Asymmetric Quantum Product Codes

Guardia, Giuliano G. La

doi:10.1142/s0219749912500050

Cited by 24 publications

(21 citation statements)

References 16 publications

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“…The fact that dephasing usually happens much more often that relaxation [27] motivated the study and searching of asymmetric quantum error-correcting codes [14,15,16,30,31,32,33]. For this purpose, the most used procedure is the CSS construction because it easily allows us to get parameters d z and d x such that our previous stabilizer code detects phase-shift (respectively, qudit-flip) errors up to weight d z − 1 (respectively, d x − 1).…”

Section: Asymmetric Eaqeccsmentioning

confidence: 99%

Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes

et al. 2020

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The concept of asymmetric entanglement-assisted quantum error-correcting code (asymmetric EAQECC) is introduced in this article. Codes of this type take advantage of the asymmetry in quantum errors since phase-shift errors are more probable than qudit-flip errors. Moreover, they use pre-shared entanglement between encoder and decoder to simplify the theory of quantum error correction and increase the communication capacity. Thus, asymmetric EAQECCs can be constructed from any pair of classical linear codes over an arbitrary field. Their parameters are described and a Gilbert-Varshamov bound is presented. Explicit parameters of asymmetric EAQECCs from BCH codes are computed and examples exceeding the introduced Gilbert-Varshamov bound are shown.2010 Mathematics Subject Classification. 81P70; 94B65; 94B05.

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Section: Asymmetric Eaqeccsmentioning

confidence: 99%

Asymmetric Entanglement-Assisted Quantum Error-Correcting Codes and BCH Codes

et al. 2020

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“…In this section, we state some definitions and some basic results in [28][29][30]32,33] firstly, then we will use constacyclic codes from [11] to construct some families of optimal asymmetric quantum codes.…”

Section: Constructions Of Optimal Asymmetric Quantum Codesmentioning

confidence: 99%

“…In many quantum mechanical systems, the occurrence of qubit-flip and phase-shift errors is quite different [12]. For the past two decades, the constructions of good asymmetric quantum codes have been investigated by some researchers [28][29][30]32,33,38]. Qian and Zhang utilized q 2 -ary cyclotomic cosets to construct a family of optimal asymmetric quantum codes in [43].…”

Section: Introductionmentioning

confidence: 99%

Some families of asymmetric quantum codes and quantum convolutional codes from constacyclic codes

Chen

Huang

et al. 2015

Linear Algebra and its Applications

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Quantum maximal-distance-separable (MDS) codes are an important class of quantum codes. Recently, many scholars utilize constacyclic codes to construct some quantum MDS codes. In this paper, several new families of optimal asymmetric quantum codes and optimal quantum convolutional codes are constructed by using constacyclic codes. Moreover, these quantum codes constructed in this paper are different from the ones in the literature.

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“…Using CSS construction, researchers have always obtained good families of quantum codes from linear codes. The paper [11] extends this idea to obtain quantum product codes using linear product codes from CSS construction. Theorem 8.3 and subsequent results taken from [11] show the existence of asymmetric quantum product codes with specific parameters.…”

Section: Introductionmentioning

confidence: 99%