Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).

Article 
MathSciNet 
CAS 
ADS 

Google Scholar
 

Wen, X. G. Topological orders in rigid states. Int. J. Mod. Phys. B 04, 239–271 (1990).

Article 
MathSciNet 
ADS 

Google Scholar
 

Dennis, E., Kitaev, A., Landahl, A. & Preskill, J. Topological quantum memory. J. Math. Phys. 43, 4452–4505 (2002).

Article 
MathSciNet 
ADS 

Google Scholar
 

Freedman, M. H., Larsen, M. & Wang, Z. A modular functor which is universal for quantum computation. Commun. Math. Phys. 227, 605–622 (2002).

Article 
MathSciNet 
ADS 

Google Scholar
 

Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Sarma, S. D. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

Article 
MathSciNet 
CAS 
ADS 

Google Scholar
 

Goldin, G. A., Menikoff, R. & Sharp, D. H. Comments on ‘general theory for quantum statistics in two dimensions’. Phys. Rev. Lett. 54, 603 (1985).

Article 
MathSciNet 
CAS 
PubMed 
ADS 

Google Scholar
 

Etingof, P., Rowell, E. & Witherspoon, S. Braid group representations from twisted quantum doubles of finite groups. Pac. J. Math. 234, 33–41 (2008).

Article 
MathSciNet 

Google Scholar
 

Mochon, C. Anyons from nonsolvable finite groups are sufficient for universal quantum computation. Phys. Rev. A 67, 022315 (2003).

Article 
ADS 

Google Scholar
 

Mochon, C. Anyon computers with smaller groups. Phys. Rev. A 69, 032306 (2004).

Article 
ADS 

Google Scholar
 

Wegner, F. J. Duality in generalized Ising models and phase transitions without local order parameters. J. Math. Phys. 12, 2259–2272 (1971).

Article 
MathSciNet 
ADS 

Google Scholar
 

Leinaas, J. M. & Myrheim, J. On the theory of identical particles. Nuovo Cim. B 37, 1–23 (1977).

Article 
ADS 

Google Scholar
 

Wilczek, F. Quantum mechanics of fractional-spin particles. Phys. Rev. Lett. 49, 957–959 (1982).

Article 
MathSciNet 
CAS 
ADS 

Google Scholar
 

Bravyi, S. B. & Kitaev, A. Y. Quantum codes on a lattice with boundary. Preprint at arxiv.org/abs/quant-ph/9811052 (1998).

Freedman, M. H. & Meyer, D. A. Projective plane and planar quantum codes. Found. Comput. Math. 1, 325–332 (2001).

Article 
MathSciNet 

Google Scholar
 

Tantivasadakarn, N., Vishwanath, A. & Verresen, R. Hierarchy of topological order from finite-depth unitaries, measurement, and feedforward. PRX Quantum 4, 020339 (2023).

Article 
ADS 

Google Scholar
 

Tantivasadakarn, N., Thorngren, R., Vishwanath, A. & Verresen, R. Long-range entanglement from measuring symmetry-protected topological phases. Phys. Rev. X 14, 021040 (2024).

CAS 

Google Scholar
 

Verresen, R., Tantivasadakarn, N. & Vishwanath, A. Efficiently preparing Schrödinger’s cat, fractons and non-abelian topological order in quantum devices. Preprint at arxiv.org/abs/2112.03061 (2021).

Tantivasadakarn, N., Verresen, R. & Vishwanath, A. Shortest route to non-Abelian topological order on a quantum processor. Phys. Rev. Lett. 131, 060405 (2023).

Article 
MathSciNet 
CAS 
PubMed 
ADS 

Google Scholar
 

Bravyi, S., Kim, I., Kliesch, A. & Koenig, R. Adaptive constant-depth circuits for manipulating non-abelian anyons. Preprint at arxiv.org/abs/2205.01933 (2022).

Lyons, A., Lo, C. F. B., Tantivasadakarn, N., Vishwanath, A. & Verresen, R. Protocols for creating anyons and defects via gauging. Phys. Rev. Lett. 135, 200405 (2025).

Article 
MathSciNet 
CAS 
PubMed 
ADS 

Google Scholar
 

Ren, Y., Tantivasadakarn, N. & Williamson, D. J. Efficient preparation of solvable anyons with adaptive quantum circuits. Phys. Rev. X 15, 031060 (2025).

CAS 

Google Scholar
 

Huang, S.-J. & Chen, Y. Generating logical magic states with the aid of non-Abelian topological order. Preprint at arxiv.org/abs/2502.00998 (2025).

Davydova, M. et al. Universal fault tolerant quantum computation in 2D without getting tied in knots. Preprint at arxiv.org/abs/2503.15751 (2025).

Sajith, R., Song, Z., Roberts, B., Menon, V. & Li, Y. Non-Clifford gates between stabilizer codes via non-Abelian topological order. PRX Quantum 7, 010361 (2026).

Kobayashi, R., Zhu, G. & Hsin, P.-S. Clifford hierarchy stabilizer codes: transversal non-Clifford gates and magic states. Phys. Rev. Lett. 136, 250802 (2026).

Warman, A. & Schafer-Nameki, S. Transversal clifford-hierarchy gates via non-Abelian surface codes. Preprint at arxiv.org/abs/2512.13777 (2025).

Iqbal, M. et al. Non-Abelian topological order and anyons on a trapped-ion processor. Nature 626, 505–511 (2024).

Article 
CAS 
PubMed 
ADS 

Google Scholar
 

Google Quantum AI and Collaborators Non-Abelian braiding of graph vertices in a superconducting processor. Nature 618, 264–269 (2023).

