High-fidelity universal quantum gate compilation for non-semisimple ising anyons via genetic algorithm-optimized Solovay–Kitaev decomposition

Abstract Non-semisimple Ising anyons extend the fusion space of conventional Ising models and offer a new route toward universal topological quantum computation. However, how to construct a high-fidelity universal quantum gate set that meets fault-tolerant thresholds via braiding operations of non-semisimple Ising anyons remains unexplored. 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 ∈ [2.001, 2.022], a few braiding operations can approximate the local equivalence class [CNOT] with high precision. In contrast to prior theoretical works that established the universality of non-semisimple Ising anyons, this work provides the first complete, executable, and parameter-optimized compilation scheme for high-fidelity universal gates. It quantifies the relationship between the key physical parameter α and gate fidelity, and it delivers direct numerical evidence for the universality of non-semisimple Ising anyons.