Note its not strictly-speaking necessary to learn any linear algebra to "understand" quantum computing, there is a very simple but universal set of string-rewriting rules.
I realise for this audience most people wouldn't get much from it, but I find these rules useful for explaining quantum theory without annoying and fluffy analogies to high school students. You can find the rules in my book _Q is for Quantum_ - Part I which covers quantum computing is a free download on the book website (and the rest will be if I ever get around to producing a corrected pdf, bleh, but if you read part I and don't want to pay for the rest let me know and I'll get it to you...)
I looked at the book and it is. His way is perhaps useful for not scaring off amateurs from learning quantum theories, but ultimately he is tricking them into learning a part of linear algebra without a foundation upon which more complex concepts can be built.
Actually its not quite that simple. The approaches are "equivalent" (in terms of operational/statistical predictions) but not "isomorphic" (even if we restrict the regular linear algebra approach to the same gates as I use in the book). Basically (because of not implementing normalization/unitarity) in certain situations the "mist" retains a count of the number of "Feynman paths" that led to the output state. For example, concatenate two PETE boxes (hadamard gates) and the output is [W,W], concatenate four and its [W,W,W,W]. Operationally identical (you only observe the ball to be certainly white!) and applying a suitable simplification rule you "drop the extras" of course. But if someone (unlike me!) wants to think of these states as having ontological status maybe they would think the distinction is relevant.
A much more interesting example of something similar happens in the Deutch-Hayden version of Heisenberg picture style quantum theory. There from looking at the "state of the world" you can determine which total unitary evolution occurred to get you there. In the Schroedinger picture, if I give you the inital and final states there are many possible unitaries that get you between them. Its possible to go further and come up with versions where not only the total unitary connecting initial and final state is discernable, but also the sequence of Hamiltonian's that implemented it are too.
These things are mainly of interest to people in foundations of course (since they like to play the game of blurring the line between our math and what is "really out there"). I tried to be very careful in the book to maintain the distinction.
Downloaded part 1 of your book last night and read it, as a fellow computer scientist and educator, very very solid work! I bought the book!
Are you aware of anyone who made an interactive version (eg in the browser) of the boxes and balls model? Would be really fun to mess around with it interactively.
Thanks for buying! Any money I make eventually works its way back to Malawi where I grew up, so it not going to be squandered :)
A few weeks ago a high school physics teacher who used the book for some extension classes sent me some python code he says will do all of the calculations. I have asked the family friend who maintains the book webpage to put it on there, and I am sure she will when she gets a chance. However if you email me - terry @ qisforquantum.org - it would be great to have someone look at it - I don't know python at all and can't even run it to check it. (I also have some atrocious octave/matlab code of my own which anyone is also welcome to.)
I hate people that trick others in to learning stuff. :) This book really looks nice and short to me and I really wish the other parts comes online to.
One of the creators of this, Andy Matuschak, is the only person I support on Patreon.
I really believe that we are just now starting to scratch the surface of the learning opportunities that computers present to us and Quantum Country was an interesting step forward in that direction. It is worth looking at some of his previous work with Khan Academy as well, cool stuff.
Unfortunately the questions are utterly superficial and laughably different from the sort of thinking you need to do to understand how a 2-dimensional complex vector space is involved in quantum physics and quantum computing.
I say that not as a physicist/mathematician looking down at the oiks trying to underastand this stuff, but as one of the oiks.
Of course they are. By design the flash cards are small atomic pieces of knowledge that can be answered simply. If the grand overarching concept is a web of interconnecting ideas, then the flashcards are supposed to help you maintain that by making sure you don't forget the small ideas the structure is made of.
It's also by design that some of the questions are, as you say, laughably simple. It's to catch people who aren't properly engaging with the text as early as possible.
Nielsen and Matuschak are sensible to these sorts of critiques. Quantum country is part experiment after all and they've been learning, adjusting, and experimenting with what works best. If you want a bit of context of where they've come from and where they want to go, I recommend this: https://numinous.productions/ttft/
i tend to trust Nielsen on this one, who literally wrote the book on quantum computing and has spent years teaching it to people. his philosophy is that the biggest obstacle to understanding is memorization of basic concepts and notation.
