High-Fidelity Universal Quantum Gate Compilation for Non-semisimple Ising Anyons via Genetic Algorithm-Optimized Solovay-Kitaev Decomposition

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.