Characterization of $n$-Dimensional Toric and Burst-Error-Correcting Quantum Codes from Lattice Codes
- URL: http://arxiv.org/abs/2410.20233v1
- Date: Sat, 26 Oct 2024 17:29:20 GMT
- Title: Characterization of $n$-Dimensional Toric and Burst-Error-Correcting Quantum Codes from Lattice Codes
- Authors: Cibele Cristina Trinca, Reginaldo Palazzo Jr., J. Carmelo Interlando, Ricardo Augusto Watanabe, Clarice Dias de Albuquerque, Edson Donizete de Carvalho, Antonio Aparecido de Andrade,
- Abstract summary: 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 $ngeq 5$ are featured by lattice codes.
We derive new $n$-dimensional quantum burst-error-correcting codes.
- Score: 2.2657086779504017
- License:
- Abstract: 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 $n\geq 5$, 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.
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