Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates
Abstract
Low-space-overhead fault-tolerant quantum computation requires not only high-rate quantum error-correcting codes but also space-efficient implementations of logical operations. Transversal and fold-transversal gates are promising since they limit error propagation and require no additional qubits. However, the logical operations they enable are typically restricted, and a central challenge is to construct codes that combine a complete set of logical Clifford gates with favorable code parameters. In this work, we introduce a family of quantum codes with an asymptotically constant encoding rate and sublogarithmically growing stabilizer weight, while supporting the entire logical Clifford group using only transversal and fold-transversal gates. Our construction is based on classical codes whose code spaces are absolutely irreducible Steinberg modules of their Tanner-graph automorphism groups. Taking hypergraph products of these classical codes yields quantum codes for which all logical Clifford operations can be synthesized from a fixed set of transversal and fold-transversal gates. Moreover, the slow growth of the stabilizer weight enables a high error-correcting performance in small instances. These results provide a path toward fault-tolerant quantum computation with low space overhead using transversal and fold-transversal gates.
Related
- Exact efficient simulation of noisy logical magic states using Clifford stabilizers
- Parallelizable and addressable transversal non-Clifford gates on good quantum LDPC codes
- Clifford gates with logical transversality for self-dual CSS codes
- Improved Transversal Non-Clifford Gates from Cup Products
- Realizing Logical Diagonal Gates via Transversal Physical Z-Rotations in CSS Codes
BibTeX
@misc{matsuura2026constantrate,
title = {{Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates}},
author = {Takaya Matsuura and Yohji Chin and Shohei Kiryu and Kosuke Fukui},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37699},
eprint = {2609.37699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37699},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates
AU - Takaya Matsuura
AU - Yohji Chin
AU - Shohei Kiryu
AU - Kosuke Fukui
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37699
UR - https://arxiv.org/abs/2609.37699
AB - Low-space-overhead fault-tolerant quantum computation requires not only high-rate quantum error-correcting codes but also space-efficient implementations of logical operations. Transversal and fold-transversal gates are promising since they limit error propagation and require no additional qubits. However, the logical operations they enable are typically restricted, and a central challenge is to construct codes that combine a complete set of logical Clifford gates with favorable code parameters. In this work, we introduce a family of quantum codes with an asymptotically constant encoding rate and sublogarithmically growing stabilizer weight, while supporting the entire logical Clifford group using only transversal and fold-transversal gates. Our construction is based on classical codes whose code spaces are absolutely irreducible Steinberg modules of their Tanner-graph automorphism groups. Taking hypergraph products of these classical codes yields quantum codes for which all logical Clifford operations can be synthesized from a fixed set of transversal and fold-transversal gates. Moreover, the slow growth of the stabilizer weight enables a high error-correcting performance in small instances. These results provide a path toward fault-tolerant quantum computation with low space overhead using transversal and fold-transversal gates.
ER -