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The representation of braid group in mixed-boundary punctures model of ising anyons on the toric code.

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Title: The representation of braid group in mixed-boundary punctures model of ising anyons on the toric code.
Authors: Shen, Yao1 (AUTHOR) shenyaophysics@hotmail.com, Zhang, Fu-Lin2 (AUTHOR)
Source: Physics Letters A. Jan2026, Vol. 565, pN.PAG-N.PAG. 1p.
Subjects: Braid group (Knot theory), Anyons, Quantum error correcting codes, Quantum gates, Fault tolerance (Engineering), Error-correcting codes, Quantum information science, Quantum computing
Abstract: • We introduce the realization of single qubit gates and universal quantum gates based on the mixed-boundary punctures model. • Our work delivers a concrete and practical blueprint for achieving universal topological quantum computation. • We offer new methods and insights into the feasibility and realizability of TQC on the toric code. • We present the representation of the braid group in the mixed-boundary punctures model. • We investigate 3-qubit and 5-qubit stabilizer codes to demonstrate the fault-tolerance. This work explores a theoretical scheme for universal topological quantum computation using non-Abelian anyons within a modified toric code setting. Recent developments, particularly the mixed-boundary punctures model proposed by Benhemou et al., provide a pathway toward realizing Ising anyons on Kitaev toric code. Based on this model, we construct single-qubit Pauli X and Z gates, as well as universal Clifford gate set including CNOT, Hadamard, and Phase gates. We also design 3- and 5-qubit stabilizer codes within the same framework. Furthermore, we establish an explicit correspondence between the braid group representation in the mixed-boundary puncture model and the qubit representation enabling its quantum circuit realization. Our results offer a concrete theoretical framework for leveraging non-Abelian anyons in scalable and fault-tolerant quantum computation. [ABSTRACT FROM AUTHOR]
Copyright of Physics Letters A is the property of Elsevier B.V. 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.)
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DbLabel: Engineering Source
An: 189669153
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  Label: Title
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  Data: The representation of braid group in mixed-boundary punctures model of ising anyons on the toric code.
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  Data: <searchLink fieldCode="AR" term="%22Shen%2C+Yao%22">Shen, Yao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> shenyaophysics@hotmail.com</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Fu-Lin%22">Zhang, Fu-Lin</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Physics+Letters+A%22">Physics Letters A</searchLink>. Jan2026, Vol. 565, pN.PAG-N.PAG. 1p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Braid+group+%28Knot+theory%29%22">Braid group (Knot theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Anyons%22">Anyons</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+error+correcting+codes%22">Quantum error correcting codes</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+gates%22">Quantum gates</searchLink><br /><searchLink fieldCode="DE" term="%22Fault+tolerance+%28Engineering%29%22">Fault tolerance (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Error-correcting+codes%22">Error-correcting codes</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+information+science%22">Quantum information science</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+computing%22">Quantum computing</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: • We introduce the realization of single qubit gates and universal quantum gates based on the mixed-boundary punctures model. • Our work delivers a concrete and practical blueprint for achieving universal topological quantum computation. • We offer new methods and insights into the feasibility and realizability of TQC on the toric code. • We present the representation of the braid group in the mixed-boundary punctures model. • We investigate 3-qubit and 5-qubit stabilizer codes to demonstrate the fault-tolerance. This work explores a theoretical scheme for universal topological quantum computation using non-Abelian anyons within a modified toric code setting. Recent developments, particularly the mixed-boundary punctures model proposed by Benhemou et al., provide a pathway toward realizing Ising anyons on Kitaev toric code. Based on this model, we construct single-qubit Pauli X and Z gates, as well as universal Clifford gate set including CNOT, Hadamard, and Phase gates. We also design 3- and 5-qubit stabilizer codes within the same framework. Furthermore, we establish an explicit correspondence between the braid group representation in the mixed-boundary puncture model and the qubit representation enabling its quantum circuit realization. Our results offer a concrete theoretical framework for leveraging non-Abelian anyons in scalable and fault-tolerant quantum computation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Physics Letters A is the property of Elsevier B.V. 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:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.physleta.2025.131175
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 1
        StartPage: N.PAG
    Subjects:
      – SubjectFull: Braid group (Knot theory)
        Type: general
      – SubjectFull: Anyons
        Type: general
      – SubjectFull: Quantum error correcting codes
        Type: general
      – SubjectFull: Quantum gates
        Type: general
      – SubjectFull: Fault tolerance (Engineering)
        Type: general
      – SubjectFull: Error-correcting codes
        Type: general
      – SubjectFull: Quantum information science
        Type: general
      – SubjectFull: Quantum computing
        Type: general
    Titles:
      – TitleFull: The representation of braid group in mixed-boundary punctures model of ising anyons on the toric code.
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      – PersonEntity:
          Name:
            NameFull: Shen, Yao
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          Name:
            NameFull: Zhang, Fu-Lin
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          Dates:
            – D: 05
              M: 01
              Text: Jan2026
              Type: published
              Y: 2026
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              Value: 565
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            – TitleFull: Physics Letters A
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