CAJ | 학술논문

量子纠错码在量子通信和量子计算中起着非常重要的作用,之前的量子纠错码的构造大部分都集中在对称的量子信道,即量子比特翻转的错误概率与量子相位翻转的错误概率相等.该文在非对称量子信道上,即量子比特翻转的错误概率小于量子相位翻转的错误概率,利用经典的平方剩余码和Reed-Muller码构造一批非对称的量子纠错码.同已知的非对称量子纠错码的构造方法相比,该构造方法简单.并且,利用有限域的扩域到其子域的迹映射,构造得到了更多的非对称量子纠错码.
양자규착마재양자통신화양자계산중기착비상중요적작용,지전적양자규착마적구조대부분도집중재대칭적양자신도,즉양자비특번전적착오개솔여양자상위번전적착오개솔상등.해문재비대칭양자신도상,즉양자비특번전적착오개솔소우양자상위번전적착오개솔,이용경전적평방잉여마화Reed-Muller마구조일비비대칭적양자규착마.동이지적비대칭양자규착마적구조방법상비,해구조방법간단.병차,이용유한역적확역도기자역적적영사,구조득도료경다적비대칭양자규착마.
Quantum error-correcting codes play an important role in not only quantum communication but also quantum computation. Previous work in constructing quantum error-correcting codes focuses on code constructions for symmetric quantum channels, i.e., qubit-flip and phase-shift errors have equal probabilities. This paper focuses on the asymmetric quantum channels, i.e., qubit-flip and phase-shift errors have different probabilities Some present families of asymmetric quantum codes are constructed with classical quadratic residue codes and Reed-Muller codes. Compared to previously known methods, the method is simple. Furthermore, using the Trace map, more asymmetric quantum error-correcting codes are obtained.