Asymptotically Good Quantum Codes with Addressable Transversal T Gates
Abstract
Designing quantum codes with both transversal non-Clifford gates and good error-correcting parameters is an important goal in fault-tolerant quantum computation. Here, we construct an explicit family of binary CSS codes with constant rate and linear distance that admit fully addressable transversal T gates. Specifically, any prescribed tensor product of logical powers of T is implemented by a tensor product of physical powers of T, without any subsequent correction. Our construction combines algebraic-geometry codes with suitable binary embedding to obtain generalized divisibility of binary codes. This divisibility then enables fully addressable transversal T gates. Furthermore, we formulate the minimum binary embedding length problem as a minimum-weight problem over an affine space and numerically improve the constants in the asymptotic rate and relative-distance bounds.
Related
- Parallelizable and addressable transversal non-Clifford gates on good quantum LDPC codes
- Asymptotically good binary triorthogonal codes and higher-level transversal gates
- Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates
- Substantially Improved Rate and Distance for Addressable Transversal Phase Gates
- Constant Rate Codes with Fully Addressable Transversal T: Good Codes, Sparse Checks
BibTeX
@misc{lin2026asymptotically,
title = {{Asymptotically Good Quantum Codes with Addressable Transversal T Gates}},
author = {Tongyin Lin and Bujiao Wu and Bin Cheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35129},
eprint = {2609.35129},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35129},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Asymptotically Good Quantum Codes with Addressable Transversal T Gates
AU - Tongyin Lin
AU - Bujiao Wu
AU - Bin Cheng
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35129
UR - https://arxiv.org/abs/2609.35129
AB - Designing quantum codes with both transversal non-Clifford gates and good error-correcting parameters is an important goal in fault-tolerant quantum computation. Here, we construct an explicit family of binary CSS codes with constant rate and linear distance that admit fully addressable transversal T gates. Specifically, any prescribed tensor product of logical powers of T is implemented by a tensor product of physical powers of T, without any subsequent correction. Our construction combines algebraic-geometry codes with suitable binary embedding to obtain generalized divisibility of binary codes. This divisibility then enables fully addressable transversal T gates. Furthermore, we formulate the minimum binary embedding length problem as a minimum-weight problem over an affine space and numerically improve the constants in the asymptotic rate and relative-distance bounds.
ER -