Binary Triorthogonal and CSS-T Codes for Quantum Error Correction
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909280497565696 |
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| author | Camps-Moreno, Eduardo López, Hiram H. Matthews, Gretchen L. Ruano, Diego San-José, Rodrigo Soprunov, Ivan |
| author_facet | Camps-Moreno, Eduardo López, Hiram H. Matthews, Gretchen L. Ruano, Diego San-José, Rodrigo Soprunov, Ivan |
| contents | In this paper, we study binary triorthogonal codes and their relation to CSS-T quantum codes. We characterize the binary triorthogonal codes that are minimal or maximal with respect to the CSS-T poset, and we also study how to derive new triorthogonal matrices from existing ones. Given a binary triorthogonal matrix, we characterize which of its equivalent matrices are also triorthogonal. As a consequence, we show that a binary triorthogonal matrix uniquely determines the parameters of the corresponding triorthogonal quantum code, meaning that any other equivalent matrix that is also triorthogonal gives rise to a triorthogonal quantum code with the same parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02916 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Binary Triorthogonal and CSS-T Codes for Quantum Error Correction Camps-Moreno, Eduardo López, Hiram H. Matthews, Gretchen L. Ruano, Diego San-José, Rodrigo Soprunov, Ivan Information Theory In this paper, we study binary triorthogonal codes and their relation to CSS-T quantum codes. We characterize the binary triorthogonal codes that are minimal or maximal with respect to the CSS-T poset, and we also study how to derive new triorthogonal matrices from existing ones. Given a binary triorthogonal matrix, we characterize which of its equivalent matrices are also triorthogonal. As a consequence, we show that a binary triorthogonal matrix uniquely determines the parameters of the corresponding triorthogonal quantum code, meaning that any other equivalent matrix that is also triorthogonal gives rise to a triorthogonal quantum code with the same parameters. |
| title | Binary Triorthogonal and CSS-T Codes for Quantum Error Correction |
| topic | Information Theory |
| url | https://arxiv.org/abs/2408.02916 |