标题： 关于伊辛任意子的克莱夫德稳定子码的一篇笔记 显示英文标题

标题： A Note on Clifford Stabilizer Codes for Ising Anyons

摘要： 我们提供了一种简化的阐述，说明现有的将Ising任意子（或等价地，马约拉纳）稳定码与某些二进制经典码类联系起来的想法。这种基于马约拉纳的量子码的基础工作可以在早期的研究中找到（包括例如Bravyi（arXiv:1004.3791）和Vijay等人（arXiv:1703.00459）），其中观察到交换的费米子（Clifford）算子族通常可以从弱自对偶或自正交的二进制码系统地提升出来。在这里，我们将这些想法重新表述并统一为一个分类定理，明确展示了$\mathbb{F}_2^{2n}$中的q-余向量空间如何产生与Ising任意子相关的交换Clifford算子，以及这些子空间如何自然对应于$\mathbb{F}_2^{2n+1}$中的删减自正交码。 显示英文摘要

摘要： We provide a streamlined elaboration on existing ideas that link Ising anyon (or equivalently, Majorana) stabilizer codes to certain classes of binary classical codes. The groundwork for such Majorana-based quantum codes can be found in earlier works (including, for example, Bravyi (arXiv:1004.3791) and Vijay et al. (arXiv:1703.00459)), where it was observed that commuting families of fermionic (Clifford) operators can often be systematically lifted from weakly self-dual or self-orthogonal binary codes. Here, we recast and unify these ideas into a classification theorem that explicitly shows how q-isotropic subspaces in $\mathbb{F}_2^{2n}$ yield commuting Clifford operators relevant to Ising anyons, and how these subspaces naturally correspond to punctured self-orthogonal codes in $\mathbb{F}_2^{2n+1}$.