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Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…

Quantum Physics · Physics 2023-12-11 Zi-Wen Liu , Sisi Zhou

One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized…

Information Theory · Computer Science 2015-08-06 Tao Zhang , Gennian Ge

Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. In this paper, we give two new constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes and…

Information Theory · Computer Science 2015-11-06 Baokun Ding , Tao Zhang , Gennian Ge

It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…

Information Theory · Computer Science 2023-01-09 Chaofeng Guan , Ruihu Li , Liangdong Lu , Yu Yao

Recently, the theory of quantum error control codes has been extended to subsystem codes over symmetric and asymmetric quantum channels -- qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in…

Quantum Physics · Physics 2008-11-11 Salah A. Aly

We study the subfield subcodes of projective Reed-Solomon codes and their duals: we provide bases for these codes and estimate their parameters. With this knowledge, we can construct symmetric and asymmetric entanglement-assisted quantum…

Information Theory · Computer Science 2023-11-28 Philippe Gimenez , Diego Ruano , Rodrigo San-José

Galois hulls of linear codes have important applications in quantum coding theory. In this paper, we construct some new classes of (extended) generalized Reed-Solomon (GRS) codes with Galois hulls of arbitrary dimensions. We also propose a…

Information Theory · Computer Science 2021-08-03 Xiaolei Fang , Renjie Jin , Jinquan Luo , Wen Ma

Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic…

Information Theory · Computer Science 2020-09-08 Jingjie Lv , Ruihu Li , Yu Yao

We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…

Quantum Physics · Physics 2009-05-24 Markus Grassl , Peter Shor , Graeme Smith , John Smolin , Bei Zeng

We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional…

Quantum Physics · Physics 2007-05-23 Eric M. Rains

We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of…

Algebraic Geometry · Mathematics 2025-01-17 Fernando Hernando , Gary McGuire , Francisco Monserrat , Julio José Moyano-Fernández

Entanglement-assisted concatenated quantum codes (EACQCs), constructed by concatenating two quantum codes, are proposed. These EACQCs show several advantages over the standard concatenated quantum codes (CQCs). Several families of EACQCs…

Quantum Physics · Physics 2023-02-28 Jihao Fan , Jun Li , Yongbin Zhou , Min-Hsiu Hsieh , H. Vincent Poor

After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…

Quantum Physics · Physics 2011-10-20 Markus Grassl , Willi Geiselmann , Thomas Beth

Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…

Quantum Physics · Physics 2015-06-05 Zhuo Wang , Sixia Yu , Heng Fan , C. H. Oh

Entanglement-assisted quantum error-correcting codes (EAQECCs) to desired rate, error-correcting capability and maximum shared entanglement are constructed. Thus for a required rate $R$, required error-correcting capability to correct $t$…

Information Theory · Computer Science 2019-03-05 Ted Hurley , Donny Hurley , Barry Hurley

Algebraic-geometric codes on Garcia-Stichtenoth family of curves are used to construct the asymptotically good quantum codes.

Quantum Physics · Physics 2007-05-23 Hao Chen

It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…

Information Theory · Computer Science 2009-08-15 Salah A. Aly

We study Algebraic Geometry codes producing quantum error-correcting codes by the CSS construction. We pay particular attention to the family of Castle codes. We show that many of the examples known in the literature in fact belong to this…

Information Theory · Computer Science 2016-06-30 Carlos Munuera , Wanderson Tenório , Fernando Torres

By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality…

Information Theory · Computer Science 2024-03-19 Xiujing Zheng , Liqi Wang , Shixin Zhu

Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable…

Quantum Physics · Physics 2013-07-19 Yuichiro Fujiwara , Vladimir D. Tonchev , Tony W. H. Wong