We present a fault-tolerant [[8, 1, 3]] non-CSS quantum error correcting code and study its logical error rates. We choose the unitary encoding procedure for stabilizer codes given by Gottesman and modify it to suit the setting of a class of non- CSS codes. Considering two types of noise models for this study, namely the depolarising noise and anisotropic noise, to depict the logical error rates obtained in decoding, we adopt the procedure of the bare ancilla method presented by Brown et al. to reorder the measurement sequence in the syndrome extraction step and upgrade it to obtain higher pseudo-thresholds and lower leading order terms of logical error rates.

翻译：我们提出了一种容错的[[8,1,3]]非CSS量子纠错码，并研究了其逻辑错误率。我们采用了Gottesman给出的稳定子码酉编码过程，并对其进行了修改，以适应一类非CSS码的设置。本研究考虑两种类型的噪声模型，即去极化噪声和各向异性噪声，以描述解码中获得的逻辑错误率。我们采用Brown等人提出的裸辅助比特方法中的流程，对症状提取步骤中的测量序列进行重新排序，并对其进行升级，以获得更高的伪阈值和更低的逻辑错误率主导项。