CSS-$T$ codes over Binary Extension Fields and their Physical Foundations

• URL: http://arxiv.org/abs/2507.17611v1
• Date: Wed, 23 Jul 2025 15:41:47 GMT
• Title: CSS-$T$ codes over Binary Extension Fields and their Physical Foundations
• Authors: Jasper J. Postema, F. Conca, A. Ravagnani,
• Abstract summary: We investigate the class of CSS-$T$ codes, a family of quantum error-correcting codes that allows for a $T$-gate.<n>We extend the definition of a pair of linear codes $(C_2)$, $C_isubseteqmathbbF_qn$, forming a $q$-ary CSS-$$ code over binary extension fields.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the class of CSS-$T$ codes, a family of quantum error-correcting codes that allows for a transversal $T$-gate. We extend the definition of a pair of linear codes $(C_1,C_2)$, $C_i\subseteq\mathbb{F}_q^n$, forming a $q$-ary CSS-$T$ code over binary extension fields, and demonstrate the existence of asymptotically good sequences of LDPC CSS-$T$ codes over any such field.

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