论文标题
链复合物的某些量子产品代码和张量产品的最小距离
Minimal distances for certain quantum product codes and tensor products of chain complexes
论文作者
论文摘要
我们使用映射来量子误差校正代码和一个子空间投影，以获取有限场上两个向量空间链络合物的张量产物中最小同源距离的下限。这种复合物的同源组由Künneth定理描述。当其中一个复合物是两个空间之间的线性图时，我们给出了距离的明确表达式。构造，子系统产品代码及其固定变体中的代码概括了几个已知的量子误差校正代码。
We use a map to quantum error-correcting codes and a subspace projection to get lower bounds for minimal homological distances in a tensor product of two chain complexes of vector spaces over a finite field. Homology groups of such a complex are described by the Künneth theorem. We give an explicit expression for the distances when one of the complexes is a linear map between two spaces. The codes in the construction, subsystem product codes and their gauge-fixed variants, generalize several known families of quantum error-correcting codes.
