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"Fast decoders for qudit topological codes", Hussain Anwar, Benjamin Brown, Earl Campbell, Dan Browne, 2014

Reviewed August 17, 2023

Citation: Anwar, Hussain, et al. "Fast decoders for qudit topological codes." New Journal of Physics 16.6 (2014): 063038.

Web: https://iopscience.iop.org/article/10.1088/1367-2630/16/6/063038

Tags: Abelian-anyons, Computer-scientific, Toric-code

This paper gives an algorithm for "decoding" the qudit topological code. That is, it gives an algorithm for determining the most likely error to have occurred from a given syndrome in Zd topological order.

This isn't particularly useful for the abstract theory of topological quantum computing, but it does demonstrate some sort of maturity in the field of surface codes on larger abelian groups. If these were objects nobody cared about, we wouldn't write decoding algorithms for them.

This work was extended the next year with the following follow-up work:

> Watson, Fern HE, Hussain Anwar, and Dan E. Browne. "Fast fault-tolerant decoder for qubit and qudit surface codes." Physical Review A 92.3 (2015): 032309.