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

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 bursts 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 characterized by lattice codes and apply a quantum interleaving method to such new three- and four-dimensional toric quantum codes. By applying such an interleaving 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 higher code rate and coding gain 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 the code rate and coding gain, they can be used for burst error correction in errors which are located, quantum data stored and quantum channels with memory.