Asymptotically good CSS codes that realize the logical transversal Clifford group fault-tolerantly

• URL: http://arxiv.org/abs/2601.08568v1
• Date: Tue, 13 Jan 2026 13:52:03 GMT
• Title: Asymptotically good CSS codes that realize the logical transversal Clifford group fault-tolerantly
• Authors: K. Sai Mineesh Reddy, Navin Kashyap,
• Abstract summary: This paper introduces a framework for constructing Calderbank-Shor-Steane (CSS) codes that support fault-tolerant logical $Z$-rotations.
• Score: 6.416957991576607
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper introduces a framework for constructing Calderbank-Shor-Steane (CSS) codes that support fault-tolerant logical transversal $Z$-rotations. Using this framework, we obtain asymptotically good CSS codes that fault-tolerantly realize the logical transversal Clifford group. Furthermore, investigating CSS-T codes, we: (a) demonstrate asymptotically good CSS-T codes wherein the transversal $T$ realizes the logical transversal $S^{\dagger}$; (b) show that the condition $C_2 \ast C_1 \subseteq C_1^{\perp}$ is necessary but not sufficient for CSS-T codes; and (c) revise the characterizations of CSS-T codes wherein the transversal $T$ implements the logical identity and the logical transversal $T$, respectively.

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