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arXiv · 2507.05392

Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates

Zhiyang He·Vinod Vaikuntanathan·Adam Wills·Rachel Yun Zhang
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Abstract

Constructing quantum codes with good parameters and useful transversal gates is a central problem in quantum error correction. In this paper, we continue our work in arXiv:2502.01864 and construct the first family of asymptotically good quantum codes (over qubits) supporting transversally addressable non-Clifford gates. More precisely, given any three logical qubits across one, two, or three codeblocks, the logical $\mathsf{CCZ}$ gate can be executed on those three logical qubits via a depth-one physical circuit of $\mathsf{CCZ}$ gates. This construction is based on the transitive, iso-orthogonal algebraic geometry codes constructed by Stichtenoth (IEEE Trans. Inf. Theory, 2006). This improves upon our construction from arXiv:2502.01864, which also supports transversally addressable $\mathsf{CCZ}$ gates and has inverse-polylogarithmic rate and relative distance.

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Zhiyang He, Vinod Vaikuntanathan, Adam Wills, Rachel Yun Zhang. 2025-07-07. Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates. https://arxiv.org/abs/2507.05392

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