标题： 彭罗斯镶嵌是一种量子纠错码 显示英文标题

标题： The Penrose Tiling is a Quantum Error-Correcting Code

摘要： 彭罗斯镶嵌（PT）是一种本质上非周期性的平面镶嵌方式，具有许多显著的性质。 量子纠错码（QECC）是一种巧妙的方式，通过使用复杂类型的冗余来保护量子信息免受噪声影响。 尽管PT和QECC看起来似乎完全不相关，但在本文中我们指出，PT会产生（或者在某种意义上来说，就是）一种显著的新类型的QECC。 在这个码中，量子信息通过量子几何进行编码，任何有限区域内的局部错误或丢失，无论多大，都可以被诊断和纠正。 我们还构建了这种码的变体（基于阿曼-比恩克和斐波那契镶嵌），它们可以在有限的空间环面上存在，在离散自旋系统中，或者在任意数量的空间维度中。 我们讨论了与量子计算、凝聚态物理和量子引力的联系。 显示英文摘要

摘要： The Penrose tiling (PT) is an intrinsically non-periodic way of tiling the plane, with many remarkable properties. A quantum error-correcting code (QECC) is a clever way of protecting quantum information from noise, by encoding the information with a sophisticated type of redundancy. Although PTs and QECCs might seem completely unrelated, in this paper we point out that PTs give rise to (or, in a sense, are) a remarkable new type of QECC. In this code, quantum information is encoded through quantum geometry, and any local errors or erasures in any finite region, no matter how large, may be diagnosed and corrected. We also construct variants of this code (based on the Ammann-Beenker and Fibonacci tilings) that can live on finite spatial tori, in discrete spin systems, or in an arbitrary number of spatial dimensions. We discuss connections to quantum computing, condensed matter physics, and quantum gravity.