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arXiv · 2505.01774

The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm

Jiangwei Long·Yizhi Li·Jianxin Zhong·Lijun Meng
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Abstract

We study systematically numerical method into constructing a universal quantum gate set for topological quantum computation (TQC) using SU(2)k anyon models. The F-matrices and R-symbol were computed through the q-deformed representation theory of SU(2), enabling precise determination of elementary braiding matrices (EBMs) for SU(2)k anyon systems. Quantum gates were derived from these EBMs. One-qubit gates were synthesized using a genetic algorithm-enhanced Solovay-Kitaev algorithm (GA-enhanced SKA), while two-qubit gates were constructed through brute-force search or GA optimization to approximate local equivalence classes [CNOT]. Implementing this framework for SU(2)5, SU(2)6, and SU(2)7 models successfully generated the canonical universal gate set {H-gate, T-gate, CNOT-gate}. These numerical results provide conclusive verification of the universal quantum computation capabilities inherent in SU(2)k anyon models. Furthermore, we get exact implementations of the local equivalence class [SWAP] using nine EBMs in each model.

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Jiangwei Long, Yizhi Li, Jianxin Zhong, Lijun Meng. 2025-05-03. The construction of a universal quantum gate set for the SU(2)k (k=5,6,7) anyon models via genetic optimized algorithm. https://doi.org/10.1016/j.physleta.2025.131142

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