Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916831594283008 |
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| author | He, Zhiyang Vaikuntanathan, Vinod Wills, Adam Zhang, Rachel Yun |
| author_facet | He, Zhiyang Vaikuntanathan, Vinod Wills, Adam Zhang, Rachel Yun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05392 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates He, Zhiyang Vaikuntanathan, Vinod Wills, Adam Zhang, Rachel Yun Quantum Physics 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. |
| title | Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.05392 |