A free introduction to quantum computing with spaced repetition (2019) | Hacker News Reader

A free introduction to quantum computing with spaced repetition (2019)

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59 pointselamje15 comments

Quantum Computing for the very Curious - https://news.ycombinator.com/item?id=23581810 - June 2020 (8 comments)

A free introduction to quantum computing and quantum mechanics - https://news.ycombinator.com/item?id=23561018 - June 2020 (49 comments)

How Quantum Teleportation Works - https://news.ycombinator.com/item?id=21519134 - Nov 2019 (16 comments)

How the quantum search algorithm works - https://news.ycombinator.com/item?id=19684141 - April 2019 (17 comments)

Quantum Computing for the Curious - https://news.ycombinator.com/item?id=19426573 - March 2019 (24 comments)

This doesn’t provide solutions to the problems and doesn’t show you how to do the mathematical calculations. It assumes you know proof based linear algebra and if you’re a math beginner the level that this is written at will be beyond you.

Instead I recommend http://www.thomaswong.net/introduction-to-classical-and-quan... which doesn’t assume much pre-req knowledge and contains solutions so you can check your work

Who is this for? I never understood the idea of using notecards in subjects that are math heavy. Sure you can memorize some definitions or equations but the second you have to calculate yourself you will be hopelessly lost. I saw this time and time again teaching undergrad Physics. They study the textbook like its a History book, underlining and highlighting things and then can't do a single calculation come exam time. It just doesn't work to study certain subjects this way.

It's like trying to learn how to ride a bike by reading about it.

> I never understood the idea of using notecards in subjects that are math heavy.

I would suggest that people should use notecards for subjects that are math heavy. Even if you don't fully learn by using notecards. Even then.

When you use notecards, and stick to a spaced repeatation algorithm, if nothing else happens, you at least get to familiarise your brain to notations, jargon, graphs, diagrams and so on. This especially helps if you are learning alone. When none of your classmates or colleagues or mentees is learning what you are learning, i.e. you are not in a classroom or training program.

It's a book (well, a digital book), not just a set of flashcards. The SRS parts are to reinforce what's been read and studied from the prior sections.

Ok I read the book "How to ride a bike" and used it's flashcard. I should be able to ride one on the street now right?

Don't know if this true, but George Boole taught himself to swim just by reading a book, i.e. he successfully swam the very first time he got into water.

You can memorize problem solving techniques or approaches and add them to your toolbox of tricks. I used spaced repetition to memorize 100+ difficult leetcode problems and learn math. I've found it consistently will get you between 0.5-1 standard deviation better performance, as measured by comparing myself to the university course websites I'm using to learn. The trick is just to put problems rather than definitions, etc. as the card to be memorized.

Can you give an example? I found only memorizing key ideas is the way to go, as opposed to trying to solve whole problem in your head, which gets tedious

You don't solve the problem in your head, you actually take the time to solve it either on Leetcode or on a piece of paper. I've found that in the long run you don't end up memorizing the problem itself but the technique to solve the problem.

For example, I was learning Manacher's algorithm and I directly put the link to the corresponding Leetcode problem into Anki. Set your minimum interval to 1 day and just follow whatever Anki tells you to study. You don't need many cards to memorize the problem solving techniques, my entire probability deck has under 150 cards and half of that is concepts. It turns out the human brain is pretty good at generalizing from a few problems.

Make sure you don't put every problem you encounter because the review workload will get very heavy very fast if you do that. Only put the challenging ones or the ones you get wrong.

Sure you can memorize some definitions or equations but the second you have to calculate yourself you will be hopelessly lost.

At least two mathematicians used spaced repetition to further understand mathematics and make new insight.

Conceptual understanding is a good memorization techque.

Underlining and highlighting however, are an ineffective method of studying for any subject, even history.

Who are such historic examples?

What would be a better approach to grok quantum computing in your opinion? Asking because genuinely interested in learning more about quantum computing.

That's why I asked who this is for. If you really want to have a good understanding then you need to calculate, a lot. If you just care about concepts then I'm sure this is sufficient.

I recently read this lesson and enjoyed it, but it felt like there was too much emphasis on memorizing, and not enough on actually understanding stuff. In my humble opinion, understanding should always come first.

For example, there is the part that explains that the "ket" vector is the amplitudes arranged vertically, and the "bra" vector is the same amplitudes arranged horizontally, but their imaginary parts have a sign flipped. On one hand, thank you! This is the part that in my previous experience no one ever bothered to explain: everyone either only talks in metaphors with no math, or writes equations that use these symbols without an explanation what they mean. And it's quite simple and it only takes one sentence to explain.

On the other hand, what is the actual meaning of flipping the sign of the imaginary part of the amplitude? Why are we even doing that? Took me a moment, and then I realized: oh, that's just a mathematical trick how to express the (square of) length of a complex number without having to talk about its real and imaginary parts explicitly. Like, if you have a complex number "x = a+bi", you could say that the square of its length is "aa+bb", but you could also say it is "x'x" (where x' = a-bi). And the "<xyz|xyz>" is a sum of them, which is supposed to be normalized to 1.

But this second part was not explained in the lesson. To be fair, the authors said that you were supposed to know the math before reading this. But there is a difference between knowing enough math to understand what it means to flip the sign of the imaginary part of a complex number, and understanding why are you doing that specific operation in this specific context.

Similarly, the reader is told at the beginning that |0> is vector [1 0], and |1> is vector [0 1]. Later at some moment there are also introduced things like |00> and [1 0 0 0], and you are supposed to guess how they map to each other, which is not really difficult, but why not say it explicitly? (It would help to know whether |01> is [0 1 0 0], and |10> is [0 0 1 0] or the other way round.)

The explanation that I would like to hear is something like: If you have N possible classical outcomes, you represent it by a vector with N positions, each position containing the amplitude of one classical outcome. (So you have 2-sized vectors for 1 qubit, 4-sized vectors for 2 qubits, 8-sized vectors for 3 qubits, etc.) The mapping between the classical outcomes and the positions in the vector is completely arbitrary -- by convention we use [1 0] for "the value is 0", and [0 1] for "the value is 1", but it would also work the other way round. With the matrices that represent quantum gateways, the rows and columns need to match the vectors; the columns represent the situation before applying the gate, and the rows represent the situation after applying the gate.

I had to read the lesson carefully three times, until I understood all these details. And I am grateful for that, because with most other lessons merely "reading carefully three times" would not be enough for me to understand. But, ironically, it defeats the meta-lesson about the effectiveness of spaced repetition -- if instead I only read the lesson once and then kept doing the spaced repetition, I would remember the selected key sentences, but I would have no idea about what half of that actually means. I would definitely not be able to actually apply any of the mathematical knowledge in real life; for example, I would remember the 2x2 matrix for Hadamard gate, but I would have no idea how to change it into a 8x8 matrix necessary for "we have three qubits, and the Hadamard gate is applied to the second one".

So my impression is that the parts about quantum physics are awesome, but the parts about spaced repetition are... actually kinda harmful for people who desire to learn.

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