>While we will take a brief glance at topology here, I am planning to write a separate blog post fully dedicated to the maths behind topological quantum error-correction. The goal of this post is to gain a first intuitive understanding of the surface code.

All the brief mentions of homotopy and homology (the actual topology at play) are relegated to footnotes.

I taught myself most of this last year (actually including one of this guy's other posts) so that I could then teach it to a high schooler. My background was a degree in physics+math ~10 years ago and then more recently a really lame grad class in QC (that only covered up to repetition codes). I am a PhD student but not in QC.

So how many people are like me? Probably a 200-400 minted each year just in the US - how many undergrad QC classes are there taught each year? 20-40 of 10-20 students?

The real difficulty with this stuff is not the math but all the "awe gee wow" treatment people give it so that every paragraph seems like it's dripping in profundity; junk like this

> surface code is also one of the most beautiful ideas of quantum computing, and if you ask me, of all physics.

> ...

> And indeed, the surface code has deep connections to many areas of maths and physics.

You ever wonder to yourself how it's possible that so many things are "the most beautiful idea" and have "deep connections"? In reality it's really just a bunch of cute tricks and convenient definitions that make the proofs work out (basically like all of pure math).

I think I’m actually the target audience. I come from a physics academic background - with a focus on quantum computing on the physics side - and what I’ve seen so far (I’m about a third the way through) feels like it’s pitched at my level.

Because the word topology gets thrown around a lot in topological quantum computation (funny, that…), that gives a lot of authors the impression that they can start using terminology that mathematicians understand, but is fairly inaccessible to physicists. From what I’ve seen so far, this article is the first one I’ve seen that I think I might stand a chance at learning something from without consulting a mathematics glossary.

I would estimate there are about a couple of thousand people at most who can, without any other resources, make an accurate technical summary of the essential concepts in this post.

I think if people understand quantum computing a little bit, then his earlier posts are much better

https://arthurpesah.me/blog/2022-01-25-intro-qec-1/

https://arthurpesah.me/blog/2023-01-31-stabilizer-formalism-...

In all sincerity, I did not guess it.