发表机构
Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过杯积规范层丛码，构建了具有恒定编码率和线性距离的非阿贝尔qLDPC码族，并证明其码空间具有长程魔幻性，为超越Pauli稳定子的量子纠错码奠定基础。
AI 中文摘要
非阿贝尔量子码将量子纠错、物质相和计算资源联系起来。在本工作中，我们开发了一个通用框架，通过杯积对层丛码进行规范构造非阿贝尔量子低密度奇偶校验（qLDPC）码，并利用该框架获得具有恒定编码率和线性距离的码族。我们使用显式代表元解决耦合的逻辑约束，以刻画完整的规范码空间。我们基于一般Knill-Laflamme条件对码距进行了基础性处理，并将扩张与清洗相结合，以建立对任意低权重错误的防护。我们进一步构造了一个几乎优良的码族，其整个码空间展现出长程魔幻性。规范与去规范还使得逻辑Clifford测量成为可能，从而制备编码魔幻态。这些结果将优良qLDPC码推广到Pauli稳定子设定之外，并为探索超越几何局域性的非阿贝尔相以及追求无低能平凡魔幻猜想提供了具体基础。
英文摘要
Non-Abelian quantum codes connect quantum error correction, phases of matter, and computational resources. In this work, we develop a general framework for constructing non-Abelian quantum low-density parity-check (qLDPC) codes by gauging sheaf codes via cup products and use it to obtain families with constant encoding rate and linear distance. We resolve the coupled logical constraints using explicit representatives to characterize the full gauged code space. We provide a fundamental treatment of code distance based on the general Knill--Laflamme condition and combine expansion with cleaning to establish protection against arbitrary low-weight errors. We further construct an almost-good family whose entire code space exhibits long-range magic. Gauging and ungauging also enable logical Clifford measurements that prepare encoded magic states. These results extend good qLDPC codes beyond the Pauli stabilizer setting and provide a concrete foundation for exploring non-Abelian phases beyond geometric locality and pursuing the no low-energy trivial magic conjecture.
