新的非对称量子纠错码的构造  

New Construction of Asymmetric Quantum Error-correcting Codes

作　　者：钱建发[1] 马文平[1] 

机构地区：[1]西安电子科技大学ISN国家重点实验室西安7100711

出　　处：《电子与信息学报》2009年第12期2922-2925,共4页Journal of Electronics & Information Technology

基　　金：国家自然科学基金(60773002,60672119,60873144);教育部留学回国人员科研启动基金;新世纪优秀人才支持计划;国家863计划项目(2007AA01Z472);ISN国家重点实验室开放基金资助课题

摘　　要：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。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.

关 键 词：量子纠错码 非对称量子纠错码 平方剩余码 REED-MULLER码 自正交码 

分 类 号：TN911.22[电子电信—通信与信息系统]