AI 中文总结
该研究证明二维平移不变拓扑CSS码可解耦为环面码和乘积态，给出解耦映射的高效算法及相关边界，解耦无需额外辅助量子比特且适用于有限系统。
AI 中文摘要
已知量子比特上的二维平移不变拓扑CSS码，在粗粒化后局部等价于环面码的堆叠。然而，现有构造通常会破坏比消除任意子置换平移所需更多的平移对称性，从而留下是否存在进一步阻碍的问题。我们证明不存在此类阻碍：在过渡到最大任意子保持超晶格后，每个此类码都可局部幺正解耦为环面码和乘积态。我们进一步提供了一种高效算法，用于显式构造解耦映射，以及所需超胞大小和算子扩散的边界。该解耦在一般情况下不需要额外的辅助量子比特，且可扩展到具有合适边界条件的有限系统。
英文摘要
Two-dimensional translation-invariant topological CSS codes on qubits are known to be locally equivalent, after coarse-graining, to stacks of toric codes. However, existing constructions generally break more translation symmetry than is required to remove anyon-permuting translations, leaving open whether any further obstruction exists. We prove that no such obstruction occurs: after passing to the maximal anyon-preserving superlattice, every such code admits a local unitary decoupling into toric codes and product states. We further provide an efficient algorithm for explicitly constructing the decoupling map, together with bounds on the required supercell size and operator spreading. The decoupling requires no additional ancillas in generic cases and extends to finite systems with suitable boundary conditions.
Comments7+26 pages, 0+8 figures
