New Three and Four-Dimensional Toric and Burst-Error-Correcting Quantum Codes
Abstract
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.
Keywords
Cite
@article{arxiv.2307.06241,
title = {New Three and Four-Dimensional Toric and Burst-Error-Correcting Quantum Codes},
author = {Cibele Cristina Trinca and Reginaldo Palazzo and Ricardo Augusto Watanabe and Clarice Dias de Albuquerque and José Carmelo Interlando and Antônio Aparecido de Andrade},
journal= {arXiv preprint arXiv:2307.06241},
year = {2023}
}
Comments
16 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2205.13582