AI 中文总结
本文推广统一框架以适配非CSS量子稳定子码，解决了CSS码之外逻辑测量、量子重量约化等领域的问题，使qLDPC手术等构造可推广至非CSS码。
AI 中文摘要
我们将[Phys. Rev. A 113, 022438 (2026)]中的统一框架进行推广，以适配任意稳定子码（为强调而称为非CSS码）。该推广在逻辑测量、量子重量约化和欧几里得嵌入等领域有直接应用。例如，目前基于（高度为1的）锥的CSS（纯X、Z型）逻辑测量已被充分理解，而非CSS（如Y型）逻辑测量则是临时的（如依赖局域Clifford变换）；类似地，量子重量约化和最优欧几里得嵌入仅存在于CSS输入码中。在此，我们表明我们的推广框架解决了这一问题，因此许多构造（包括qLDPC手术、Layer Codes和量子重量约化）可相对直接地推广到非CSS码。为清晰起见，我们对上述例子进行了详细推导。
英文摘要
We generalize the unified framework in [Phys. Rev. A 113, 022438 (2026)] to accommodate arbitrary stabilizer codes (referred as non-CSS for emphasis). The generalization has immediate consequences in areas including logical measurement, quantum weight reduction and Euclidean embedding. For example, currently CSS (pure $X,Z$-type) logical measurements are well-understood based on the (height-1) cone, while non-CSS (e.g., $Y$-type) logical measurements are ad hoc (e.g., rely on local Clifford transform). Similarly, quantum weight reduction and optimal Euclidean embeddings only exist for CSS input codes. Here, we show that our generalized framework addresses this issue, and thus many constructions, including qLDPC surgery, Layer Codes and quantum weight reduction generalize to non-CSS codes in a relatively straightforward fashion. The previously mentioned examples are derived in detail for clarity.
