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 meth..., This dataset represents $H{\Gamma}$ and $H{\Delta}$, the error-correcting codes evaluated in the manuscript., , # Quantum LDPC Code Orthogonal Parity-Check Matrix Pairs $H\_\Gamma, H\_\Delta$

[Access this dataset on Dryad](https://doi.org/10.5061/dryad.8gtht76zs)

This dataset contains orthogonal parity-check matrix pairs $H_\Gamma, H_\Delta$ used for quantum low-density parity-check (QLDPC) codes. These matrices are designed to satisfy the quantum orthogonality condition, ensuring the validity of the quantum code. The dataset includes various instances of $H_\Gamma, H_\Delta$ generated under different conditions, along with metadata describing their structural properties. These matrices play a crucial role in the construction and evaluation of quantum error-correcting codes.

## Description of the data and file structure

The dataset consists of orthogonal parity-check matrix pairs $H_\Gamma, H_\Delta$ used in quantum LDPC codes. These matrices are stored in plain text (.txt) format and follow a structured naming convention that encodes important parameters.

### **File Naming Convention**

Eac...,