On topological quantum computation by braiding of anyon worldlines:
Gavin K. Brennen, Jiannis K. Pachos, Why should anyone care about computing with anyons?, Proc. R. Soc. A 464 (2008) 1-24 arXiv:0704.2241, doi:10.1098/rspa.2007.0026
Jiannis K. Pachos, Introduction to Topological Quantum Computation, Cambridge University Press (2012) doi:10.1017/CBO9780511792908
Ville Lahtinen, Jiannis K. Pachos, A Short Introduction to Topological Quantum Computation, SciPost Phys. 3 021 (2017) [arXiv:1705.04103, doi:10.21468/SciPostPhys.3.3.021]
and with focus on abelian anyons:
On simulating anyons:
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