We construct a general family of quantum codes that protect against all emission, absorption, dephasing, and raising/lowering errors up to an arbitrary fixed order. Such codes are known in the literature as absorption-emission (AE) codes. We derive simplified error correction conditions for a general AE code and show that any permutation-invariant code that corrects $\le t$ errors can be mapped to an AE code that corrects up to order-$t$ transitions. Carefully tuning the parameters of permutationally invariant codes, we construct several examples of efficient AE codes, hosted in systems with low total angular momentum. Our results also imply that spin codes can be mapped to AE codes, enabling us to characterize logical operators for certain subclasses of such codes.

翻译：我们构建了一类通用的量子码族，能够防护任意固定阶数以下的所有发射、吸收、退相干及能级升降错误。此类码在文献中被称为吸收-发射（AE）码。我们推导了通用AE码的简化纠错条件，并证明任何可纠正$\le t$个错误的置换不变码均可映射为能纠正t阶以下跃迁的AE码。通过精细调节置换不变码的参数，我们构建了多个高效AE码实例，这些码可嵌入总角动量较低的系统。我们的研究结果同时表明自旋码可映射为AE码，这使得我们能够刻画此类码特定子类的逻辑算子。