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

Published Mar 17, 2025 on Dryad. https://doi.org/10.5061/dryad.8gtht76zs

Data files

Mar 17, 2025 version files 1.70 MB

codefiles.tar.gz
1.70 MB
README.md
3.14 KB

Abstract

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.

Access this dataset on Dryad

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

Each file name follows the format:

{QC-LDPC="QC", APM-LDPC="APM"}_{H_Δ="Delta", H_Γ="Gamma"}_n{cols×p}_m{rows×p}_N{cols}_M{cols}_J{J}_L{L}_P{P}_alpha{QC-LDPC="1", APM-LDPC="2"}_GF{2^p}_GIRTH{girth}_SEED{seed}

where:

QC or APM: Specifies whether the matrix is Quasi-Cyclic LDPC (QC-LDPC) or Array-Based LDPC (APM-LDPC).
Delta or Gamma: Specifies whether the file contains $H_\Delta$ or $H_\Gamma$.
n: Number of columns in the parity-check matrix multiplied by $p$.
m: Number of rows in the parity-check matrix multiplied by $p$.
N: Number of columns in the parity-check matrix.
M: Number of columns in the parity-check matrix.
J, L, P: Parameters defining the matrix structure.
alpha: Value 1 for QC-LDPC, 2 for APM-LDPC.
GF: The size of the finite field $GF(2^p)$.
GIRTH: The minimum cycle length in the parity-check matrix.
SEED: The random seed used for generating the matrix.

File Types and Contents

Each matrix is represented by three different files:

Matrix structure file ({prefix}.txt):
- Contains the nonzero entry column indices for each row.
Size descriptor file ({prefix}_size.txt):
- Contains three values:
  1. Number of rows in the parity-check matrix.
  2. Number of columns in the parity-check matrix.
  3. The field size $2^p$.
Finite field value file ({prefix}_value.txt):
- Stores the finite field nonzero values corresponding to each nonzero position in the parity-check matrix.
- Values are listed in the same order as in the structure file.

This structured format allows users to reconstruct the full parity-check matrix while keeping the storage efficient.

Sharing/Access information

The dataset is publicly available on Dryad and can be accessed via the following link:\
Access this dataset on Dryad

There are no other publicly accessible locations where this dataset is hosted.

Data Origin

The data in this repository was entirely generated as part of our research. No external datasets were used or modified to create this dataset.