Error-correcting codes for quantum computing are crucial to address the fundamental problem of communication in the presence of noise and imperfections. Audoux used Khovanov homology to define families of quantum error-correcting codes with desirable properties. We explore Khovanov homology and some of its many extensions, namely reduced, annular, and $\mathfrak{sl}_3$ homology, to generate new families of quantum codes and to establish several properties about codes that arise in this way, such as behavior of distance under Reidemeister moves or connected sums.

翻译：量子计算中的纠错码对于解决噪声和缺陷存在下的通信基本问题至关重要。Audoux利用Khovanov同调定义了一系列具有优良性质的量子纠错码族。我们探究Khovanov同调及其若干重要扩展——约化同调、环形同调和$\mathfrak{sl}_3$同调，以构建新的量子码族，并确立此类编码的若干性质，例如在Reidemeister移动或连通和运算下距离参数的行为规律。