You're right that the spaced repetition questions are different from the really interesting questions, but that's the point. They're supposed to be aids in internalising the "lower-level"/"boring" terms, definitions, properties, etc., which is necessary to be able to follow along.
>At least in popular media accounts, a very common description is that a state like 0.6∣0⟩ + 0.8∣1⟩ is “simultaneously” in the ∣0⟩ state and the ∣1⟩ state.
>I must confess, I don’t understand what people mean by this.
I think they're just trying to tie it to Schrödinger's cat somehow since that's the only other topic that seems to be covered in pop science.
To me (but then I already know a lot about both of these topics) the format is actually much more interesting. Although it looks like the material is well presented.
It does make sense that if we're going to have learning interfaces they have spaced repetition built in rather than requiring users to do that themselves.
This is a great study resource. A downside is there are no solutions to check your work, or look up if you get stuck. I’d imagine a lot of people reading this wouldn’t necessarily be university students with a professor to ask questions to, so such a resource would be useful.
Beware, there is a sign-in wall on this "free" introduction that comes up after a couple of topics.
Edit: this seems to be the case only on the mobile version
The intent behind the sign-in seems to be to allow you to participate in the built-in SRS system for learning the material. Obviously there's no guarantee that behind the scenes your email is not being sold off to NefariousMarketers Inc., but given the past projects and work of both authors, that seems perhaps unlikely.
This is a really great resource that introduces some fairly sophisticated ideas. I'm about to be negative but I genuinely mean that; I'm planning to go back to it. I was finding it took time to take in the ideas about C^2.
However
> Presented in a new mnemonic medium which makes it almost effortless to remember what you read
This is just nonsense and quite distracting, even irritating. Quantum computing and quantum mechanics is hard and involves sophisticated concepts. The spaced repetition questions are utterly superficial and represent unhelpful dumbing down.
Apologies for the rant and slightly silly comparison between quantum physics and a programming language but the same goes for the Rust book. Rust is a hard language with sophisticated ideas. Despite the best intentions of the nice people at Mozilla, no amount of dumbing down changes that. And patronizing readers does not make the resource more approachable to women and under-represented minorities, unless you believe that those groups need to be patronized.
> The set of curly brackets, {}, is a placeholder: think of {} as little crab pincers that hold a value in place.
> This is just nonsense and quite distracting, even irritating. Quantum computing and quantum mechanics is hard and involves sophisticated concepts. The spaced repetition questions are utterly superficial and represent unhelpful dumbing down.
I can see why you would think that. However, consider the following points:
1. One of the authors is/was[1] one of the most well known experts on quantum computing, and he literally wrote the book on quantum computing.
2. He has written elsewhere on how spaced repetition really helped him understand new disciplines and read journal papers.
So while you may not like spaced repetition, think twice before saying "unhelpful dumbing down", given that it really helped him, and he's very clearly not a dumb person.
There's no harm in simply saying it doesn't work for you. I suggest you examine the need to justify that by making broad statements.
Perhaps there's more to the Rust/Mozilla story that I don't know of, but going from the example you gave and connecting it to making things approachable to minorities is a giant leap I'm having trouble fathoming.
And while the statement is annoying, I did not find it in the least patronizing. I don't doubt that it helps some people, and I think you need to realize that not all books are written for you, and that there likely won't be any book that is good for everyone. If you don't like it, find another book - don't expect the world to cater to you.
When it comes to technical books, particularly math/physics text books, everyone has his/her own opinion and that's OK. There's no shortage of people who hate math books that give too many examples ("Just give me the theorems, proofs, and maybe one example!"), and there's no shortage of people who want examples and hate books that are "theorems/proofs". The same goes for pretty plots, color coding important theorems, etc. Yet not once in my time in academia and beyond did I hear someone say "These distracting elements and examples are dumbing things down and are patronizing, and it's because they're trying to appeal to women and minorities!"
