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

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dc.authoridhttps://orcid.org/0000-0002-2084-6260en_US
dc.authoridhttps://orcid.org/0000-0002-5229-4018en_US
dc.authorscopusid36728602600en_US
dc.authorscopusid55420759300en_US
dc.authorwosidABB-4228-2020en_US
dc.authorwosidG-2829-2015en_US
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.issued2022en_US
dc.departmentFakülteler, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümüen_US
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).en_US
dc.identifier.citationŞahinkaya, S., Korban, A. ve Ustun, D. (2022). Maximal entanglement-assisted quantum error correction codes from the skew group ring F4 (sic)φ G by a heuristic search scheme. Quantum Inf Process 21, (4), 156 (2022). Erişim adresi: https://doi.org/10.1007/s11128-022-03500-1en_US
dc.identifier.doi10.1007/s11128-022-03500-1en_US
dc.identifier.issn1570-0755
dc.identifier.issn1573-1332
dc.identifier.issue4en_US
dc.identifier.scopus2-s2.0-85128212367en_US
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.wos000781928600001en_US
dc.identifier.wosqualityQ2en_US
dc.institutionauthorÜstün, Deniz
dc.language.isoengen_US
dc.publisherSpringer Linken_US
dc.relation.ispartofQuantum Information Processingen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/restrictedAccessen_US
dc.subjectG-codesen_US
dc.subjectSkew codesen_US
dc.subjectEntanglement-assisted quantum error correction codesen_US
dc.titleMaximal entanglement-assisted quantum error correction codes from the skew group ring F4 (sic)φ G by a heuristic search schemeen_US
dc.typearticleen_US

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