Article 
CAS 
ADS 

Google Scholar
 

Xu, S. et al. Non-Abelian braiding of fibonacci anyons with a superconducting processor. Nat. Phys. 20, 1469–1475 (2024).

Article 
CAS 

Google Scholar
 

Iqbal, M. et al. Qutrit toric code and parafermions in trapped ions. Nat. Commun. 16, 6301 (2025).

Article 
CAS 
PubMed 
PubMed Central 
ADS 

Google Scholar
 

Minev, Z. K. et al. Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials. Nat. Commun. 16, 6225 (2025).

Article 
CAS 
PubMed 
PubMed Central 
ADS 

Google Scholar
 

Aghaee, M. et al. Distinct lifetimes for X and Z loop measurements in a Majorana tetron device. Preprint at arxiv.org/abs/2507.08795 (2025).

Aghaee, M. et al. Interferometric single-shot parity measurement in InAs–Al hybrid devices. Nature 638, 651–655 (2025).

Article 
PubMed 
PubMed Central 
ADS 

Google Scholar
 

Ainsworth, R. & Slingerland, J. K. Topological qubit design and leakage. New J. Phys. 13, 065030 (2011).

Article 
ADS 

Google Scholar
 

Cui, S. X., Tian, K. T., Vasquez, J. F., Wang, Z. & Wong, H. M. The search for leakage-free entangling Fibonacci braiding gates. J. Phys. A Math. Theor. 52, 455301 (2019).

Article 
MathSciNet 
ADS 

Google Scholar
 

Burke, P. C., Aravanis, C., Aspman, J., Mareček, J. & Vala, J. Topological quantum compilation of two-qubit gates. Phys. Rev. A 110, 052616 (2024).

Article 
MathSciNet 
CAS 
ADS 

Google Scholar
 

Lyons, A. & Brown, B. J. Universal quantum computing with anyons is fault-tolerant. Preprint at arxiv.org/abs/2602.11258 (2026).

Overbosch, B. J. & Bais, F. A. Inequivalent classes of interference experiments with non-Abelian anyons. Phys. Rev. A 64, 062107 (2001).

Article 
ADS 

Google Scholar
 

Dauphinais, G. & Poulin, D. Fault-tolerant quantum error correction for non-Abelian anyons. Commun. Math. Phys. 355, 519–560 (2017).

Article 
MathSciNet 
ADS 

Google Scholar
 

Galindo, C., Rowell, E. & Wang, Z. On acyclic anyon models. Quantum Inf. Process. 17, 245 (2018).

Kitaev, A. Anyons based on a finite group. https://preskill.caltech.edu/ph219/prob7_07-kitaev.pdf (2007).

Levaillant, C., Bauer, B., Freedman, M., Wang, Z. & Bonderson, P. Universal gates via fusion and measurement operations on SU(2)4 anyons. Phys. Rev. A 92, 012301 (2015).

Article 
ADS 

Google Scholar
 

Cui, S. X. & Wang, Z. Universal quantum computation with metaplectic anyons. J. Math. Phys. 56, 032202 (2015).

Article 
MathSciNet 
ADS 

Google Scholar
 

Bonderson, P., Freedman, M. & Nayak, C. Measurement-only topological quantum computation. Phys. Rev. Lett. 101, 010501 (2008).

Article 
MathSciNet 
PubMed 
ADS 

Google Scholar
 

Cui, S. X., Hong, S.-M. & Wang, Z. Universal quantum computation with weakly integral anyons. Quantum Inf. Process. 14, 2687–2727 (2014).

Article 
MathSciNet 
ADS 

Google Scholar
 

Chen, L., Ren, Y., Fan, R. & Jaffe, A. A universal circuit set using the S3 quantum double. npj Quantum Inf. 11, 112 (2025).

Article 
ADS 

Google Scholar
 

Lo, C. F. B., Lyons, A., Verresen, R., Vishwanath, A. & Tantivasadakarn, N. Universal quantum computation with the S3 quantum double: a pedagogical exposition. Preprint at arxiv.org/abs/2502.14974 (2025).

Moses, S. A. et al. A race-track trapped-ion quantum processor. Phys. Rev. X 13, 041052 (2023).

CAS 

Google Scholar
 

Bombin, H. & Martin-Delgado, M. A. Family of non-Abelian Kitaev models on a lattice: topological condensation and confinement. Phys. Rev. B 78, 115421 (2008).

Article 
ADS 

Google Scholar
 

Beverland, M. F. et al. Protected gates for topological quantum field theories. J. Math. Phys. 57, 022201 (2016).

Article 
MathSciNet 
ADS 

Google Scholar
 

Shi, B. Seeing topological entanglement through the information convex. Phys. Rev. Res. 1, 033048 (2019).

Article 
CAS 

Google Scholar
 

Preskill, J. Topological quantum computation. https://www.preskill.caltech.edu/ph219/topological.pdf (2004).

Wootton, J. R., Burri, J., Iblisdir, S. & Loss, D. Error correction for non-Abelian topological quantum computation. Phys. Rev. X 4, 011051 (2014).


Google Scholar
 

de la Fuente, J. C. M., Feldman, N., Eisert, J. & Bauer, A. High-threshold decoding of non-Pauli codes for 2D universality. Preprint at arxiv.org/abs/2604.02033 (2026).

Iqbal, M., Dreyer, H. & Lo, C. F. B. Supporting data and code for “Topological Quantum Computation with S3 Quantum Double in Trapped Ions”. Zenodo. https://doi.org/10.5281/zenodo.18054264 (2025).