Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates
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 gate can be executed on those three logical qubits via a depth-one physical circuit of 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 gates and has inverse-polylogarithmic rate and relative distance.
Cite
@article{arxiv.2507.05392,
title = {Asymptotically Good Quantum Codes with Addressable and Transversal Non-Clifford Gates},
author = {Zhiyang He and Vinod Vaikuntanathan and Adam Wills and Rachel Yun Zhang},
journal= {arXiv preprint arXiv:2507.05392},
year = {2025}
}