Robust Universal Braiding with Non-semisimple Ising Anyons
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915948024299520 |
|---|---|
| author | Iulianelli, Filippo Kim, Sung Sussan, Joshua Lauda, Aaron D. |
| author_facet | Iulianelli, Filippo Kim, Sung Sussan, Joshua Lauda, Aaron D. |
| contents | 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 $α$, 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 $α$ where the computational subspace remains positive-definite. We identify special values of $α$ 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 $α$ is not required for efficient gate compilation, significantly enhancing the physical plausibility of non-semisimple anyonic architectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02843 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Universal Braiding with Non-semisimple Ising Anyons Iulianelli, Filippo Kim, Sung Sussan, Joshua Lauda, Aaron D. Quantum Physics Strongly Correlated Electrons Geometric Topology Quantum Algebra 81P68, 18M20, 57K16, 17B37, 81R50 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 $α$, 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 $α$ where the computational subspace remains positive-definite. We identify special values of $α$ 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 $α$ is not required for efficient gate compilation, significantly enhancing the physical plausibility of non-semisimple anyonic architectures. |
| title | Robust Universal Braiding with Non-semisimple Ising Anyons |
| topic | Quantum Physics Strongly Correlated Electrons Geometric Topology Quantum Algebra 81P68, 18M20, 57K16, 17B37, 81R50 |
| url | https://arxiv.org/abs/2509.02843 |