Kitaev, AY Fault-tolerant quantum computing by anyone. Ana. Physics. 3032–30 (2003). Article MathSciNet CAS ADS Google Scholar Wen, XG Topological orders in rigid states. Int. J.Mod. Physics. b 04239–271 (1990). Article MathSciNet ADS Google Scholar Dennis, E., Kitaev, A., Landahl, A., and Preskill, J. Topological quantum memory. J. Mathematics. Physics. 434452–4505 (2002). Article MathSciNet ADS
Kitaev, AY Fault-tolerant quantum computing by anyone. Ana. Physics. 3032–30 (2003).
Wen, XG Topological orders in rigid states. Int. J.Mod. Physics. b 04239–271 (1990).
Dennis, E., Kitaev, A., Landahl, A., and Preskill, J. Topological quantum memory. J. Mathematics. Physics. 434452–4505 (2002).
Freedman, M.H., Larsen, M. & Wang, Z. A modular functor that is universal for quantum computing. Community. Math. Physics. 227605–622 (2002).
Nayak, C., Simon, S.H., Stern, A., Freedman, M., and Sarma, S.D. Non-Abelian Anyons and Topological Quantum Computation. Mod. Rev. Physics. 801083-1159 (2008).
Goldin, G.A., Menikoff, R. & Sharp, D.H. Comments on the “general theory of quantum statistics in two dimensions.” Physics. Rev. Lett. 54603 (1985).
Etingof, P., Rowell, E., and Witherspoon, S. Representations of twisted groups from twisted quantum doubles of finite groups. Pac J. Mathematics. 23433–41 (2008).
Mochon, C. Anyons of non-soluble finite groups are sufficient for universal quantum calculus. Physics. Rev. A 67022315 (2003).
Mochon, C. Anyon computers with smaller groups. Physics. Rev. A 69032306 (2004).
Wegner, FJ Duality in generalized Ising models and phase transitions without local order parameters. J. Mathematics. Physics. 122259–2272 (1971).
Leinaas, JM & Myrheim, J. On the theory of identical particles. New Cim. b 371–23 (1977).
Wilczek, F. Quantum mechanics of fractional spin particles. Physics. Rev. Lett. 49957–959 (1982).
Bravyi, SB & Kitaev, AY Quantum codes in a boundary network. Preprint at arxiv.org/abs/quant-ph/9811052 (1998).
Freedman, MH & Meyer, DA Projective plane and planar quantum codes. Found. Computer. Math. 1325–332 (2001).
Tantivasadakarn, N., Vishwanath, A. & Verresen, R. Hierarchy of topological order from units of finite depth, measurement and advance. quantum PRX 4020339 (2023).
Tantivasadakarn, N., Thorngren, R., Vishwanath, A. and Verresen, R. Long-range entanglement from measurement of symmetry-protected topological phases. Physics. Rev.X 14021040 (2024).
Verresen, R., Tantivasadakarn, N. and Vishwanath, A. Efficient preparation of Schrödinger’s cat, fractons and non-Abelian topological order in quantum devices. Preprint at arxiv.org/abs/2112.03061 (2021).
Tantivasadakarn, N., Verresen, R., and Vishwanath, A. The shortest path to non-abelian topological order in a quantum processor. Physics. Rev. Lett. 131060405 (2023).
Bravyi, S., Kim, I., Kliesch, A., and Koenig, R. Constant-depth adaptive circuits for manipulating non-abelian anons. Preprint at arxiv.org/abs/2205.01933 (2022).
Lyons, A., Lo, CFB, Tantivasadakarn, N., Vishwanath, A., and Verresen, R. Protocols for creating defects and defects by measurement. Physics. Rev. Lett. 135200405 (2025).
Ren, Y., Tantivasadakarn, N., and Williamson, DJ Efficiently preparing any solvable problem with adaptive quantum circuits. Physics. Rev.X 15031060 (2025).
Huang, S.-J. & Chen, Y. Generation of logical magic states with the help of non-abelian topological order. Preprint at arxiv.org/abs/2502.00998 (2025).
Davydova, M. et al. Hassle-free 2D fault-tolerant universal quantum computing. Preprint at arxiv.org/abs/2503.15751 (2025).
Sajith, R., Song, Z., Roberts, B., Menon, V. and Li, Y. Non-Clifford gates between stabilizing codes using non-Abelian topological order. quantum PRX 7010361 (2026).
