2014
DOI: 10.26421/qic14.15-16-8
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Families of codes of topological quantum codes from tessellations tessellations {4i+2,2i+1}, {4i,4i}, {8i-4,4} and ${12i-6,3}

Abstract: In this paper we present some classes of topological quantum codes on surfaces with genus $g \geq 2$ derived from hyperbolic tessellations with a specific property. We find classes of codes with distance $d = 3$ and encoding rates asymptotically going to 1, $\frac{1}{2}$ and $\frac{1}{3}$, depending on the considered tessellation. Furthermore, these codes are associated with embedding of complete bipartite graphs. We also analyze the parameters of these codes, mainly its distance, in addition to show a class o… Show more

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Cited by 6 publications
(10 citation statements)
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“…There are many works related to the control of quantum computing errors, in addition to those already mentioned above. General studies and surveys on the subject [20,21,22,23,24,25,26,27], about the quantum computation threshold theorem [28,29,30,31], quantum error correction codes [32,33,34,35], concatenated quantum error correction codes [36,37] and articles related to topological quantum codes [38,39]. Lately, quantum computing error control has focused on both coherent errors [40,41] and cross-talk errors [42,43].…”
Section: Introductionmentioning
confidence: 99%
“…There are many works related to the control of quantum computing errors, in addition to those already mentioned above. General studies and surveys on the subject [20,21,22,23,24,25,26,27], about the quantum computation threshold theorem [28,29,30,31], quantum error correction codes [32,33,34,35], concatenated quantum error correction codes [36,37] and articles related to topological quantum codes [38,39]. Lately, quantum computing error control has focused on both coherent errors [40,41] and cross-talk errors [42,43].…”
Section: Introductionmentioning
confidence: 99%
“…In [3], families of topological quantum codes derived from the {4i + 2, 2i + 1}, {8i − 4, 4} and {12i − 6, 3} tessellations, where i is an integer i ≥ 2, were analyzed; the encoding rates go asymptotically to 1, 1/2 and 1/3, respectively. These families of topological quantum codes can be viewed as families of ATQCs by considering the distances d x and d z individually, instead of considering the minimum of them.…”
Section: Families Of Hyperbolic Atqcsmentioning
confidence: 99%
“…Much other research stems from the initial proposal of topological quantum codes, such as the generalization to qudits, the search for calculating thresholds for various error models, decoding algorithms, and even another proposed construction of topological codes important enough, the color codes, [5,2,3,10,7].…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…[30] [31], quantum error correction codes [32] [33] [34] [35], concatenated quantum error correction codes [36] [37] and articles related to topological quantum codes [38] [39]. Lately, quantum computing error control has focused on both coherent errors [40] [41] and cross-talk errors [42] [43].…”
Section: Introductionmentioning
confidence: 99%