Topological quantum codes on compact surfaces with genus g≥2

被引：25

作者：

Albuquerque, C. D. ^{[1
]}

Palazzo, R., Jr. ^{[1
]}

Silva, E. B. ^{[2
]}

机构：

[1] Univ Estadual Campinas, Fac Engn Eletr & Comp, Dept Telemat, BR-13083970 Campinas, SP, Brazil

[2] Univ Estadual Maringa, Dept Matemat, BR-87020900 Maringa, Parana, Brazil

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2009年 / 50卷 / 02期

基金：

巴西圣保罗研究基金会;

关键词：

error correction codes; graph theory; quantum computing; topology; ERROR-CORRECTING CODES; MEMORY;

D O I：

10.1063/1.3081056

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

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