Maximal entanglement-assisted quantum error correction codes from the skew group ring F4 (sic)? G by a heuristic search scheme

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dc.authoridhttps://orcid.org/0000-0002-2084-6260
dc.authoridhttps://orcid.org/0000-0002-5229-4018
dc.authorscopusid36728602600
dc.authorscopusid55420759300
dc.authorwosidABB-4228-2020
dc.authorwosidG-2829-2015
dc.contributor.authorŞahinkaya, Serap
dc.contributor.authorKorban, Adrian
dc.contributor.authorÜstün, Deniz
dc.date.accessioned2024-08-01T12:22:27Z
dc.date.available2024-08-01T12:22:27Z
dc.date.issued2022
dc.departmentFakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
dc.description.abstractConstruction of maximal entanglement-assisted quantum error correction (EAQEC) codes is one of the fundamental problems of quantum computing and quantum information. The objective of this paper is twofold: firstly, to obtain all possible construction matrices of the linear codes over the skew group ring F-4 (sic)(phi) G, where G is the cyclic and dihedral groups of finite orders; and secondly, to obtain some good maximal EAQEC codes over the finite field F-4 by using skew construction matrices. Additionally, to speed up the computational search time, we employ a nature inspired heuristic optimisation algorithm, the virus optimisation (VO) algorithm. With our method, we obtain a number of good maximal EAQEC codes over the finite field F-4 in a reasonably short time. In particular, we improve the lower bounds of 18 maximal EAQEC codes that exist in the literature. Moreover, some of our EAQEC codes turn out to be also maximum distance separable (MDS) codes. Also, by using our construction matrices, we provide counterexamples to Theorems 4 and 5 of Lai et al. (Quantum Inf Process 13(4):957-990, 2014), on the non-existence of maximal EAQEC codes with parameters [En, 1, n; n - 1]] and [[n, n - 1, 2; 1]] for an even length n. We also give a counterexample to another Theorem found in Lai and Ashikhmin (IEEE Trans Inf Theory 64:(1), 622-639, 2018), which states that there is no entanglement-assisted stabilizer code with parameters [[4, 2, 3; 2]](4).
dc.identifier.citationŞahinkaya, S., Korban, A. ve Ustun, D. (2022). Maximal entanglement-assisted quantum error correction codes from the skew group ring F4 (sic)? G by a heuristic search scheme. Quantum Inf Process 21, (4), 156 (2022). Erişim adresi: https://doi.org/10.1007/s11128-022-03500-1
dc.identifier.doi10.1007/s11128-022-03500-1
dc.identifier.issn1570-0755
dc.identifier.issn1573-1332
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85128212367
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1007/s11128-022-03500-1
dc.identifier.urihttps://hdl.handle.net/20.500.13099/313
dc.identifier.volume21en_US
dc.identifier.wosWOS:000781928600001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorÜstün, Deniz
dc.language.isoen
dc.publisherSpringer Link
dc.relation.ispartofQuantum Information Processing
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/restrictedAccess
dc.subjectG-codes
dc.subjectSkew codes
dc.subjectEntanglement-assisted quantum error correction codes
dc.titleMaximal entanglement-assisted quantum error correction codes from the skew group ring F4 (sic)? G by a heuristic search scheme
dc.typeArticle

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