High-Fidelity Universal Quantum Gate Compilation for Non-semisimple Ising Anyons via Genetic Algorithm-Optimized Solovay-Kitaev Decomposition
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914259875659776 |
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| author | Long, Jiangwei Liu, Zihui Li, Yizhi Zhong, Jianxin Meng, Lijun |
| author_facet | Long, Jiangwei Liu, Zihui Li, Yizhi Zhong, Jianxin Meng, Lijun |
| contents | We present a systematic numerical construction of a universal quantum gate set for topological quantum computation based on the non-semisimple Ising anyons model. By employing a Genetic Algorithm-enhanced Solovay-Kitaev Algorithm (GA-enhanced SKA), we achieve high-fidelity approximations of standard single-qubit gates (Hadamard H-gate and phase T-gate) with a recursion level of just three, meeting the fidelity requirements for fault-tolerant quantum computation. Our numerical results demonstrate that for the critical parameter range α \in [2.001, 2.022], a few braiding operations can approximate the local equivalence class [CNOT] with high precision. Specifically, at α =2.012, 2.015, 2.020, and 2.022, we successfully construct a universal gate set {H, T, CNOT} with leakage errors of two-qubit gate below 0.07,0.08,0.09 and 0.10, respectively. This work establishes a new pathway towards universal quantum computation using non-semisimple Ising anyons, overcoming the limitations of traditional Ising models through optimized braiding sequences and Genetic Algorithm-driven compilation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Fidelity Universal Quantum Gate Compilation for Non-semisimple Ising Anyons via Genetic Algorithm-Optimized Solovay-Kitaev Decomposition Long, Jiangwei Liu, Zihui Li, Yizhi Zhong, Jianxin Meng, Lijun Quantum Physics We present a systematic numerical construction of a universal quantum gate set for topological quantum computation based on the non-semisimple Ising anyons model. By employing a Genetic Algorithm-enhanced Solovay-Kitaev Algorithm (GA-enhanced SKA), we achieve high-fidelity approximations of standard single-qubit gates (Hadamard H-gate and phase T-gate) with a recursion level of just three, meeting the fidelity requirements for fault-tolerant quantum computation. Our numerical results demonstrate that for the critical parameter range α \in [2.001, 2.022], a few braiding operations can approximate the local equivalence class [CNOT] with high precision. Specifically, at α =2.012, 2.015, 2.020, and 2.022, we successfully construct a universal gate set {H, T, CNOT} with leakage errors of two-qubit gate below 0.07,0.08,0.09 and 0.10, respectively. This work establishes a new pathway towards universal quantum computation using non-semisimple Ising anyons, overcoming the limitations of traditional Ising models through optimized braiding sequences and Genetic Algorithm-driven compilation. |
| title | High-Fidelity Universal Quantum Gate Compilation for Non-semisimple Ising Anyons via Genetic Algorithm-Optimized Solovay-Kitaev Decomposition |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.13194 |