Hyperbolic quantum color codes

Eduardo Brandani da Silva; Waldir Silva Soares Jr

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arXiv · 1804.06382

Hyperbolic quantum color codes

Eduardo Brandani da Silva·Waldir Silva Soares Jr

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Abstract

Current work presents a new approach to quantum color codes on compact surfaces with genus $g \geq 2$ using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before. We also present a family of codes with minimum distance $d=4$ and the encoding rate asymptotically going to 1 while $n \rightarrow \infty$.

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Eduardo Brandani da Silva, Waldir Silva Soares Jr. 2018-04-17. Hyperbolic quantum color codes. https://arxiv.org/abs/1804.06382

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