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Ongoing research and experiments have enabled quantum memory to realize thestorage of qubits. On the other hand, interleaving techniques are used to dealwith burst of errors. Effective interleaving techniques for combating burst oferrors by using classical error-correcting codes have been proposed in severalarticles found in the literature, however, to the best of our knowledge, littleis known regarding interleaving techniques for combating clusters of errors intopological quantum error-correcting codes. Motivated by that, in this work, wepresent new three and four-dimensional toric quantum codes which are featuredby lattice codes and apply a quantum interleaving method to such new three andfour-dimensional toric quantum codes. By applying such a method to these newcodes we provide new three and four-dimensional quantum burst-error-correctingcodes. As a consequence, new three and four-dimensional toric andburst-error-correcting quantum codes are obtained which have better informationrates than those three and four-dimensional toric quantum codes from theliterature. In addition to these proposed three and four-dimensional quantumburst-error-correcting codes improve such information rates, they can be usedfor burst-error-correction in errors which are located, quantum data stored andquantum channels with memory.

New Three and Four-Dimensional Toric and Burst-Error-Correcting Quantum Codes