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I am reading surface code theory with this paper. The paper is great but there are some parts of the explanations for which I am struggling to understand. In such cases, another source is always nice to have.

I found the lecture videos (here, here and here) associated to the paper which are a good complement.

I am looking for other sources following the same spirit: explaining the surface code to the beginner who has no experience in it. However, I am familiar with the stabilizer formalism so I don't need a source explaining to me the basics of error correction.

Any idea of such papers/video lectures?

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Topological quantum memory by Eric Dennis, Alexei Kitaev, Andrew Landahl and John Preskill is a very nice introduction to the surface code. It develops intuitive description of the code in topological language from the low level combinatorial properties of the lattice focusing on the planar surface code with hole-free encoding.

It is notable for its breadth as it covers code construction and basic properties, statistical-mechanical model, threshold theorem, fault tolerant logical gates, syndrome extraction circuits, hook errors, classical syndrome processing and generalizations to 3D and 4D lattices.

The paper is fairly old and predates many essential developments such as lattice surgery, but it is nonetheless an excellent introduction and assumes no prior knowledge of the surface code.

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    $\begingroup$ Very good reference. It provides definition I haven't found in the other papers I am using. I hope it will solve my misunderstanding from the other post we exchanged on. $\endgroup$ Jan 21 at 15:12
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Surface code ideas make contact with several different areas of physics and coding theory. Toric code introductions from error-correction perspective by J. Haah and condensed-matter perspective by M. Levin and C. Nayak are listed in the EC Zoo entry: https://errorcorrectionzoo.org/c/surface.

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