Asymptotically good CSS-T codes and a new construction of triorthogonal codes
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913902547173376 |
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| author | Berardini, Elena Dastbasteh, Reza Martinez, Josu Etxezarreta Jain, Shreyas Larrarte, Olatz Sanz |
| author_facet | Berardini, Elena Dastbasteh, Reza Martinez, Josu Etxezarreta Jain, Shreyas Larrarte, Olatz Sanz |
| contents | We propose a new systematic construction of CSS-T codes from any given CSS code using a map $ϕ$. When $ϕ$ is the identity map $I$, we retrieve the construction of [1] and use it to prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature, and of asymptotically good quantum LDPC CSS-T codes. We analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from this construction ($ϕ= I$), concluding that they always result in the logical identity. An immediate application of these codes in dealing with coherent noise is discussed. We then develop a new doubling transformation for obtaining triorthogonal codes, which generalizes the doubling construction presented in [2]. Our approach permits using self-orthogonal codes, instead of only doubly-even codes, as building blocks for triorthogonal codes. This broadens the range of codes available for magic state distillation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotically good CSS-T codes and a new construction of triorthogonal codes Berardini, Elena Dastbasteh, Reza Martinez, Josu Etxezarreta Jain, Shreyas Larrarte, Olatz Sanz Quantum Physics Information Theory We propose a new systematic construction of CSS-T codes from any given CSS code using a map $ϕ$. When $ϕ$ is the identity map $I$, we retrieve the construction of [1] and use it to prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature, and of asymptotically good quantum LDPC CSS-T codes. We analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from this construction ($ϕ= I$), concluding that they always result in the logical identity. An immediate application of these codes in dealing with coherent noise is discussed. We then develop a new doubling transformation for obtaining triorthogonal codes, which generalizes the doubling construction presented in [2]. Our approach permits using self-orthogonal codes, instead of only doubly-even codes, as building blocks for triorthogonal codes. This broadens the range of codes available for magic state distillation. |
| title | Asymptotically good CSS-T codes and a new construction of triorthogonal codes |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2412.08586 |