PreprintarXiv licencearXiv
High-Rate Quasi-Dyadic Quantum LDPC Codes
Abstract
In this work, we propose a novel design of high-rate Calderbank--Shor--Steane (CSS) quantum low-density parity-check (QLDPC) codes based on quasi-dyadic matrices. The Tanner graphs associated with the two component classical codes used to construct the proposed CSS codes are characterized by a girth of at least $6$. We also derive an exact count of length-$4$ cycles in the quaternary representation of the parity-check matrix. Monte Carlo simulations under code-capacity and phenomenological noise models show that the proposed codes have competitive finite-length logical error rate performance compared with state-of-the-art codes in both these settings.
Related
- Quantum LDPC and High-Rate CSS Codes from Fair-Density Parity-Check Codes
- Fast and accurate neural triage decoding of ultra-high-rate quantum LDPC codes
- Towards Block-Level Fault-Tolerant Quantum Simulation on Small High-Rate Non-CSS Codes
- New distance bounds for one-generator quasi-cyclic codes with applications to Hermitian LCD codes and entanglement-assisted quantum codes
- Ancestor Lifting of Quasi-Cyclic Additive Codes and Certified Quantum Codes
BibTeX
@misc{baldelli2026highrate,
title = {{High-Rate Quasi-Dyadic Quantum LDPC Codes}},
author = {Alessio Baldelli and Sisi Miao and Laurent Schmalen and Massimo Battaglioni and Marco Baldi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24201},
eprint = {2609.24201},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24201},
}
RIS
TY - UNPB
TI - High-Rate Quasi-Dyadic Quantum LDPC Codes
AU - Alessio Baldelli
AU - Sisi Miao
AU - Laurent Schmalen
AU - Massimo Battaglioni
AU - Marco Baldi
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.24201
UR - https://arxiv.org/abs/2609.24201
AB - In this work, we propose a novel design of high-rate Calderbank--Shor--Steane (CSS) quantum low-density parity-check (QLDPC) codes based on quasi-dyadic matrices. The Tanner graphs associated with the two component classical codes used to construct the proposed CSS codes are characterized by a girth of at least $6$. We also derive an exact count of length-$4$ cycles in the quaternary representation of the parity-check matrix. Monte Carlo simulations under code-capacity and phenomenological noise models show that the proposed codes have competitive finite-length logical error rate performance compared with state-of-the-art codes in both these settings.
ER -