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We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff and efficient list decoding up to the Johnson bound in polynomial time. Previous constructions of list decodable good distance…

Information Theory · Computer Science 2024-11-08 Thiago Bergamaschi , Fernando Granha Jeronimo , Tushant Mittal , Shashank Srivastava , Madhur Tulsiani

One approach to designing structured low-density parity-check (LDPC) codes with large girth is to shorten codes with small girth in such a manner that the deleted columns of the parity-check matrix contain all the variables involved in…

Discrete Mathematics · Computer Science 2016-11-18 Olgica Milenkovic , Navin Kashyap , David Leyba

Quantum low-density parity-check (QLDPC) codes offer a promising path to low-overhead fault-tolerant quantum computation but lack systematic strategies for exploration. In this Letter, we establish a topological framework for studying the…

Quantum Physics · Physics 2025-08-21 Keyang Chen , Yuanting Liu , Yiming Zhang , Zijian Liang , Yu-An Chen , Ke Liu , Hao Song

There have been lots of efforts on the construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes with large girth. However, most of them are focused on protographs with single edges and little research has been done for the…

Information Theory · Computer Science 2016-11-17 Hosung Park , Seokbeom Hong , Jong-Seon No , Dong-Joon Shin

The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary…

Information Theory · Computer Science 2016-11-17 Ian P. Mulholland , Enrico Paolini , Mark F. Flanagan

Quantum low-density parity-check (qLDPC) codes are a promising construction for drastically reducing the overhead of fault-tolerant quantum computing (FTQC) architectures. However, all of the known hardware implementations of these codes…

Although high-threshold and low-overhead quantum low-density parity-check (qLDPC) codes, such as bivariate bicycle (BB) codes, can reduce the physical-qubit cost by an order of magnitude compared to the Kitaev toric code, their torus layout…

Quantum Physics · Physics 2025-08-25 Zijian Liang , Jens Niklas Eberhardt , Yu-An Chen

In this work, we propose a fully differentiable iterative decoder for quantum low-density parity-check (LDPC) codes. The proposed algorithm is composed of classical belief propagation (BP) decoding stages and intermediate graph neural…

Quantum Physics · Physics 2026-05-14 Anqi Gong , Sebastian Cammerer , Joseph M. Renes

An algorithm for constructing Tanner graphs of non-binary irregular quasi-cyclic LDPC codes is introduced. It employs a new method for selection of edge labels allowing control over the code's non-binary ACE spectrum and resulting in low…

Information Theory · Computer Science 2016-11-17 Alex Bazarsky , Noam Presman , Simon Litsyn

Identifying the best families of quantum error correction (QEC) codes for near-term experiments is key to enabling fault-tolerant quantum computing. Ideally, such codes should have low overhead in qubit number, high physical error…

Quantum Physics · Physics 2025-11-17 Laura Pecorari , Guido Pupillo

We study finite-length qudit quantum low-density parity-check (LDPC) codes from translation-invariant CSS constructions on two-dimensional tori with twisted boundary conditions. Recent qubit work [PRX Quantum 6, 020357 (2025)] showed that,…

Quantum Physics · Physics 2026-02-05 Mourad Halla

Quasi-cyclic low-density parity-check (QC-LDPC) codes based on protographs are of great interest to code designers because analysis and implementation are facilitated by the protograph structure and the use of circulant permutation matrices…

Information Theory · Computer Science 2014-07-22 David G. M. Mitchell , Roxana Smarandache , Daniel J. Costello

Spatially-coupled (SC) codes is a class of convolutional LDPC codes that has been well investigated in classical coding theory thanks to their high performance and compatibility with low-latency decoders. We describe toric codes as quantum…

Quantum Physics · Physics 2025-04-09 Siyi Yang , Robert Calderbank

We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC) low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the conventional factor graph is equivariant to the quasi-cyclic automorphisms and therefore…

Information Theory · Computer Science 2022-08-17 Marvin Geiselhart , Moustafa Ebada , Ahmed Elkelesh , Jannis Clausius , Stephan ten Brink

In our recent paper entitled "Quantum Quasi-Cyclic Low-Density Parity-Check codes" [ICIC 2009. LNCS 5754], it was claimed that some new quantum codes can be constructed via the CSS encoding/decoding approach with various lengths and rates.…

Information Theory · Computer Science 2015-03-14 Dazu Huang , Zhigang Chen , Xin Li , Ying Guo

Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of…

Quantum Physics · Physics 2024-07-08 Jens Niklas Eberhardt , Vincent Steffan

In this paper, we deal with time-invariant spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs). Classic design approaches usually start from quasi-cyclic low-density parity-check (QC-LDPC) block codes and exploit…

Information Theory · Computer Science 2017-11-30 Massimo Battaglioni , Alireza Tasdighi , Giovanni Cancellieri , Franco Chiaraluce , Marco Baldi

Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes which affects code performance and ease of physical realization. For device architectures restricted to 2D local gates,…

As in classical coding theory, quantum analogues of low-density parity-check (LDPC) codes have offered good error correction performance and low decoding complexity by employing the Calderbank-Shor-Steane (CSS) construction. However,…

Information Theory · Computer Science 2013-05-21 Yuichiro Fujiwara , Vladimir D. Tonchev

We construct several explicit instances of quantum Tanner codes, a class of asymptotically good quantum low-density parity check (qLDPC) codes. The codes are constructed using dihedral groups and random pairs of classical codes and exhibit…

Quantum Physics · Physics 2025-11-17 Rebecca Katharina Radebold , Stephen D. Bartlett , Andrew C. Doherty