标题： 量子位稳定子码、共形场理论和拓扑表面 显示英文标题

标题： Qudit Stabilizer Codes, CFTs, and Topological Surfaces

摘要： 我们研究从具有固定chiral代数和相关Chern-Simons (CS)理论的有理CFT空间到具有固定广义Pauli群的qudit稳定化码空间的一般映射。 我们考虑这种映射上的某些自然约束，并表明该映射可以描述为从一个轨道图到一个码图的图同态，其中轨道图捕捉了CFT的轨道结构，而码图捕捉了自对偶稳定化码的结构。 通过研究显式示例，我们表明这种图同态并不总是图嵌入。 然而，我们构建了一个物理上有动机的映射，从CFT的通用轨道子图到广义Pauli群中的算子。 我们表明，当与这些CFT对应的体表面算子在CS理论中是自对偶时，该映射才会产生一个自对偶稳定化码。 对于可以描述为稳定化码的CFT，我们表明完整的阿贝尔化广义Pauli群可以从CFT的某些0形式对称性的扭扇区获得。 最后，我们将我们的构造与SymTFTs联系起来，并认为我们在设置中出现的许多码等价性对应于在与可逆表面融合下体拓扑表面的等价类。 显示英文摘要

摘要： We study general maps from the space of rational CFTs with a fixed chiral algebra and associated Chern-Simons (CS) theories to the space of qudit stabilizer codes with a fixed generalized Pauli group. We consider certain natural constraints on such a map and show that the map can be described as a graph homomorphism from an orbifold graph, which captures the orbifold structure of CFTs, to a code graph, which captures the structure of self-dual stabilizer codes. By studying explicit examples, we show that this graph homomorphism cannot always be a graph embedding. However, we construct a physically motivated map from universal orbifold subgraphs of CFTs to operators in a generalized Pauli group. We show that this map results in a self-dual stabilizer code if and only if the surface operators in the bulk CS theories corresponding to the CFTs in question are self-dual. For CFTs admitting a stabilizer code description, we show that the full abelianized generalized Pauli group can be obtained from twisted sectors of certain 0-form symmetries of the CFT. Finally, we connect our construction with SymTFTs, and we argue that many equivalences between codes that arise in our setup correspond to equivalence classes of bulk topological surfaces under fusion with invertible surfaces.