Realizing a Universal Quantum Gate Set via Double-Braiding of SU(2)k Anyon Models

• URL: http://arxiv.org/abs/2602.15324v1
• Date: Tue, 17 Feb 2026 03:11:09 GMT
• Title: Realizing a Universal Quantum Gate Set via Double-Braiding of SU(2)k Anyon Models
• Authors: Jiangwei Long, Zihui Liu, Yizhi Li, Jianxin Zhong, Lijun Meng,
• Abstract summary: We investigate the implementation of a universal gate set via double-braiding within SU(2)k anyon models.<n>For two-qubit entangling gates, Genetic Algorithm (GA) yields braidwords of 30 braiding operations that approximate the local equivalence class [CNOT]<n>Our numerical results provide strong evidence that double-braiding in SU(2)k anyons models is capable of universal quantum computation.
• Score: 7.648391361564701
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We systematically investigate the implementation of a universal gate set via double-braiding within SU(2)k anyon models. The explicit form of the double elementary braiding matrices (DEBMs) in these models are derived from the F-matrices and R-symbols obtained via the q-deformed representation theory of SU(2). Using these EBMs, standard single-qubit gates are synthesized up to a global phase by a Genetic Algorithm-enhanced Solovay-Kitaev Algorithm (GA-enhanced SKA), achieving the accuracy required for fault-tolerant quantum computation with only 2-level decomposition. For two-qubit entangling gates, Genetic Algorithm (GA) yields braidwords of 30 braiding operations that approximate the local equivalence class [CNOT]. Theoretically, we demonstrate that performing double-braiding in a three-anyon (six-anyon) encoding of single-qubit (two-qubit) is topologically equivalent to a protocol requiring the physical manipulation of only one (three) anyons to execute arbitrary braids. Our numerical results provide strong evidence that double-braiding in SU(2)k anyons models is capable of universal quantum computation. Moreover, the proposed protocol offers a potential new strategy for significantly reducing the number of non-Abelian anyons that need to be physically manipulated in future braiding-based topological quantum computations (TQC).

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