Xiang Zou

Quantum error correction (QEC) has many connections with quantum communication and cryptography, which holds significant academic and commercial value. Among the various QEC paradigms, topological quantum error correction (TQEC) stands out with the most experimental successes. In this extended abstract, we build upon existing knowledge of TQEC by developing a generalized theoretical framework for future communication and computation. We provide theoretical frameworks for using 2-manifolds for TQEC purposes. Subsequently, we extend the construction of TQEC codes to higher-dimensional manifolds and present a methodology for their implementation. Finally, we apply these principles to construct TQEC codes on the Klein bottle $K$ and evaluate their efficacy for quantum error correction. This work contributes to the advancement of TQEC by proposing a broader class of codes and demonstrating their theoretical and practical potential, especially for quantum communication purposes.