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arXiv:2511.13194 · Journal of Physics A Mathematical and Theoretical

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

Jiangwei Long, Zihui Liu, Yizhi Li, Jianxin Zhong, Lijun Meng

quant-phSubmitted Nov 17, 2025• Announced Nov 18, 2025• 0 citations• Revised Oct 29, 2026 (v3)
v1 · Nov 17, 2025v2 · Jan 17, 2026v3 · Oct 29, 2026
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Abstract

Non-semisimple Ising anyons extend the fusion space of conventional Ising models and offer a new route toward universal topological quantum computation (TQC). 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 $α\in [2.001,\, 2.022]$, a few braiding operations can approximate the local equivalence class $[\mathrm{CNOT}]$ 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.

Journal reference
J. Phys. A: Math. Theor. (2026)
DOI
10.1088/1751-8121/ae91a0
Comments
20 pages, 7 figures

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Non-semisimple extensions of the Ising anyon model developed in our previous work enable universal topological quantum computation via braiding alone, overcoming the Clifford-only limitation of semisimple theories. The non-semisimple theory provides new anyon types indexed by a real parameter ααα, the neglecton. Braiding acts unitarily with respect to an indefinite Hermitian form, while the computational subspace sits in a positive-definite sector. We demonstrate that this universality is robust, persisting over an open interval of the neglecton parameter ααα where the computational subspace remains positive-definite. We identify special values of ααα where the physical subspace decouples exactly from negative-norm components, ensuring fully unitary evolution and suppressed leakage. We further present an alternative encoding supporting exact single-qubit Clifford gates alongside a non-Clifford phase gate. We show that high-precision tuning of ααα is not required for efficient gate compilation, significantly enhancing the physical plausibility of non-semisimple anyonic architectures.
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