analiza aiqbench
This is a numerical study of compiling standard single-qubit gates (H and T) and approximating a CNOT-equivalent operation using braids of non-semisimple Ising anyons, with a genetic algorithm tuning a Solovay-Kitaev decomposition. The fidelity results are simulations, and the CNOT approximation holds only in a narrow parameter window (α ≈ 2.001 to 2.022), so the work doesn't yet show a practical route to hardware. Readers should treat it as a step toward a compilation framework for topological quantum computing, not as evidence that such anyons can be realized or scaled.
High-Fidelity Universal Quantum Gate Compilation for Non-semisimple Ising Anyons via Genetic Algorithm-Optimized Solovay-Kitaev Decomposition
arXiv:2511.13194v3 Announce Type: replace 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 $\alpha \in [2.001,\, 2.022]$, 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 $\alpha$ and gate fidelity, and it delivers direct numerical evidence for the universality of non-semisimple Ising anyons.
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 $\alpha \in [2.001,\, 2.022]$, 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 $\alpha$ and gate fidelity, and it delivers direct numerical evidence for the universality of non-semisimple Ising anyons.
arXiv:2511.13194 [quant-ph]
(or arXiv:2511.13194v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2511.13194 Focus to learn more arXiv-issued DOI via DataCite
J. Phys. A: Math. Theor. (2026)
https://doi.org/10.1088/1751-8121/ae91a0 Focus to learn more DOI(s) linking to related resources
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 270 cuvinte