Constant Rate Codes with Fully Addressable Transversal T: Good Codes, Sparse Checks
Abstract
Recent work by Wills constructed codes with constant rate and transversal T. Extending this line of work, we construct asymptotically good CSS codes with \textbf{fully addressable} transversal T, permitting selective control over which logical qubits receive a T gate. We also give Pauli-LDPC codes with transversal T and growing distance at vanishing rate; and a protected-subsystem construction with fully addressable transversal T, constant protected rate, distance Ω(√n), and sparse (non-Pauli) checks. More generally, we obtain asymptotically good binary codes with full transversal addressability for every fixed finite-order one-qubit gate, retaining CSS realizations for dyadic phase gates such as √T and using generally nonadditive codes for rotations such as Rz(π/7). The remaining challenge is to construct asymptotically good Pauli-LDPC codes with fully addressable transversal non-Clifford one-qubit gates.
Related
- Asymptotically Good Quantum Codes with Addressable Transversal T Gates
- Parallelizable and addressable transversal non-Clifford gates on good quantum LDPC codes
- A lower bound on the overhead of addressable surgery on sparse stabiliser codes
- 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
BibTeX
@misc{meiburg2026constant,
title = {{Constant Rate Codes with Fully Addressable Transversal T: Good Codes, Sparse Checks}},
author = {Alexander Meiburg},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38996},
eprint = {2609.38996},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38996},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constant Rate Codes with Fully Addressable Transversal T: Good Codes, Sparse Checks
AU - Alexander Meiburg
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38996
UR - https://arxiv.org/abs/2609.38996
AB - Recent work by Wills constructed codes with constant rate and transversal T. Extending this line of work, we construct asymptotically good CSS codes with \textbf{fully addressable} transversal T, permitting selective control over which logical qubits receive a T gate. We also give Pauli-LDPC codes with transversal T and growing distance at vanishing rate; and a protected-subsystem construction with fully addressable transversal T, constant protected rate, distance Ω(√n), and sparse (non-Pauli) checks. More generally, we obtain asymptotically good binary codes with full transversal addressability for every fixed finite-order one-qubit gate, retaining CSS realizations for dyadic phase gates such as √T and using generally nonadditive codes for rotations such as R_z(π/7). The remaining challenge is to construct asymptotically good Pauli-LDPC codes with fully addressable transversal non-Clifford one-qubit gates.
ER -