Ongoing research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to deal with burst of errors. Effective interleaving techniques for combating burst of errors by using classical error-correcting codes have been proposed in several articles found in the literature, however, to the best of our knowledge, little is known regarding interleaving techniques for combating clusters of errors in topological quantum error-correcting codes. Motivated by that, in this work, we present new three and four-dimensional toric quantum codes which are featured by lattice codes and apply a quantum interleaving method to such new three and four-dimensional toric quantum codes. By applying such a method to these new codes we provide new three and four-dimensional quantum burst-error-correcting codes. As a consequence, new three and four-dimensional toric and burst-error-correcting quantum codes are obtained which have better information rates than those three and four-dimensional toric quantum codes from the literature. In addition to these proposed three and four-dimensional quantum burst-error-correcting codes improve such information rates, they can be used for burst-error-correction in errors which are located, quantum data stored and quantum channels with memory.

翻译：持续的研究与实验使量子存储器能够实现量子比特的存储。另一方面，交织技术被用于处理突发错误。文献中已有若干文章提出了利用经典纠错码应对突发错误的有效交织技术，然而据我们所知，关于在拓扑量子纠错码中应用交织技术以应对簇状错误的研究尚属空白。受此启发，本文提出了以格码为特色的新型三维与四维奇偶校验量子码，并将量子交织方法应用于这些新型三维与四维奇偶校验量子码。通过将该方法应用于此类新码，我们获得了新型三维与四维量子突发错误纠正码。由此得到的新型三维与四维奇偶校验及突发错误纠正量子码，其信息率优于文献中已有的三维与四维奇偶校验量子码。此外，这些新型三维与四维量子突发错误纠正码不仅改善了信息率，还可用于纠正位置相关的错误、存储的量子数据以及带记忆量子信道中的突发错误。