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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]
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Database: Engineering Source
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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]
ISSN:03759601
DOI:10.1016/j.physleta.2025.131175