AI 中文总结
该研究构造了亏格2黎曼曲面上的玻色子量子纠错码，证明亏格>1时稳定子群非可和，与稳定子群为ℤ²的GKP码形成对比，为量子纠错码研究提供了新结果。
AI 中文摘要
我们给出了亏格为2的黎曼曲面上玻色子量子纠错码的代数结构，将码字明确构造为自守形式，并解析生成所有权重下的完整码空间塔。我们证明了一条基础禁则定理：对于亏格大于1的任意情形，稳定子群是非可和的，迫使稳定子哈密顿量存在严格正的谱隙，因此不存在任何可归一化量子态能满足所有稳定子条件。这与标准的Gottesman-Kitaev-Preskill（GKP）码形成鲜明对比，后者的稳定子群ℤ²具有可和性，允许任意精度的近似码字。
英文摘要
We present the algebraic structure of bosonic quantum error-correcting codes on genus-two Riemann surfaces. We explicitly construct the code words as automorphic forms and analytically generate the full tower of code spaces at all weights. We prove a fundamental no-go theorem: for any genus greater than one, the stabilizer group is non-amenable, forcing a strictly positive spectral gap in the stabilizer Hamiltonian. Consequently, no normalizable quantum state can satisfy all stabilizer conditions. This sharply contrasts with standard Gottesman-Kitaev-Preskill (GKP) codes, where the amenability of the stabilizer group $\mathbb{Z}^2$ permits approximate code words with arbitrary precision.
Comments7 pages, 3 figures + Supplemental Material (30 pages, 4 figures). Code, notebooks, and data at https://doi.org/10.5281/zenodo.20585488
