通过ZX演算重新审视全息码
Holographic codes seen through ZX-calculus
AI总结：
本文通过ZX演算重新审视全息码，研究其稳定子结构和逻辑算子，并提出基于双曲镶嵌的新型码家族，分析其逻辑错误率。
摘要：
我们从ZX演算的角度重新审视五边形全息量子纠错码。通过将底层张量表示为ZX图，我们通过Pauli网络研究该码的稳定子结构。此外，我们通过图示方法理解其逻辑算子、编码等距映射、Rényi熵以及黑洞/虫洞的玩具模型。然后，受五边形全息码的ZX图启发，我们引入了一种由其对偶双曲镶嵌上的ZX图构造的码家族，并利用信念传播解码器研究其逻辑错误率。
英文摘要：
We re-visit the pentagon holographic quantum error correcting code from a ZX-calculus perspective. By expressing the underlying tensors as ZX-diagrams, we study the stabiliser structure of the code via Pauli webs. In addition, we obtain a diagrammatic understanding of its logical operators, encoding isometries, Rényi entropy and toy models of black holes/wormholes. Then, motivated by the pentagon holographic code's ZX-diagram, we introduce a family of codes constructed from ZX-diagrams on its dual hyperbolic tessellations and study their logical error rates using belief propagation decoders. Finally, we show how to construct spacetime ZX-diagrams that realise a fault-tolerant quantum channel in which every internal edge is a protected fault location.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
