论文标题
与表面图关联的新类量子代码
New Classes of Quantum Codes Associated with Surface Maps
论文作者
论文摘要
如果{face types} {at}的循环序列相同，则映射被认为是半等级地图。特别是，如果面部相同的类型，则半等级图是等效的。同源量子代码代表拓扑量子代码的子类。在本文中，我们介绍{13}新类量子代码。这些代码与以下内容相关联：（i）类型$ [k^k] $，（ii）在双曲线上的epivelar映射以及覆盖地图的覆盖，以及（iii）半等级地图，以及\ echar {-1}的表面上的半等级地图，以及{-1}的表面。 （i）中与地图相关的代码类的编码速率是如此，以至于$ \ frac {k} {n} \ rightarrow 1 $ as $ n \ rightarrow \ infty $ as of rightArrow \ infty $，对于其余的代码类，编码率为$ \ frac {k} {n} {n} {n} {n} { $。
If the cyclic sequences of {face types} {at} all vertices in a map are the same, then the map is said to be a semi-equivelar map. In particular, a semi-equivelar map is equivelar if the faces are the same type. Homological quantum codes represent a subclass of topological quantum codes. In this article, we introduce {thirteen} new classes of quantum codes. These codes are associated with the following: (i) equivelar maps of type $ [k^k]$, (ii) equivelar maps on the double torus along with the covering of the maps, and (iii) semi-equivelar maps on the surface of \Echar{-1}, along with {their} covering maps. The encoding rate of the class of codes associated with the maps in (i) is such that $ \frac{k}{n}\rightarrow 1 $ as $ n\rightarrow\infty $, and for the remaining classes of codes, the encoding rate is $ \frac{k}{n}\rightarrow α$ as $ n\rightarrow \infty $ with $ α< 1 $.
