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Depth-Optimized Quantum Circuit of Gauss–Jordan Elimination

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Titel: Depth-Optimized Quantum Circuit of Gauss–Jordan Elimination
Autoren: Kyungbae Jang, Yujin Oh, Hwajeong Seo
Quelle: Applied Sciences, Vol 14, Iss 19, p 8579 (2024)
Verlagsinformationen: MDPI AG
Publikationsjahr: 2024
Bestand: Directory of Open Access Journals: DOAJ Articles
Schlagwörter: quantum computers, information set decoding, Gauss–Jordan elimination, Grover’s search, Technology, Engineering (General). Civil engineering (General), TA1-2040, Biology (General), QH301-705.5, Physics, QC1-999, Chemistry, QD1-999
Beschreibung: Quantum computers have the capacity to solve certain complex problems more efficiently than classical computers. To fully leverage these quantum advantages, adapting classical arithmetic for quantum systems in a circuit level is essential. In this paper, we introduce a depth-optimized quantum circuit of Gauss–Jordan elimination for matrices in binary. This quantum circuit is a crucial module for accelerating Information Set Decoding (ISD) using Grover’s algorithm. ISD is a cryptographic technique used in analyzing code-based cryptographic algorithms. When combined with Grover’s search, it achieves a square root reduction in complexity. The proposed method emphasizes the potential for parallelization in the quantum circuit implementation of Gauss–Jordan elimination. We allocate additional ancilla qubits to enable parallel operations within the target matrix and further reuse these ancilla qubits to minimize overhead from our additional allocation. The proposed quantum circuit for Gauss–Jordan elimination achieves the lowest Toffoli depth compared to the-state-of-art previous works.
Publikationsart: article in journal/newspaper
Sprache: English
Relation: https://www.mdpi.com/2076-3417/14/19/8579; https://doaj.org/toc/2076-3417; https://doaj.org/article/b94346b6a324428b90e755f833367c81
DOI: 10.3390/app14198579
Verfügbarkeit: https://doi.org/10.3390/app14198579
https://doaj.org/article/b94346b6a324428b90e755f833367c81
Dokumentencode: edsbas.CF3700DC
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  – Url: https://doi.org/10.3390/app14198579#
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  Data: Depth-Optimized Quantum Circuit of Gauss–Jordan Elimination
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  Data: <searchLink fieldCode="AR" term="%22Kyungbae+Jang%22">Kyungbae Jang</searchLink><br /><searchLink fieldCode="AR" term="%22Yujin+Oh%22">Yujin Oh</searchLink><br /><searchLink fieldCode="AR" term="%22Hwajeong+Seo%22">Hwajeong Seo</searchLink>
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  Data: Applied Sciences, Vol 14, Iss 19, p 8579 (2024)
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  Data: MDPI AG
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  Data: 2024
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  Data: <searchLink fieldCode="DE" term="%22quantum+computers%22">quantum computers</searchLink><br /><searchLink fieldCode="DE" term="%22information+set+decoding%22">information set decoding</searchLink><br /><searchLink fieldCode="DE" term="%22Gauss–Jordan+elimination%22">Gauss–Jordan elimination</searchLink><br /><searchLink fieldCode="DE" term="%22Grover%27s+search%22">Grover’s search</searchLink><br /><searchLink fieldCode="DE" term="%22Technology%22">Technology</searchLink><br /><searchLink fieldCode="DE" term="%22Engineering+%28General%29%2E+Civil+engineering+%28General%29%22">Engineering (General). Civil engineering (General)</searchLink><br /><searchLink fieldCode="DE" term="%22TA1-2040%22">TA1-2040</searchLink><br /><searchLink fieldCode="DE" term="%22Biology+%28General%29%22">Biology (General)</searchLink><br /><searchLink fieldCode="DE" term="%22QH301-705%2E5%22">QH301-705.5</searchLink><br /><searchLink fieldCode="DE" term="%22Physics%22">Physics</searchLink><br /><searchLink fieldCode="DE" term="%22QC1-999%22">QC1-999</searchLink><br /><searchLink fieldCode="DE" term="%22Chemistry%22">Chemistry</searchLink><br /><searchLink fieldCode="DE" term="%22QD1-999%22">QD1-999</searchLink>
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  Label: Description
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  Data: Quantum computers have the capacity to solve certain complex problems more efficiently than classical computers. To fully leverage these quantum advantages, adapting classical arithmetic for quantum systems in a circuit level is essential. In this paper, we introduce a depth-optimized quantum circuit of Gauss–Jordan elimination for matrices in binary. This quantum circuit is a crucial module for accelerating Information Set Decoding (ISD) using Grover’s algorithm. ISD is a cryptographic technique used in analyzing code-based cryptographic algorithms. When combined with Grover’s search, it achieves a square root reduction in complexity. The proposed method emphasizes the potential for parallelization in the quantum circuit implementation of Gauss–Jordan elimination. We allocate additional ancilla qubits to enable parallel operations within the target matrix and further reuse these ancilla qubits to minimize overhead from our additional allocation. The proposed quantum circuit for Gauss–Jordan elimination achieves the lowest Toffoli depth compared to the-state-of-art previous works.
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  Data: https://www.mdpi.com/2076-3417/14/19/8579; https://doaj.org/toc/2076-3417; https://doaj.org/article/b94346b6a324428b90e755f833367c81
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        Value: 10.3390/app14198579
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: quantum computers
        Type: general
      – SubjectFull: information set decoding
        Type: general
      – SubjectFull: Gauss–Jordan elimination
        Type: general
      – SubjectFull: Grover’s search
        Type: general
      – SubjectFull: Technology
        Type: general
      – SubjectFull: Engineering (General). Civil engineering (General)
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      – SubjectFull: QH301-705.5
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      – SubjectFull: QD1-999
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      – TitleFull: Depth-Optimized Quantum Circuit of Gauss–Jordan Elimination
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            NameFull: Hwajeong Seo
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              Y: 2024
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