发表机构
Yale University; Yale Quantum Institute, Yale University（耶鲁大学; 耶鲁量子研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于容错信息传输的混合态量子相分类，证明恢复阈值是相的性质，并展示二维与三维色码的相位等价性，同时揭示综合征结构对容错性的影响。
AI 中文摘要
我们基于保持和容错传输信息的能力，引入了一类混合态量子相的分类。我们制定了编码逻辑量子信息的状态集合之间的相位等价性，这些状态集合通过浅层局域信道电路连接，并辅以局域测量和测量结果的全局经典通信，其中所有量子操作（包括测量）都必须对噪声具有鲁棒性。我们证明了局域噪声的恢复阈值的存在是整个相的一个性质。我们证明了任何两个具有非零阈值且通过有限深度局域信道电路相关联的状态集合都属于同一容错相。我们的方法导致了对子系统码的分类，而不偏向规范子系统的任何状态，并且我们通过三维规范色码内的维度跳跃展示了二维和三维色码之间的相位等价性。最后，我们研究了综合征结构如何影响带测量的电路中的容错性。我们证明了具有扩展综合征的量子位稳定器码允许单发态制备，而测量点状综合征的广泛浅层电路类别（包括二维拓扑码和非阿贝尔拓扑序（具有可解任意子理论）的态制备）不是容错的。
英文摘要
We introduce a classification of quantum phases of mixed states based on the ability to preserve and fault tolerantly transfer information. We formulate phase equivalence between sets of states that encode logical quantum information and are connected by shallow local channel circuits assisted by local measurements and global classical communication of measurement outcomes, where all quantum operations, including measurements, must be robust to noise. We show that the existence of a recovery threshold for local noise is a property of an entire phase. We prove that any two sets of states with nonzero thresholds that are related by finite-depth local channel circuits belong to the same fault tolerant phase. Our approach leads to a classification of subsystem codes without favoring any state of the gauge subsystem, and we demonstrate phase equivalence between 2D and 3D color codes using dimensional jumps within the 3D gauge color code. Lastly, we study how syndrome structure affects fault tolerance in circuits with measurements. We show that qudit stabilizer codes with extended syndromes permit single-shot state preparation, whereas a broad class of shallow circuits measuring point-like syndromes, including state preparation for 2D topological codes and non-Abelian topological orders with solvable anyon theories, is not fault tolerant.
Comments24 + 24 pages, 8 figures
