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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.