Topological quantum codes on compact surfaces with genus g≥ 2
CD Albuquerque, R Palazzo, EB Silva - Journal of mathematical …, 2009 - pubs.aip.org
In this paper we propose a construction procedure of a class of topological quantum error-
correcting codes on surfaces with genus g≥ 2. This generalizes the toric codes
construction. We also tabulate all possible surface codes with genus 2–5. In particular, this
construction reproduces the class of codes obtained when considering the embedding of
complete graphs K s, for s≡ 1 mod 4, on surfaces with appropriate genus. We also show
a table comparing the rate of different codes when fixing the distance to 3–5.
correcting codes on surfaces with genus g≥ 2. This generalizes the toric codes
construction. We also tabulate all possible surface codes with genus 2–5. In particular, this
construction reproduces the class of codes obtained when considering the embedding of
complete graphs K s, for s≡ 1 mod 4, on surfaces with appropriate genus. We also show
a table comparing the rate of different codes when fixing the distance to 3–5.
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