发表机构
Harvard University（哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究与连续对称性兼容的量子纠错问题，构建\(SU(d)\)协变近似码，证明其在特定擦除情况下的纯化距离缩放，构建单量子比特擦除解码器，用作编码模拟动力学构建块，提供非阿贝尔协变码及稳健模拟量子模拟框架。
AI 中文摘要
与连续对称性兼容的量子纠错是量子信息中的一个基本问题，也是实现稳健模拟量子模拟的一条可能途径。由于Eastin-Knill定理禁止具有连续横向对称性的精确码，我们构建了明确的\(SU(d)\)协变近似码，利用置换对称性将逻辑信息均匀分布在所有物理子系统上。对于已知位置的单、二、三量子比特擦除，我们证明了最坏情况下纯化距离缩放为\(\Theta(1/N)\)，与近似Eastin-Knill下界匹配到常数，并将约化态分析扩展到一般标记局部噪声。对于单量子比特擦除，我们从Petz恢复映射构建了一个明确的近似最优解码器。然后我们将这些码用作编码模拟动力学的构建块。对称保持哈密顿量生成可横向实现的块结构动力学李代数，而受控对称破缺项用作通用动力学的非横向资源。这些结果提供了明确的非阿贝尔协变码和稳健模拟量子模拟的框架。
英文摘要
Quantum error correction compatible with continuous symmetries is a fundamental problem in quantum information and a possible route to robust analog quantum simulation. Because the Eastin-Knill theorem forbids exact codes with continuous transversal symmetries, we construct explicit $SU(d)$-covariant approximate codes that exploit permutation symmetry to spread logical information uniformly across all physical subsystems. For one-, two-, and three-qudit erasures at known locations, we prove worst-case purified-distance scaling $O(1/N)$, which matches known approximate Eastin-Knill lower bounds up to constants, and we extend the reduced-state analysis to general flagged local noise. Exact permutation symmetry of this kind is available only up to three erased sites; for an arbitrary fixed number $k$ of erased sites, we instead show that Haar-random and efficiently sampled encodings achieve worst-case distance $O(\sqrt{k}/N)$ with probability exponentially close to one. For single-qudit erasure, we construct an explicit near-optimal decoder from the Petz recovery map. We then use these codes as building blocks for encoded analog dynamics. Symmetry-preserving Hamiltonians generate block-structured dynamical Lie algebras implementable transversally, while controlled symmetry-breaking terms serve as non-transversal resources for universal dynamics. These results provide explicit non-Abelian covariant codes and a framework for robust analog quantum simulation.
Commentsv2: added a full analysis of k-qudit erasure noise, showing that Haar-random and efficiently sampled encodings achieve worst-case purified distance O(sqrt(k)/N) with probability exponentially close to one; minor errors corrected and presentation improved. 96 pages, 3 figures
