Nonsemisimple extensions of the Ising anyon model developed in our previous work Iulianelli et al., [Nat. Commun. 16, 6408 (2025)] enable universal topological quantum computation via braiding alone, overcoming the Clifford-only limitation of semisimple theories. The nonsemisimple theory provides new anyon types indexed by a real parameter $\alpha$, 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 $\alpha$ where the computational subspace remains positive-definite. We identify special values of $\alpha$ 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 $\alpha$ is not required for efficient gate compilation, significantly enhancing the physical plausibility of nonsemisimple anyonic architectures.

Close

PrevNext

View figure in article

• Geometric & topological phases
• PT-symmetric quantum mechanics
• Topological field theories
• Topological quantum computing
• Non-Hermitian systems
• Ising model