728 x 90

Universal Gates for Braiding and Fusing Any Material into Quantum Hardware – Nature

Universal Gates for Braiding and Fusing Any Material into Quantum Hardware – Nature

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).

    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 Google Scholar

  • Freedman, M.H., Larsen, M. & Wang, Z. A modular functor that is universal for quantum computing. Community. Math. Physics. 227605–622 (2002).

    Article MathSciNet ADS Google Scholar

  • 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).

    Article MathSciNet CAS ADS Google Scholar

  • Goldin, G.A., Menikoff, R. & Sharp, D.H. Comments on the “general theory of quantum statistics in two dimensions.” Physics. Rev. Lett. 54603 (1985).

    Article MathSciNet CAS PubMed ADS Google Scholar

  • Etingof, P., Rowell, E., and Witherspoon, S. Representations of twisted groups from twisted quantum doubles of finite groups. Pac J. Mathematics. 23433–41 (2008).

    Article MathSciNet Google Scholar

  • Mochon, C. Anyons of non-soluble finite groups are sufficient for universal quantum calculus. Physics. Rev. A 67022315 (2003).

    ADS of the article Google Scholar

  • Mochon, C. Anyon computers with smaller groups. Physics. Rev. A 69032306 (2004).

    ADS of the article Google Scholar

  • Wegner, FJ Duality in generalized Ising models and phase transitions without local order parameters. J. Mathematics. Physics. 122259–2272 (1971).

    Article MathSciNet ADS Google Scholar

  • Leinaas, JM & Myrheim, J. On the theory of identical particles. New Cim. b 371–23 (1977).

    ADS of the article Google Scholar

  • Wilczek, F. Quantum mechanics of fractional spin particles. Physics. Rev. Lett. 49957–959 (1982).

    Article MathSciNet CAS ADS Google Scholar

  • 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).

    Article MathSciNet Google Scholar

  • Tantivasadakarn, N., Vishwanath, A. & Verresen, R. Hierarchy of topological order from units of finite depth, measurement and advance. quantum PRX 4020339 (2023).

    ADS of the article Google Scholar

  • Tantivasadakarn, N., Thorngren, R., Vishwanath, A. and Verresen, R. Long-range entanglement from measurement of symmetry-protected topological phases. Physics. Rev.X 14021040 (2024).

    CAS Google Scholar

  • 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).

    Article MathSciNet CAS PubMed ADS Google Scholar

  • 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).

    Article MathSciNet CAS PubMed ADS Google Scholar

  • Ren, Y., Tantivasadakarn, N., and Williamson, DJ Efficiently preparing any solvable problem with adaptive quantum circuits. Physics. Rev.X 15031060 (2025).

    CAS Google Scholar

  • 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).

    Article CAS PubMed ADS Google Scholar

  • Google Quantum AI and collaborators Non-Abelian braiding of graphics vertices on a superconducting processor. Nature 618264–269 (2023).

    CAS ADS Article Google Scholar

  • Xu, S. et al. Non-abelian twisting of fibonacci anyons with a superconducting processor. Nat. Physics. 201469-1475 (2024).

    CAS Article Google Scholar

  • Iqbal, M. et al. Qutrit toric code and parafermions in trapped ions. Community Nat. 166301 (2025).

    Article CAS PubMed PubMed Central ADS Google Scholar

  • Minev, ZK et al. Performing String Network Condensation: Fibonacci Anyon Braiding for Universal Gates and Sampling Chromatic Polynomials. Community Nat. 166225 (2025).

    Article CAS PubMed PubMed Central ADS Google Scholar

  • 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).

    Article PubMed PubMed Central ADS Google Scholar

  • Ainsworth, R. & Slingerland, JK Design and leakage of topological qubits. New J. Phys. 13065030 (2011).

    ADS of the article Google Scholar

  • 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).

    Article MathSciNet ADS Google Scholar

  • Burke, P.C., Aravanis, C., Aspman, J., Mareček, J., and Vala, J. Topological quantum compilation of two-qubit gates. Physics. Rev. A 110052616 (2024).

    Article MathSciNet CAS ADS Google Scholar

  • 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).

    ADS of the article Google Scholar

  • Dauphinais, G. & Poulin, D. Fault-tolerant quantum error correction for any non-abelian. Community. Math. Physics. 355519–560 (2017).

    Article MathSciNet ADS Google Scholar

  • 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).

    ADS of the article Google Scholar

  • Cui, SX and Wang, Z. Universal quantum computing with metaplectic anions. J. Mathematics. Physics. 56032202 (2015).

    Article MathSciNet ADS Google Scholar

  • Bonderson, P., Freedman, M., and Nayak, C. Measurement-only topological quantum computing. Physics. Rev. Lett. 101010501 (2008).

    Article MathSciNet PubMed ADS Google Scholar

  • Cui, S.X., Hong, S.-M. & Wang, Z. Universal quantum computing with weakly integral anyons. Quantum info. Process. 142687–2727 (2014).

    Article MathSciNet ADS Google Scholar

  • Chen, L., Ren, Y., Fan, R. and Jaffe, A. A universal circuit using the Yes3 quantum double. npj Quantum information. 11112 (2025).

    ADS of the article Google Scholar

  • 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).

    CAS Google Scholar

  • Bombin, H. & Martin-Delgado, MA Kitaev family of non-Abelian models on a network: topological condensation and confinement. Physics. Rev. B 78115421 (2008).

    ADS of the article Google Scholar

  • Beverly, MF et al. Guarded gates for topological quantum field theories. J. Mathematics. Physics. 57022201 (2016).

    Article MathSciNet ADS Google Scholar

  • Shi, B. Viewing topological entanglement through convex information. Physics. Rev. Res. 1033048 (2019).

    CAS Article Google Scholar

  • 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).

  • For more tech updates, stay tuned to our blog.

    Posts Carousel

    Latest Posts

    Top Authors

    Most Commented

    Featured Videos