A Novel and Efficient Stabilizer Codes Over NonCyclic Hadamard Difference Sets for Quantum System.
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| Title: | A Novel and Efficient Stabilizer Codes Over NonCyclic Hadamard Difference Sets for Quantum System. |
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| Authors: | Goswami, Shivender1 shivendrgoswami@gmail.com, Kumar, Manoj2 sdmkg1@gmail.com, Mishra, R. K.3 rkmsit@rediffmail.com, Rathor, Akash1 akashrathor9760@gmail.com |
| Source: | IAENG International Journal of Applied Mathematics. Jul2024, Vol. 54 Issue 7, p1416-1426. 11p. |
| Subjects: | Difference sets, Parity-check matrix, Binary operations, Circulant matrices, Information storage & retrieval systems, Hadamard codes, Permutations, Cyclic codes, Markov spectrum |
| Abstract: | Quantum error correction lies at the heart of building reliable quantum information processing systems. Stabilizer codes, a fundamental class of quantum errorcorrecting codes, play a pivotal role in mitigating the adverse effects of noise and decoherence in quantum systems. This paper introduces a novel construction of quantum stabilizer codes using Hadamard difference sets, an elegant mathematical concept derived from combinatorial design theory. In this paper, the construction of the quantum stabilizer codes over non- cyclic Hadamard difference sets with parameters (4m²,2m²-m, m²-m), where m is a positive integer is discussed. Firstly, the parity check matrices are constructed from the Circulant permutation matrices with the help of Hadamard difference sets and then, the Symplectic inner product condition for Hadamard difference sets over binary operation for parity check matrices are obtained to affirm the commutative condition for Stabilizer operators which is vital for the error detection. For application, we constructed a Hadamard difference sets with parameters (16,6,2) for m = 2 of ordered pair of the group Z2 Z8 × (non-cyclic group) and quantum stabilizer codes are obtained by parity-check matrix. [ABSTRACT FROM AUTHOR] |
| Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: A Novel and Efficient Stabilizer Codes Over NonCyclic Hadamard Difference Sets for Quantum System. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Goswami%2C+Shivender%22">Goswami, Shivender</searchLink><relatesTo>1</relatesTo><i> shivendrgoswami@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Kumar%2C+Manoj%22">Kumar, Manoj</searchLink><relatesTo>2</relatesTo><i> sdmkg1@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Mishra%2C+R%2E+K%2E%22">Mishra, R. K.</searchLink><relatesTo>3</relatesTo><i> rkmsit@rediffmail.com</i><br /><searchLink fieldCode="AR" term="%22Rathor%2C+Akash%22">Rathor, Akash</searchLink><relatesTo>1</relatesTo><i> akashrathor9760@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jul2024, Vol. 54 Issue 7, p1416-1426. 11p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Difference+sets%22">Difference sets</searchLink><br /><searchLink fieldCode="DE" term="%22Parity-check+matrix%22">Parity-check matrix</searchLink><br /><searchLink fieldCode="DE" term="%22Binary+operations%22">Binary operations</searchLink><br /><searchLink fieldCode="DE" term="%22Circulant+matrices%22">Circulant matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Information+storage+%26+retrieval+systems%22">Information storage & retrieval systems</searchLink><br /><searchLink fieldCode="DE" term="%22Hadamard+codes%22">Hadamard codes</searchLink><br /><searchLink fieldCode="DE" term="%22Permutations%22">Permutations</searchLink><br /><searchLink fieldCode="DE" term="%22Cyclic+codes%22">Cyclic codes</searchLink><br /><searchLink fieldCode="DE" term="%22Markov+spectrum%22">Markov spectrum</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Quantum error correction lies at the heart of building reliable quantum information processing systems. Stabilizer codes, a fundamental class of quantum errorcorrecting codes, play a pivotal role in mitigating the adverse effects of noise and decoherence in quantum systems. This paper introduces a novel construction of quantum stabilizer codes using Hadamard difference sets, an elegant mathematical concept derived from combinatorial design theory. In this paper, the construction of the quantum stabilizer codes over non- cyclic Hadamard difference sets with parameters (4m²,2m²-m, m²-m), where m is a positive integer is discussed. Firstly, the parity check matrices are constructed from the Circulant permutation matrices with the help of Hadamard difference sets and then, the Symplectic inner product condition for Hadamard difference sets over binary operation for parity check matrices are obtained to affirm the commutative condition for Stabilizer operators which is vital for the error detection. For application, we constructed a Hadamard difference sets with parameters (16,6,2) for m = 2 of ordered pair of the group Z2 Z8 × (non-cyclic group) and quantum stabilizer codes are obtained by parity-check matrix. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 1416 Subjects: – SubjectFull: Difference sets Type: general – SubjectFull: Parity-check matrix Type: general – SubjectFull: Binary operations Type: general – SubjectFull: Circulant matrices Type: general – SubjectFull: Information storage & retrieval systems Type: general – SubjectFull: Hadamard codes Type: general – SubjectFull: Permutations Type: general – SubjectFull: Cyclic codes Type: general – SubjectFull: Markov spectrum Type: general Titles: – TitleFull: A Novel and Efficient Stabilizer Codes Over NonCyclic Hadamard Difference Sets for Quantum System. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Goswami, Shivender – PersonEntity: Name: NameFull: Kumar, Manoj – PersonEntity: Name: NameFull: Mishra, R. K. – PersonEntity: Name: NameFull: Rathor, Akash IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 07 Text: Jul2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 19929978 Numbering: – Type: volume Value: 54 – Type: issue Value: 7 Titles: – TitleFull: IAENG International Journal of Applied Mathematics Type: main |
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