New Non-Binary Quantum Codes Derived From a Class of Linear Codes

Gao, Jian; Wang, Yongkang

doi:10.1109/access.2019.2899383

Cited by 11 publications

(4 citation statements)

References 15 publications

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“…The code bounds such as Hamming bound and quantum Singleton bound for high-dimensional cases were analyzed in [40]. Various quantum codes can be generalized to the nonbinary cases, such as nonbinary quantum cyclic codes constructed using graph method [41], nonbinary codeword stabilized quantum codes with nonadditive properties [42], or nonbinary entanglement-assisted quantum codes [43].…”

Section: ) Nonbinary Quantum Codesmentioning

confidence: 99%

Some Progress on Quantum Error Correction for Discrete and Continuous Error Models

2020

IEEE Access

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Quantum computing has increasingly gained attention for decades since it can surpass classical computing in various aspects. A crucial issue of quantum computing is how to protect information from noise interference such that the error rate during quantum information processing can be limited within an acceptable bound. The technique to address this issue is quantum error correction (QEC). Developing QEC technologies needs to define noise as formal error models and design QEC approaches for these error models. Discrete error models and continuous error models are two kinds of definitions of noise. The former assumes noise occurs independently and can be discretized into a set of basic errors. The former also has a tool, named quantum operations, to describe a specific error model. The latter describes that noise is continuous in time by using differential equations. In this paper, we categorize QEC approaches into three types according to the different error models: discrete error models, specific error models, and continuous error models. We also analyze the state-of-the-art QEC approaches and discuss some future directions. Furthermore, we propose the perturbed error models and their possible definitions, aiming to find the effect of the perturbation during quantum information processing.

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Section: ) Nonbinary Quantum Codesmentioning

confidence: 99%

Some Progress on Quantum Error Correction for Discrete and Continuous Error Models

2020

IEEE Access

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“…Then, Ashikhmin et al [2] generalized these results to non-binary case . Afterwards, many good QECCs have been constructed by using classical linear codes over finite fields [1,9,12,16,18,25,27,34,38]. Another important discovery in the quantum errorcorrecting area was the entanglement-assisted quantum codes (EAQECCs, for short).…”

Section: Introductionmentioning

confidence: 99%

“…In fact, extended constructions can also be utilized to construct QECCs and EAQECCs. In [34], Tonchev presented doubling extended constructions and obtained a new optimal binary [ [28,12,6]] QECC, which improved the corresponding lower bounds on minimum distance at that time. In 2018, Guenda et al [14] applied extended constructions to design families of EAQECCs with good error-correcting performance requiring desirable amounts of entanglement.…”

Section: Introductionmentioning

confidence: 99%

Extended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codes

Lv¹,

Li²,

Yao³

2020

Preprint

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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 codes, we provide quasi-cyclic extended constructions that preserve the self-orthogonality to obtain stabilizer quantum codes. As for the computational results, some binary and ternary stabilizer codes with good parameters are constructed. Moreover, we present methods to construct maximal-entanglement entanglement-assisted quantum codes by means of the class of quasi-cyclic codes and their extended codes. As an application, some good maximal-entanglement entanglement-assisted quantum codes are obtained and their parameters are compared.

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“…In 2001, Ashikhmin et al generalized these results to non-binary case in [5]. Afterwards, many good quantum codes have been constructed by using classical linear codes over finite fields [6]- [10].…”

Section: Introductionmentioning

confidence: 99%

New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes

Wang

2019

IEEE Access

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New Non-Binary Quantum Codes Derived From a Class of Linear Codes

Abstract: In this short paper, we consider the non-binary quantum codes construction from a class of linear codes, which are not self-orthogonal over finite fields. As the computational results, new quantum codes

Cited by 11 publications

References 15 publications

Some Progress on Quantum Error Correction for Discrete and Continuous Error Models

Some Progress on Quantum Error Correction for Discrete and Continuous Error Models

Extended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codes

New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes

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