
Ha ha - his blog tagline is "If you take just one piece of information from this blog:
Quantum computers would not solve hard search problems
instantaneously by simply trying all the possible solutions at once."
So you don't have a second revelation: there's also hover text, but only for the past couple years, whereas there's a red button image on almost every comic (for 17 years).
Accidentally clicked on an ad on the site at the bottom, trying to close it. It sent me to one of those, sites that hijacks the vibrate of your phone, and a back button that does nothing.
If the creator of the comic is here -- please pick a more ethical ad provider.
I noticed their ads got drastically worse recently; I'm not sure if I got used to them, or if they toned them back a bit, though. Anything could happen if you actually click them, though, that's going to happen on any network
That sounds like a failure of your web browser as much as anything. How on Earth is your phone vibrating without you granting a site notification permission? And recent versions of Chrome limit the degree to which history.pushState() can hijack your back button.
No, I didn't know about that api. Thanks for the link. I stand by the statement that it's a browser failure, though, as IMO that should be restricted by a permission and/or user action, but it appears to require neither.
> recent versions of Chrome limit the degree to which history.pushState() can hijack your back button.
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.
This inspired me to submit https://news.ycombinator.com/item?id=21380480 . It's a fairly short (34 page) introduction to QM from a mathematical POV, emphasizing QM as a generalization of classical probability.
For anyone who's curious about what quantum computing actually is, I recommend Quantum Computing for the Very Curious [1]. Most articles online either get it wrong in the "free parallelism for everybody!" way that the comic warns about, or just scratches the surface and vaguely indicates that that's not what's going on (like the comic itself does). QCVC was what made me finally feel like I actually had a little foothold in QC land in the sense of slightly understanding what people do when they do quantum computing. It's pretty long but a pretty easy read.
So how do you formulate a useful problem such that a quantum computer will have the amplitudes interfere to create the answer? Can the low number of Q-bit computers available factor small integers, for instance?
I'm not qualified to answer, but just wanted to let you know that I found this post hard to parse. The last point is a constraint and not an assumption, but the others are. The second point is not a property of a problem, but the others are. They also all have different moods. And I don't know what "SE" is in this context.
I have been fascinated how once we figure out the relationship between quantum mechanics and relativity, we will be Gods. Is it just a matter of misinterpretation? Is there no spooky action at distance?
At this point, it is not terribly likely that any such breakthrough is going to surprise us all that much at the engineering level: https://en.wikipedia.org/wiki/Correspondence_principle If it does, I rather suspect it's going to take something like a Kardeshev level 2 [1] civilization to be able to take any advantage of it... and that may still not be enough.
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.
I don't see that we'd be gods. I mean classical mechanics is well understood¹ but it's not like it allows people to move mountains and fly out the window at will etc...
I feel like the author of that comment looks at it kind of like the discovery of the electron: once we learn how to control it, we can achieve things that were never possible before.
Another recent SMBC was about the Elitzur Vaidman bomb tester, which I had never heard of before, and after staring at Wikipedia for a while, I have a somewhat better understanding of what quantum interference means, and sort of proved to myself that all this quantum stuff is actually real/has potential useful applications.
I remember looking up stuff on quantum computing a few years back. At the time a lot of the YouTube videos were by maths professors, and they were all very good and didn't skip on the complex maths (although I got the gist, a lot went over my head, but I knew I could probably get it if I reviewed all my polar/complex notation and maths).
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 :)
Great comic! How I visualize this stuff is really simple, and so far it doesn't seem to be wrong...
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.
I'm wondering what you mean by "doesn't seem to be wrong" -- are you doing any calculations? I'm not able to follow exactly what you mean by the quantum amplitude coming from a pair of tennis balls.
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.
Very cool, I had not seen Lie algebras before. More fuel for the organic AI ;-).
Your description sounds perfectly accurate; uberdelicate electromagnetic manipulation would be the first logical approach.
...Actually Gizmodo just did an article on "Sycamore" a few days ago! Great read.
- Perhaps after the microwave pulses they can get even higher resolution by shining very bright images on it.?
That's just what I need, someone to lecture me patronizingly on a field like quantum computing which has absolutely zero practical utility at this point.
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.
