Good quantum codes with addressable and parallelizable non-Clifford gates

• URL: http://arxiv.org/abs/2510.19809v1
• Date: Wed, 22 Oct 2025 17:47:03 GMT
• Title: Good quantum codes with addressable and parallelizable non-Clifford gates
• Authors: Virgile Guemard,
• Abstract summary: We revisit a family of good quantum error-correcting codes presented in He $textitet al.$ (2025)<n>We show that various sets of addressable and non-Clifford multi-control-$Z$ gates can be performed in parallel.
• Score: 5.076419064097734
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We revisit a family of good quantum error-correcting codes presented in He $\textit{et al.}$ (2025), and we show that various sets of addressable and transversal non-Clifford multi-control-$Z$ gates can be performed in parallel. The construction relies on the good classical codes of Stichtenoth (IEEE Trans. Inf. Theory, 2006), which were previously instantiated in He $\textit{et al.}$ (2025), to yield quantum CSS codes over which addressable logical $\mathsf{CCZ}$ gates can be performed at least one at a time. Here, we show that for any $m$, there exists a family of good quantum error-correcting codes over qudits for which logical $\mathsf{C}^{m}\mathsf{Z}$ gates can address specific logical qudits and be performed in parallel. This leads to a significant advantage in the depth overhead of multi-control-$Z$ circuits.

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