Quantum error correction is essential for the development of any scalable quantum computer. In this work we introduce a generalization of a quantum interleaving method for combating clusters of errors in toric quantum error-correcting codes. We present new $n$-dimensional toric quantum codes, where $n\geq 5$, which are featured by lattice codes and apply the proposed quantum interleaving method to such new $n$-dimensional toric quantum codes. Through the application of this method to these novel $n$-dimensional toric quantum codes we derive new $n$-dimensional quantum burst-error-correcting codes. Consequently, $n$-dimensional toric quantum codes and burst-error-correcting quantum codes are provided offering both a good code rate and a significant coding gain when it comes to toric quantum codes. Another important consequence from the presented $n$-dimensional toric quantum codes is that if the Golomb and Welch conjecture in \cite{perfcodes} regarding the Lee sphere in $n$ dimensions for the respective close packings holds true, then it follows that these $n$-dimensional toric quantum codes are the only possible ones to be obtained from lattice codes. Moreover, such a methodology can be applied for burst error correction in cases involving localized errors, quantum data storage and quantum channels with memory.

翻译：量子纠错对于发展任何可扩展的量子计算机都至关重要。本文提出了一种针对环面量子纠错码中错误簇的量子交织方法的推广。我们提出了新的n维环面量子码（n≥5），这些码以格码为特征，并将所提出的量子交织方法应用于此类新的n维环面量子码。通过将该方法应用于这些新型n维环面量子码，我们推导出新的n维量子突发错误校正码。因此，所提供的n维环面量子码与突发错误校正量子码在环面量子码方面同时提供了良好的码率和显著的编码增益。所提出的n维环面量子码带来的另一个重要推论是：若\cite{perfcodes}中关于n维Lee球紧密堆积的Golomb与Welch猜想成立，则这些n维环面量子码将成为从格码中唯一可能获得的构造。此外，该方法可应用于涉及局部化错误的突发纠错、量子数据存储以及具有记忆效应的量子信道等场景。