Kobayashi, R., Zhu, G. and Hsin, P.-S. Clifford Hierarchy Stabilizing Codes: Non-Clifford Transverse Gates and Magical States. Physics. Rev. Lett. 136250802 (2026).
Warman, A. and Schafer-Nameki, S. Clifford hierarchy traversal gates via non-Abelian surface codes. Preprint at arxiv.org/abs/2512.13777 (2025).
Iqbal, M. et al. Non-abelian and any topological order in a trapped ion processor. Nature 626505–511 (2024).
Google Quantum AI and collaborators Non-Abelian braiding of graphics vertices on a superconducting processor. Nature 618264–269 (2023).
Xu, S. et al. Non-abelian twisting of fibonacci anyons with a superconducting processor. Nat. Physics. 201469-1475 (2024).
Iqbal, M. et al. Qutrit toric code and parafermions in trapped ions. Community Nat. 166301 (2025).
Minev, ZK et al. Performing String Network Condensation: Fibonacci Anyon Braiding for Universal Gates and Sampling Chromatic Polynomials. Community Nat. 166225 (2025).
Aghaee, M. et al. Different lives for unknown and z Loop measurements on 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 638651–655 (2025).
Ainsworth, R. & Slingerland, JK Design and leakage of topological qubits. New J. Phys. 13065030 (2011).
Cui, S.X., Tian, KT, Vasquez, J.F., Wang, Z. & Wong, H.M. The Search for Intertwined and Leakageless Fibonacci Twisted Gates. J. Physics. A Mathematics. Theor. 52455301 (2019).
Burke, P.C., Aravanis, C., Aspman, J., Mareček, J., and Vala, J. Topological quantum compilation of two-qubit gates. Physics. Rev. A 110052616 (2024).
Lyons, A. & Brown, BJ Universal quantum computing with anyone is fault tolerant. Preprint at arxiv.org/abs/2602.11258 (2026).
Overbosch, BJ & Bais, FA Unequal classes of interference experiments with non-abelian anons. Physics. Rev. A 64062107 (2001).
Dauphinais, G. & Poulin, D. Fault-tolerant quantum error correction for any non-abelian. Community. Math. Physics. 355519–560 (2017).
Galindo, C., Rowell, E., and Wang, Z. On acyclic anyon models. Quantum info. Process. 17245 (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., and Bonderson, P. Universal gates by merge and measure operations in SU(2)4 any. Physics. Rev. A 92012301 (2015).
Cui, SX and Wang, Z. Universal quantum computing with metaplectic anions. J. Mathematics. Physics. 56032202 (2015).
Bonderson, P., Freedman, M., and Nayak, C. Measurement-only topological quantum computing. Physics. Rev. Lett. 101010501 (2008).
Cui, S.X., Hong, S.-M. & Wang, Z. Universal quantum computing with weakly integral anyons. Quantum info. Process. 142687–2727 (2014).
Chen, L., Ren, Y., Fan, R. and Jaffe, A. A universal circuit using the Yes3 quantum double. npj Quantum information. 11112 (2025).
Lo, CFB, Lyons, A., Verresen, R., Vishwanath, A. and Tantivasadakarn, N. Universal quantum computing with the Yes3 Quantum double: a pedagogical exposition. Preprint at arxiv.org/abs/2502.14974 (2025).
Moisés, SA et al. A quantum processor of ions trapped on a race track. Physics. Rev.X 13041052 (2023).
Bombin, H. & Martin-Delgado, MA Kitaev family of non-Abelian models on a network: topological condensation and confinement. Physics. Rev. B 78115421 (2008).
Beverly, MF et al. Guarded gates for topological quantum field theories. J. Mathematics. Physics. 57022201 (2016).
Shi, B. Viewing topological entanglement through convex information. Physics. Rev. Res. 1033048 (2019).
Preskill, J. Topological Quantum Computation. https://www.preskill.caltech.edu/ph219/topological.pdf (2004).
Wootton, JR, Burri, J., Iblisdir, S. & Loss, D. Error correction for non-abelian topological quantum computation. Physics. Rev.X 4011051 (2014).
Google Scholar
de la Fuente, JCM, 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, CFB Data and supporting code for “Topological quantum computing with double quantum S3 in trapped ions.” Zenodo. https://doi.org/10.5281/zenodo.18054264 (2025).
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