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Related papers: Decoding Quasi-Cyclic Quantum LDPC Codes

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We introduce and analyze a family of Clifford-deformed bivariate bicycle codes that are tailored for biased noise. Our qLDPC codes are defined on a bipartite hexagonal lattice with limited-range gates and low-weight stabilizers. The code is…

Quantum Physics · Physics 2025-06-03 Catherine Leroux , Joseph K. Iverson

Locally decodable codes (LDCs) are error-correcting codes $C : \Sigma^k \to \Sigma^n$ that admit a local decoding algorithm that recovers each individual bit of the message by querying only a few bits from a noisy codeword. An important…

Computational Complexity · Computer Science 2020-09-17 Vahid R. Asadi , Igor Shinkar

Quantum error-correcting codes (QECCs) can eliminate the negative effects of quantum noise, the major obstacle to the execution of quantum algorithms. However, realizing practical quantum error correction (QEC) requires resolving many…

We develop a topological theory for fault-tolerant quantum computation in quantum low-density parity-check (qLDPC) codes. We show that there exist hidden simplicial or CW complex structures encoding the topological data for all qLDPC and…

Quantum Physics · Physics 2025-09-24 Guanyu Zhu

Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds…

Information Theory · Computer Science 2016-11-17 Roxana Smarandache , Pascal O. Vontobel

Quantum key distribution (QKD) is a cryptographic system that generates an information-theoretically secure key shared by two legitimate parties. QKD consists of two parts: quantum and classical. The latter is referred to as classical…

Information Theory · Computer Science 2018-05-15 Sunghoon Lee , Jooyoun Park , Jun Heo

In this paper, a new decoding scheme for low-density parity-check (LDPC) codes using the concept of simple product code structure is proposed based on combining two independently received soft-decision data for the same codeword. LDPC codes…

Information Theory · Computer Science 2024-10-30 Beomkyu Shin , Seokbeom Hong , Hosung Park , Jong-Seon No , Dong-Joon Shin

Quantum low density parity check (QLDPC) codes are useful primitives for quantum information processing because they can be encoded and decoded efficiently. Besides, the error correcting capability of a few QLDPC codes exceeds the quantum…

Quantum Physics · Physics 2008-07-15 K. H. Ho , H. F. Chau

Semiconductor spin qubits are a promising platform for large-scale quantum computing, but have yet to take full advantage of the broad class of quantum low-density parity check (QLDPC) codes, which promise high encoding rates and efficient…

Quantum Physics · Physics 2026-04-29 Jason D. Chadwick , Frederic T. Chong

A major goal in quantum computing is to build a fault-tolerant quantum computer. One approach involves quantum low-density parity-check (qLDPC) codes that support transversal non-Clifford gates. In this work, we provide a large family of…

Quantum Physics · Physics 2024-10-21 Ting-Chun Lin

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

Constructing quantum LDPC codes with a minimum distance that grows faster than a square root of the length has been a major challenge of the field. With this challenge in mind, we investigate constructions that come from high-dimensional…

Quantum Physics · Physics 2020-04-20 Shai Evra , Tali Kaufman , Gilles Zémor

In this paper we propose the construction of Spatially Coupled Low-Density Parity-Check (SC-LDPC) codes using a periodic time-variant Quasi-Cyclic (QC) algorithm. The QC based approach is optimized to obtain memory efficiency in storing the…

Information Theory · Computer Science 2013-10-18 Vikram Arkalgud Chandrasetty , Sarah J. Johnson , Gottfried Lechner

Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has attracted much attention in the research community in the past few years. The aim of LP decoding is to develop an algorithm which has error-correcting performance…

Information Theory · Computer Science 2010-10-05 Mayur Punekar , Mark F. Flanagan

We propose an approach for optimizing nonbinary (NB) quasi-cyclic (QC) LDPC codes. This approach combines constructing of base parity-check matrices by simulated annealing and labeling the obtained base matrices aimed at maximizing the…

Information Theory · Computer Science 2020-10-23 Irina E. Bocharova , Boris D. Kudryashov , Evgenii P. Ovsyannikov , Vitaly Skachek , Tähvend Uustalu

Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of…

Quantum Physics · Physics 2026-05-05 Shuyu Zhang , Tzu-Chieh Wei , Nathanan Tantivasadakarn

Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing. However, all families of quantum…

Quantum Physics · Physics 2014-10-20 Sergey Bravyi , Matthew B. Hastings

Hypergraph product (HGP) codes are one of the most popular family of quantum low-density parity-check (LDPC) codes. Circuit-level simulations show that they can achieve the same logical error rate as surface codes with a reduced qubit…

Quantum Physics · Physics 2026-03-23 Arda Aydin , Nicolas Delfosse , Edwin Tham

We consider a quantum key expansion (QKE) protocol based on entanglement-assisted quantum error-correcting codes (EAQECCs). In these protocols, a seed of a previously shared secret key is used in the post-processing stage of a standard…

Quantum Physics · Physics 2013-06-26 Kung-Chuan Hsu , Todd A. Brun

Families of "asymptotically regular" LDPC block code ensembles can be formed by terminating (J,K)-regular protograph-based LDPC convolutional codes. By varying the termination length, we obtain a large selection of LDPC block code ensembles…

Information Theory · Computer Science 2016-11-15 David G. M. Mitchell , Roxana Smarandache , Michael Lentmaier , Daniel J. Costello