Quantum LDPC code orthogonal parity-check matrix pairs H_Gamma, H_Delta

Quantum low-density parity-check (QLDPC) codes require orthogonal
parity-check matrices to satisfy the quantum orthogonality condition,
ensuring their validity for quantum error correction. This dataset
provides orthogonal parity-check matrix pairs $H_\Gamma, H_\Delta$, which
are essential for constructing QLDPC codes. The matrices were generated
using predefined parameters such as code size, finite field order, and
cycle length constraints. The dataset includes a variety of matrix
instances stored in structured text format. The dataset was developed as
part of a study addressing two fundamental challenges in quantum error
correction: approaching the hashing bound—a fundamental performance
benchmark and lower bound of quantum capacity—and avoiding the error floor
phenomenon, where the error rate stagnates under low noise levels. These
challenges have hindered the realization of practical quantum error
correction schemes. In our research, we propose a novel construction and
decoding method for QLDPC codes that significantly improves upon existing
quantum error-correcting codes. Our approach is the first to demonstrate
performance approaching the hashing bound while also showing no observable
error floor phenomenon in the tested parameter range. This dataset
contains the parity-check matrices used in our study, allowing for
reproducibility and further exploration of QLDPC code performance. Each
parity-check matrix is represented by three files: a structure file
containing nonzero element positions, a size descriptor file specifying
matrix dimensions and finite field order, and a value file containing
corresponding finite field elements. File names follow a systematic
convention encoding key parameters such as the number of rows and columns,
the field order, and random seed values used for matrix generation. This
dataset is a valuable resource for researchers in quantum error
correction, enabling exploration of QLDPC codes under different parameter
settings. It facilitates testing of decoding algorithms, performance
evaluation, and further development of quantum coding theory. The dataset
is publicly available on Dryad and can be freely accessed for research and
development purposes. There are no legal or ethical constraints associated
with the use of this dataset. The matrices were generated entirely within
our research and do not contain any personally identifiable or sensitive
information. This dataset supports the reproducibility of QLDPC code
studies and contributes to advancements in quantum error correction
techniques.