标题： 量子纠错码与量子参考系之间的对应关系 显示英文标题

标题： A correspondence between quantum error correcting codes and quantum reference frames

摘要： 在规范理论中，一组运动学自由度被用来冗余地描述更少的规范不变信息。 在量子纠错码（QECC）中，一组构成设备物理层的计算自由度被用来冗余地编码更少的逻辑信息。 我们通过量子参考系（QRFs）来详细阐述这一清晰的类比，QRFs 是在存在对称性的情况下进行量化的一种通用工具包。 结果是在约束系统的情景中，QECC 与 QRF 之间的一个精确字典。 量子纠错中的概念，如错误集合和可纠正性，转化为对规范理论信息结构的新见解。 相反，该字典提供了一种系统的方法来构建基于对称性的 QECC 并表征其纠错特性。 在这项初步工作中，我们仔细研究了保罗稳定子码与其对应的 QRF 设置之间的字典，这些设置具有与稳定子群同构的对称群。 我们证明了最大可纠正错误集合与将系统从框架自由度中分离的张量分解之间存在一一对应关系，相对于这些框架自由度，错误仅破坏冗余的框架数据。 当通过字典传递时，来自代码的标准保罗错误本质上表现为电激发，它们通过庞特里亚金对偶性恰好与与规范固定相关的磁激发相对应。 我们在表面码中全面展示了我们的发现，这些表面码本身明显地将量子纠错与规范系统联系起来。 本文中的探索性研究为量子规范理论的更深层次基础应用以及最终的量子模拟实际应用铺平了道路。 显示英文摘要

摘要： In a gauge theory, a collection of kinematical degrees of freedom is used to redundantly describe a smaller amount of gauge-invariant information. In a quantum error correcting code (QECC), a collection of computational degrees of freedom that make up a device's physical layer is used to redundantly encode a smaller amount of logical information. We elaborate this clear parallel in terms of quantum reference frames (QRFs), which are a universal toolkit for quantization in the presence of symmetries. The result is a precise dictionary between QECCs and QRFs within the perspective-neutral framework for constrained systems. Concepts from quantum error correction like error sets and correctability translate to novel insights into the informational architecture of gauge theories. Conversely, the dictionary provides a systematic procedure for constructing symmetry-based QECCs and characterizing their error correcting properties. In this initial work, we scrutinize the dictionary between Pauli stabilizer codes and their corresponding QRF setups, which possess symmetry groups that are isomorphic to the stabilizer group. We show that there is a one-to-one correspondence between maximal correctable error sets and tensor factorizations splitting system from frame degrees of freedom, relative to which errors corrupt only redundant frame data. When passed through the dictionary, standard Pauli errors from the code essentially behave as electric excitations that are exactly dual, via Pontryagin duality, to magnetic excitations related to gauge-fixing. We comprehensively illustrate our findings in surface codes, which themselves manifestly connect quantum error correction with gauge systems. The exploratory investigations in this article pave the way for deeper foundational applications to quantum gauge theories and for eventual practical applications to quantum simulation.