Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

Quantum error-correction using codes with low density generator matrix

Hatuying Lou, Javier Garcia‐Frias

Published Sep 12, 2005• 16 citations
Publisher

Abstract

We propose the use of linear codes with low-density generator matrix in the context of quantum error correction. The proposed codes allow greater flexibility and are easier to design than existing sparse-graph quantum codes, while leading to better performance.
DOI
10.1109/spawc.2005.1506298

Related papers

On the Application of Error-Correcting Codes with Low-Density Generator Matrix over Different Quantum Channels

Hanqing Lou, Javier Garcia‐Frias

We propose the use of linear codes with low-density generator matrix in the context of error correction over different quantum channels. The basic idea is to construct a Calderbank-Shor-Steane (CSS) code based on the generator matrix and the parity-check matrix of an LDGM code, applying row operations in both matrices to achieve the desired quantum rate. Decoding is performed in an iterative manner, using message passing over the corresponding graphs. The proposed codes allow greater flexibility and are easier to design than existing sparse-graph quantum codes, while leading to better performance.

•Apr 3, 2006•23 citations

Sparse-Graph Codes for Quantum Error Correction

David Mackay, Graeme Mitchison, Paul L. McFadden

Sparse-graph codes appropriate for use in quantum error-correction are presented. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse-graph codes keep the number of quantum interactions associated with the quantum error-correction process small: a constant number per quantum bit, independent of the block length. Third, sparse-graph codes often offer great flexibility with respect to block length and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.

arXiv:quant-ph/0304161•IEEE Transactions on Information Theory•Sep 28, 2004•380 citations

Design of low-density-generator-matrix–based quantum codes for asymmetric quantum channels

Patricio Fuentes, Josu Etxezarreta Martínez, Pedro M. Crespo +1 more

Quantum low-density-generator-matrix (QLDGM) codes are known to exhibit great error correction capabilities, surpassing existing quantum low-density-parity-check (QLDPC) codes and other sparse-graph schemes over the depolarizing channel. Most of the research on QLDPC codes and quantum error correction (QEC) is conducted for the symmetric instance of the generic Pauli channel, which incurs bit flips, phase flips, or a combination of both with the same probability. However, due to the behavior of the materials they are built from, some quantum devices must be modelled using a different channel model capable of accurately representing asymmetric scenarios in which the likelihood of a phase flip is higher than that of a bit flip. In this work, we study the design of QLDGM CSS codes for such Pauli channels. We show how codes tailored to the depolarizing channel are not well suited to these asymmetric environments and we derive methods to aptly design QLDGM CSS codes for this paradigm.

Physical Review A•Feb 26, 2021•9 citations

Design of near-optimum quantum error-correcting codes based on generator and parity-check matrices of LDGM codes

Javier Garcia‐Frias, Kejing Liu

We study the design of near-optimum quantum error correcting codes based on the use of sparse matrices. The basic idea is to construct a Calderbank-Shor-Steane (CSS) code based on the generator and parity-check matrices of a classical channel code with low density generator matrix (LDGM code), which is designed with a specific structure inspired in the parallel concatenation of regular LDGM codes. Then, row operations are performed in both matrices to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the corresponding graphs. The proposed codes allow greater flexibility and are easier to design than existing sparse-graph quantum codes, while leading to better performance.

Conference on Information Sciences and Systems•Mar 1, 2008•13 citations

High-Rate Quantum Low-Density Parity-Check Codes Assisted by Reliable Qubits

Yuichiro Fujiwara, Alexander Gruner, Peter Vandendriessche

Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find.

arXiv:1309.5587•IEEE Transactions on Information Theory•Jan 30, 2015•14 citations

Quantum Coding with Low-Depth Random Circuits

Michael J. Gullans, Stefan Krastanov, David A. Huse +2 more

Quantum error-correction codes generated by random circuits can offer robust performance with low circuit depth, suggesting that practical error correction is within reach on near-term quantum devices.

arXiv:2010.09775•Physical Review X•Sep 24, 2021•59 citations
We propose the use of linear codes with low-density generator matrix in the context of error correction over different quantum channels. The basic idea is to construct a Calderbank-Shor-Steane (CSS) code based on the generator matrix and the parity-check matrix of an LDGM code, applying row operations in both matrices to achieve the desired quantum rate. Decoding is performed in an iterative manner, using message passing over the corresponding graphs. The proposed codes allow greater flexibility and are easier to design than existing sparse-graph quantum codes, while leading to better performance.
Sparse-graph codes appropriate for use in quantum error-correction are presented. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse-graph codes keep the number of quantum interactions associated with the quantum error-correction process small: a constant number per quantum bit, independent of the block length. Third, sparse-graph codes often offer great flexibility with respect to block length and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.
Quantum low-density-generator-matrix (QLDGM) codes are known to exhibit great error correction capabilities, surpassing existing quantum low-density-parity-check (QLDPC) codes and other sparse-graph schemes over the depolarizing channel. Most of the research on QLDPC codes and quantum error correction (QEC) is conducted for the symmetric instance of the generic Pauli channel, which incurs bit flips, phase flips, or a combination of both with the same probability. However, due to the behavior of the materials they are built from, some quantum devices must be modelled using a different channel model capable of accurately representing asymmetric scenarios in which the likelihood of a phase flip is higher than that of a bit flip. In this work, we study the design of QLDGM CSS codes for such Pauli channels. We show how codes tailored to the depolarizing channel are not well suited to these asymmetric environments and we derive methods to aptly design QLDGM CSS codes for this paradigm.
We study the design of near-optimum quantum error correcting codes based on the use of sparse matrices. The basic idea is to construct a Calderbank-Shor-Steane (CSS) code based on the generator and parity-check matrices of a classical channel code with low density generator matrix (LDGM code), which is designed with a specific structure inspired in the parallel concatenation of regular LDGM codes. Then, row operations are performed in both matrices to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the corresponding graphs. The proposed codes allow greater flexibility and are easier to design than existing sparse-graph quantum codes, while leading to better performance.
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes with desirable properties for quantum information processing than for traditional digital communications and computation. A typical obstacle to constructing a variety of strong quantum error-correcting codes is the complicated restrictions imposed on the structure of a code. Recently, promising solutions to this problem have been proposed in quantum information science, where in principle any binary linear code can be turned into a quantum error-correcting code by assuming a small number of reliable quantum bits. This paper studies how best to take advantage of these latest ideas to construct desirable quantum error-correcting codes of very high information rate. Our methods exploit structured high-rate low-density parity-check codes available in the classical domain and provide quantum analogues that inherit their characteristic low decoding complexity and high error correction performance even at moderate code lengths. Our approach to designing high-rate quantum error-correcting codes also allows for making direct use of other major syndrome decoding methods for linear codes, making it possible to deal with a situation where promising quantum analogues of low-density parity-check codes are difficult to find.