Journal
JOURNAL OF MATHEMATICAL PHYSICS
Volume 50, Issue 2, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.3081056
Keywords
error correction codes; graph theory; quantum computing; topology
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Funding
- FAPESP [02/07473-7]
- CNPq [306617/2007-2, 140642/2005-6, 155141/2006-6]
- CAPES [0121/01-0]
- Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [02/07473-7] Funding Source: FAPESP
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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 equivalent to 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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