AI 中文总结
本文提出由二维拓扑有序相手征边界实现的近似量子纠错码，其鲁棒性优于降维共形场论码，数值计算验证了幂律标度的理论预测。
AI 中文摘要
拓扑有序相通过量子信息的非局域编码自然实现量子纠错。近年来，共形场论被证实可实现近似量子纠错码，但这类构造通常需要精细调谐至临界态。本文提出一类由二维拓扑有序相的手征边界实现的近似量子纠错码，该编码结合了有能隙拓扑体的鲁棒性与无能隙边界共形场论的灵活性。为表征其鲁棒性，我们研究了局域擦除下的相干信息损失，推导了将相干信息损失与相对熵关联的精确表达式，将可恢复性问题简化为边界理论的普适性质，这使得相干信息损失随擦除区域大小呈幂律标度。我们进一步证明，对于靠近单一边界的几何局域擦除，二维手征边界码的鲁棒性至少与降维后的CFT码相当，且在多个代表性例子中严格更优。对于阿贝尔码子空间，我们还构造了一个由擦除区域支撑的幂律范围恢复映射及一个幂律范围缓冲区，该恢复映射仅依赖于码子空间，与未知编码态无关。我们对紧致自由玻色子和伊辛CFT例子的格点实现进行了数值计算，验证了幂律指数的理论预测。
英文摘要
Topologically ordered phases naturally realize quantum error correction through nonlocal encoding of quantum information. More recently, conformal field theories have been shown to realize approximate quantum error-correcting codes, but such constructions generally require fine tuning to criticality. Here we introduce a family of approximate quantum error-correcting codes realized by the chiral edges of two-dimensional topologically ordered phases. The proposed encoding combines the robustness of a gapped topological bulk with the flexibility of gapless edge conformal field theories. To characterize its robustness, we study coherent-information loss under local erasure. We derive an exact expression relating coherent-information loss to relative entropy, reducing the recoverability problem to universal properties of the edge theory. This leads to power-law scaling of coherent-information loss with the size of the erased region. We further show that, for geometrically local erasures near one edge, the two-dimensional chiral edge code is at least as robust as the dimensionally reduced CFT code, and is strictly more robust in several representative examples. For Abelian code subspaces, we further construct a power-law-range recovery map supported on the erased region together with a power-law-range buffer; this recovery map depends only on the code subspace, not on the unknown encoded state. We provide numerical calculations for lattice realizations of compact free boson and Ising CFT examples that support the theoretical predictions of the power-law exponents.
Comments35 pages, 20 figures, 3 tables
