This article "Correcting coherent errors with surface codes" is talking in the methods section, about simulating topological codes / surface codes, using Majorana equivalent. It is also explained in the supplementary material of the article.
I found out that simulating coherent errors with surface codes with d>10 is almost impossible because of huge run-time. But here, they easily simulate coherent error with d=37, which doesn't make sense to me at all.
My question is - where is the catch? how is it possible to simulate such a big surface code with arbitrary coherent error?
And if so, why this method is not so common? It should change the world of surface codes simulation.
EDIT: also this one is getting very big $d$ with FLO of Majorana
EDIT: This article: "Classical simulation of noninteracting-fermion quantum circuits" (2002) is talking about matrices in size of $O(n*n)$, and I don't understand why those matrices are not exponential in $n$.