I really think you need to introspect about your world view that led you to these conclusions. You're being triggered, and you need to own your reactions.
> Quantum computing and quantum mechanics is hard and involves sophisticated concepts.
Although I didn't study quantum computing, I have done plenty of non-relativistic quantum mechanics at the grad level. It's hard for only two reasons:
1. Lots of introductory books start off with calculus-heavy problems (infinite square wells, harmonic oscillators, hydrogen atom, etc).
2. It differs from real world experience.
Plenty of people have advocated that item 1 above is the problem, and it is not a good way to teach QM. You get lost in the calculus and don't focus on the QM. There are plenty of advocates (e.g. David Mermin) who think QM should first be taught using spin, because it involves no calculus, and the linear algebra is necessary (and not sophisticated). Almost all, if not all, the fundamentals of QM can be taught that way, and it's not that hard. Certainly a lot easier than much of your introductory physics material (mechanics, EM, etc).
[1] I say "was" because he has left the quantum computing research world.
I don't think the central focus of this resource is to teach Quantum Mechanics, but rather to test a new teaching method - the relative importance of yet another Intro to Quantum Mechanics course is tiny compared to developing methods potentially applicable across the entire space of online learning. As you say, the SRS questions could be better, but the idea of embedding them into an online essay / course is, to my mind, novel, potentially enormously valuable, and worth highlighting.
Is it the notion of embedding SRS questions into the medium per se. that you find superficial and unhelpful, or just the specific questions that Andy and Michael chose? If the latter, would you suggest any alternative questions that might be less patronizing / more effective?
They should be testing it on something that involves more remembering and less thinking, like microbiology. Physics is the absolute worst subject to test any new book-writing method in, because the book practically doesn't matter; it's all in what happens inside the student's head as they do the exercises. The fact that the Moore method has half a chance of working for topology students shows beyond a shadow of a doubt that for highly logic-based fields like physics and math that the book matters so little that the absence of any book or lecture at all will still result in the material being taught!
Approximately half the math textbooks I study from basically do this already. It works very well, but IMO mostly because the questions are not easy. You actually have to stop and think for a few minutes before moving on.
> Quantum computing and quantum mechanics is hard and involves sophisticated concepts.
It's comments like these that in high school made me avoid calculus. Just wanted to let you know that you are discouraging. The youngsters reading this that are still developing their critical thinking skills are being scared away because of your projections. Frame it different, take responsibility for your inadequacies.
> Just wanted to let you know that you are discouraging.
It didn't strike me as discouraging at all. Discouraging would be something like "QM is so hard that 80% of people reading this are too stupid to learn it" (which I don't think is true, FWIW, so don't be discouraged by that)
Just because youngsters don't have critical thinking skills does not mean they will read words that aren't even there. If anyone does that, it's on them, the reader, and no psycho-analytical word smithing will fix that.
People of the age you're talking about aren't stupid and they're not taken in by people giving them saccharine messages about how things aren't hard and anyone can do them.
OK. If you are a student reading this then, well, firstly I'm not at all sure you're feeling discouraged from learning about the nature of reality and potentially world-changing computing frontiers because someone on the internet said it was a hard subject! But if you were, please don't be. Here's why.
Firstly, a lot of incredibly valuable and interesting things do require a bit of concentration and effort. I'm sure you know this.
But there are reasons to be optimistic! Here are some things to do:
1. Stay calm! Don't give up.
2. It's not at all obvious how to read technical stuff to start off with. Basically, the secret is to read the same paragraph a LOT of times! Everyone does that. No-one can understand it by reading it through once like a novel. If you find yourself reading the same paragraph 100 times you're on the right path because it means that you KNOW you haven't quite grasped all the ideas yet, and so you are becoming your own teacher in a way; setting your own standards for yourself.
3. You've got to be, or become, the sort of person who can concentrate on reading something challenging, in a quiet room. Talking to others is going to help a lot also, but there's a private side to this. You can compare it to training to be on a sports team at a more competitive level. There are going to be times when you're doing fitness training or whatever, and you're on your own, and it hurts because you're exhausted. You know this was always part of the deal.
