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Quantum codes are often related to the concepts in homology, such as chain complexes.

Is there an introduction to homology suitable for building a strong understanding of these results?

I am looking for something longer than the background section of QEC papers. A good book. Perhaps a review article or a PhD thesis. Something that includes worked out examples would be excellent.

Video tutorials or online courses are also acceptable as answers to this question.

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Part 3 and 4 of Dan Brown's lecture notes gives an introduction to the basics of homology including worked out examples.

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  • $\begingroup$ Thank you, these are an excellent set of notes. $\endgroup$ Jun 30, 2023 at 16:27
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There is a discussion of these topics in Fujii's book: https://arxiv.org/pdf/1504.01444.pdf, and in this paper of Hector Bombin: https://arxiv.org/pdf/1311.0277.pdf

You might also find interesting things here: https://link.springer.com/book/10.1007/978-3-030-12358-1

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  • $\begingroup$ Fujii's book seems quite useful, as does Bombin's paper. $\endgroup$ Jun 30, 2023 at 16:27
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Here you can find a nice tutorial video by Dan Browne on the concepts of Homology and how we can use them to understand surface codes. And here is the slide deck.

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