Characterization of n-Dimensional Toric and Burst-Error-Correcting Quantum Codes from Lattice Codes

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 ngeq 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.