In many quantum channels, dephasing errors occur more frequently than the amplitude errors - a phenomenon that has been exploited for performance gains and other benefits through asymmetric quantum codes (AQCs). In this paper, we present a new construction of AQCs by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs) which have the following three advantages. First, only the outer codes in AQCTPCs need to satisfy the orthogonal constraint in quantum codes, and any classical linear code can be used for the inner, which makes AQCTPCs very easy to construct. Second, most AQCTPCs are highly degenerate, which means they can correct many more errors than their classical TPC counterparts. Consequently, we construct several families of AQCs with better parameters than known results in the literature. Especially, we derive a first family of binary AQCs with the Z-distance larger than half the block length. Third, AQCTPCs can be efficiently decoded although they
翻译:在许多量子信道中,偏差发生频率比振幅误差更频繁,这个现象通过不对称量子代码(AQCs)被用于提高性能并获得其他好处。在本文中,我们展示了一个新的AQC结构,将传统混合代码(CCs)与配方产品代码(TPCs)相结合,称为不对称量子聚合和配方产品代码(AQCTPCs),这些代码具有以下三个优点。首先,只有AQCTPCs的外码需要满足量子代码的正方形限制,而任何古典线性代码都可以用于内部,这使得AQCTs非常容易构建。第二,大多数AQCTPCs都非常堕落,这意味着它们能够纠正比传统TPCs(TPCs)相近许多错误。因此,我们构建了若干AQCs家族,其参数比文献中已知的结果要好得多。特别是,我们从Z-距离大于半块长的二进式AQCs的第一个家族。第三,AQCTPCs可以有效解算,尽管它们可以有效解码。