Composite-Dimensional Topological Codes with Boundaries and Defects

Mohamad Mousa et al. · 2025 · arXiv

| 编号 QE094 | 主题 拓扑码 | 链接 arXiv:2508.19245 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

We introduce new algorithms and provide example constructions of stabilizer models for the gapped boundaries, domain walls, and $0D$ defects of Abelian composite-dimensional twisted quantum doubles. Using the physically intuitive concept of condensation, our algorithm explicitly describes how to construct the boundary and domain-wall stabilizers starting from the bulk model. This extends the utility of Pauli stabilizer models in describing non-translationally invariant topological orders with gapped boundaries. To highlight this utility, we provide a series of examples, including a new family of quantum error-correcting codes where the double of ${\mathbb{Z}}_4$ is coupled to instances of the double semion (DS) phase. We discuss the codes’ utility in the burgeoning area of quantum error correction with an emphasis on the interplay between deconfined anyons, logical operators, error rates, and decoding. We also augment our construction, built using algorithmic tools to describe the properties of explicit stabilizer layouts at the microscopic lattice-level, with dimensional counting arguments and macroscopic-level constructions building on pants decompositions. The latter outlines how

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