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## "Kitaev's quantum double model as an error correcting code", Shawn Cui, Stanford physics people, 2020

*Reviewed October 1, 2023*

*Citation:* Cui, Shawn X., et al. "Kitaev's quantum double model as an error correcting code." Quantum 4 (2020): 331.

*Web:* https://arxiv.org/abs/1908.02829

*Tags:* Kitaev-quantum-double, Error-correcting-codes, Pedagogical

This is a fantastic, pedagogical, folklore-busting paper. This paper
shows that the quantum double model gives an error correcting code for
non-abelian anyons, it shows that the quantum double
satisfies rigorous axioms of topological order, it shows that
the topological entropy of the quantum double model has the
expected value, it makes explicit the non-abelian group Fourier transform, and
it gives nice introductions to all of these subjects.

This is a must-read article for anybody getting deep into the theory of
non-abelian quantum double models. A good companion article is

> Bachmann, Sven. "Local disorder, topological ground state degeneracy and entanglement entropy, and discrete anyons." Reviews in Mathematical Physics 29.06 (2017): 1750018.

which does lots of the same stuff, but only for abelian anyons. Bachman's article
does have a more explicit nature (as afforded by its simpler context),
and gives nice philosophical connections between the different types
notions of topological order, in this context. This is a good reference for
the fact that there is no one accepted definition of topological order.
Additionally, Bachman's paper puts homology/cohomology front and center.