4. Don't listen to the people who tell you that it's "easy" and "anyone can do it". Yes, anyone can do it in in the sense that everyone has the biological potential to do it (they're human, they have a perfectly good brain). But you know perfectly well, just by looking around at your classmates that some people don't have, or at least don't currently have, the attitude that's going to let them do it. You don't have to be weird; you just need to let one side of your personality be a studious side, occupying some fraction of your time.
Would you please read and follow the site guidelines? I appreciate the positive intention behind your comments, but the way you're going about it is both against the rules here and guaranteed to make the discussion worse. That's no coincidence; the rules are the way they are because of what we've learned about discussion dynamics on the internet.
Hi dang, sorry, starting off with "What rubbish <username>" was a clear violation of a very reasonable guideline; I've edited my message to remove that.
Could you tell me if I violated any of the other guidelines / what else I have done that is likely to lower the quality of discussion?
Not sure if this is one that I might have violated here, but I don't think I agree with the guideline saying not to use HN for "ideological battle". That seems to need a clear definition of what "ideology" is, and even then it seems to risk ruling out many important contributions to HN, so I cannot promise to uphold that guideline unless it can be clarified, and possibly not even then.
The comment you edited is probably ok except for "taken in by people giving them saccharine messages", but I would say that https://news.ycombinator.com/item?id=23563745 breaks the site guidelines about calling names, shallow dismissals, and generic tangents.
You can't give precise definitions to any of the terms in the guidelines and it would be a huge mistake to try. All that an attempted formalization would do is create loopholes to be exploited, and then make moderation harder because people would excuse themselves with "it's technically not against the rules". The rules aren't technical. HN is a spirit-of-the-law place, not a letter-of-the-law place: https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu.... Here's a version of this point from 6 years ago: https://news.ycombinator.com/item?id=7606756
In practice there is an easily observable difference between how people use the site for curious conversation and how they use it for political/ideological battle. The former goes with openness, respect, and exchange of information. The latter goes with being aggressive and wanting to defeat, not hear, the other side. The former produces comments that are unpredictable and fresh; the latter produces comments that are repetitive and nasty.
> And patronizing readers does not make the resource more approachable to women and under-represented minorities, unless you believe that those groups need to be patronized.
That came out of the blue. Am I missing something? Did mozilla make such an attempt to patronize minorities?
I think your parent is suggesting that this whimsical example is patronizing.
Some fun history here: Ruby uses #{} for string interpolation. I used to teach Ruby to folks as a job, and I believe that my boss, Jeff Casimir, said that they looked like lobster pincers in one of our classes. (If Jeff reads this and that's incorrect, my apologies!)
Years later, when I was writing this part of the book, I remembered this analogy, and we had the whole crab thing going on with Rust, and I thought it was a fun thing. So I put it in the book.
Some people find whimsy inherently patronizing or something. I dunno. It's an offhanded fun comment, not some sort of desire to "dumb things down" for anyone. We don't write anything with the intention of dumbing things down.
Hi Steve, thanks for the comments and for reading my somewhat grumpy post! I expect you've heard it all before. It's true, I do believe that Rust is basically a programming language for adult brains, and so it's a bit weird for the Rust book to contain sentences that sound like they're aimed at younger teenagers. I know there are teenagers learning Rust! And that's great. But when they're doing that, they're exercising quite an adult part of their personalities and I think they'd respond better to being treated as adults while they are bravely entering an adult world.
It's also true that I worry that the whimsical sentences that seem designed for children are somehow connected with what is often called the "Diversity and Inclusion" movement. In my company, the diversity and inclusion initiatives were characterized by childish activities, such as writing "motivational phrases" on post-its in colored pens and posting them on the walls of the office. The women I've spoken to about this really resented the fact that engaging with pro-women-in-tech initiatives meant having to behave childishly, and they resented even more strongly the implication that childishness was appealing to women and under-represented minorities.
