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.

Methods
This dataset represents $H{\Gamma}$ and $H{\Delta}$, the error-correcting codes evaluated in the manuscript.