发表机构
Université de Sherbrooke（舍布鲁克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于表示论框架形式化构建多模对称玻色子编码，利用舒尔引理分析纠错性质，并基于SU(2)有限子群构建三种新编码，优化种子态以提升保真度。
AI 中文摘要
玻色子编码为实现硬件高效的容错提供了一种有前景的方法，许多主要示例（如猫码和GKP码）均由潜在对称性组织。我们基于量子纠错的表示论框架，形式化地构建和分析多模对称玻色子编码，重点关注有限群。在此，物理表示、逻辑表示和初始种子态通过协变编码共同定义码字。一个核心观察是，QEC矩阵可以被视为群表示的态射，因此舒尔引理迫使整个不可约表示块消失。我们恢复了几个已知的单模和双模玻色子编码，并基于SU(2)的有限子群构建和分析了三种编码的纠错保护能力。我们分析了逻辑表示可约性的影响，并使用近最优保真度优化种子态。
英文摘要
Bosonic codes offer a promising approach towards hardware-efficient fault tolerance, with many leading examples such as the cat-code and the GKP code organized by an underlying symmetry. We build on a representation-theoretic framework of quantum error correction to formalize the construction and analysis of multimode symmetric bosonic codes, focusing on finite groups. Here, a physical, logical representation and an initial seed state together define the codewords via a covariant encoding. A central observation is that QEC matrices can be viewed as morphisms of group representations, so that Schur's lemma forces entire irreducible representations blocks to vanish. We recover several known single- and two-mode bosonic codes and build and analyze the error protection capabilities of three codes based on finite subgroups of SU(2). We analyze the impact of reducibility of the logical representation and optimize the seed state using the near-optimal fidelity.
Comments19 pages, 6 figures