"In my company, the diversity and inclusion initiatives were characterized by childish activities"
You may have some wires understandably crossed. Companies frequently end up hiring in people for all sorts of initiatives that end up doing some really childish stuff. Diversity and inclusion do not particularly stick out on this front. This is where we end up with the mockery around "trust falls" and that sort of thing, which are childish "team-building" activities, and have you ever seen a corporate presentation on how to do better sales? Yeowzers. It's not specifically a diversity/inclusion thing, it's all the corporations.
On the other side, there is a solid reason to use whimsical, or more accurately, highly visual and emotional analogies for that sort of thing: They're the things our brains remember. You'll encounter that sort of thing in a lot of foreign language courses, memorizing alphabets or symbols with mnemonics meant to engage emotional and visual memories around the item as a bootstrap towards remembering what it is.
That said, it is true these whimsical analogies travel poorly, because your cognitive association network will be different than everybody else's. I've got some mnemonics in my language I'm studying around my kid's pet bird and my wife's interactions with her parents; obviously they wouldn't be very meaningful to you if I tried to give them to you to use as your own association. You ought to make them up yourself for maximum effect. But, my main point here is that they aren't intrinsically silly, they are a legitimate way to remember otherwise difficult-to-remember things. After a decade of programming the meaning of curly braces may be obvious, but it isn't at first.
Thanks, I understand the point you're making about childishness not being specific to Diversity and Inclusion initiatives. Two things make me hesitate regarding whether that actually changes my critique:
1. As I say, other people I've spoken to (specifically, some women) share my dismay at the childishness of Diversity and Inclusion initiatives. So that suggests that they also had higher expectations. If you are right, then all of us had poorly calibrated expectations. That starts to seem less plausible; more plausible is that the Diversity and Inclusion sessions were unexpectedly childish even taking into account the background low expectation for any "sessions" / "initiatives".
2. I can think of no reason why Mozilla's documentation for a programming language would share the characteristics of a lame corporate "session" on something non-technical: I think that the people at Mozilla are intelligent and technical-minded, and to some extent work at Mozilla to get away from those depressing and embarrassing aspects of the corporate world. However, it is, as I understand it, an aim of Mozilla to make their technical documentation more approachable to sectors of society that have traditionally been poorly served by the tech community. Therefore one can think of reasons why Mozilla's documentation might share characteristics with the "Diversity and Inclusion movement".
I know I'm sniping at worthy causes, and being slightly insulting about people who have worked hard to document a fantastic programming language, and even I don't think it really comes across pleasantly. The reason I am doing it is because I, along with many others I think, am concerned about the way the political liberal/left (with which I identify) is damaging itself by uncritical adoption of modern dogma of mostly young "progressives"./ And there, in admitting that, I guess I've violated another site guideline.
OK, I'm happy to hear you say that. It's definitely possible that I've made a totally spurious claim of a common cultural thread. I mean that sincerely: I didn't want what I was worrying about to be true and I'll remember that you say Mozilla's not like that. Thanks very much / respect for responding to this anonymous and rather odd/unfounded criticism.
It’s not that Mozilla is or is not like that even; I don’t know why you’re including Mozilla in with Rust. The contents of the Rust book have nothing to do with Mozilla in any way.
Ah, OK. I certainly had that wrong then. I had it in my head that the language was incubated at Mozilla and major efforts like documentation were funded by Mozilla / worked on by Mozilla employees.
Well, this is getting a bit philosophical but seeing as you don't mind discussing!
What you say may be true of Mozilla, but it's not true in general, is it? I mean, suppose two authors work at the same "institution". I think it's bound up in our notion of institution that the observer of this situation might expect, or at least not be surprised if, their creative output is subject to shared influences. So, OK, the theory I was floating was dubious because of its lack of real justification! But I don't think its reliance on a notion of institutional culture (shared influences) was problematic.
I realise for this audience most people wouldn't get much from it, but I find these rules useful for explaining quantum theory without annoying and fluffy analogies to high school students. You can find the rules in my book _Q is for Quantum_ - Part I which covers quantum computing is a free download on the book website (and the rest will be if I ever get around to producing a corrected pdf, bleh, but if you read part I and don't want to pay for the rest let me know and I'll get it to you...)