Goldin, G. A., Menikoff, R. & Sharp, D. H. Comments on ‘general theory for quantum statistics in two dimensions’. Phys. Rev. Lett. 54, 603–603 (1985).
Moore, G. & Seiberg, N. Classical and quantum conformal field theory. Commun. Math. Phys. 123, 177–254 (1989).
Moore, G. & Read, N. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991).
Wen, X. G. Non-Abelian statistics in the fractional quantum Hall states. Phys. Rev. Lett. 66, 802–805 (1991).
Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).
Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).
Wen, X.-G. Quantum Field Theory of Many-body Systems Oxford Graduate Texts (Oxford Univ. Press, 2010).
Leinaas, J. M. & Myrheim, J. On the theory of identical particles. Nuovo Cim. B 37, 1–23 (1977).
Goldin, G. A., Menikoff, R. & Sharp, D. H. Representations of a local current algebra in nonsimply connected space and the Aharonov–Bohm effect. J. Math. Phys. 22, 1664–1668 (1981).
Wilczek, F. Quantum mechanics of fractional-spin particles. Phys. Rev. Lett. 49, 957–959 (1982).
Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).
Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).
Bartolomei, H. et al. Fractional statistics in anyon collisions. Science 368, 173–177 (2020).
Satzinger, K. J. et al. Realizing topologically ordered states on a quantum processor. Science 374, 1237–1241 (2021).
Semeghini, G. et al. Probing topological spin liquids on a programmable quantum simulator. Science 374, 1242–1247 (2021).
Ryan-Anderson, C. et al. Implementing fault-tolerant entangling gates on the five-qubit code and the color code. Preprint at https://arxiv.org/abs/2208.01863 (2022).
Iqbal, M. et al. Topological order from measurements and feed-forward on a trapped ion quantum computer. Preprint at https://arxiv.org/abs/2302.01917 (2023).
Foss-Feig, M. et al. Experimental demonstration of the advantage of adaptive quantum circuits. Preprint at https://arxiv.org/abs/2302.03029 (2023).
Pan, W. et al. Exact quantization of even-denominator fractional quantum Hall state at ν=5/2 Landau level filling factor. Phys. Rev. Lett. 83, 3530–3533 (1999).
Banerjee, M. et al. Observation of half-integer thermal Hall conductance. Nature 559, 205–210 (2018).
Ma, K. K. W., Peterson, M. R., Scarola, V. W. & Yang, K. in Encyclopedia of Condensed Matter Physics 2nd edn (ed. Chakraborty, T.) 324–365 (Academic Press, 2024); https://www.sciencedirect.com/science/article/pii/B9780323908009001359.
Willett, R. et al. Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding. Phys. Rev. X 13, 011028 (2023).
Feldman, D. E. & Halperin, B. I. Fractional charge and fractional statistics in the quantum Hall effects. Rep. Prog. Phys. 84, 076501 (2021).
Kitaev, A. Unpaired Majorana fermions in quantum wires. Phys. Uspekhi 44, 131–136 (2001).
Microsoft Quantum InAs–Al hybrid devices passing the topological gap protocol. Phys. Rev. B 107, 245423 (2023).
Bombin, H. Topological order with a twist: Ising anyons from an Abelian model. Phys. Rev. Lett. 105, 030403 (2010).
Andersen, T. I. et al. Non-Abelian braiding of graph vertices in a superconducting processor. Nature 618, 264–269 (2023).
Xu, S. et al. Digital simulation of projective non-Abelian anyons with 68 superconducting qubits. Chin. Phys. Lett. 40, 060301 (2023).
Cui, S. X., Hong, S.-M. & Wang, Z. Universal quantum computation with weakly integral anyons. Quantum Inf. Process. 14, 2687–2727 (2015).
Barkeshli, M. & Sau, J. D. Physical architecture for a universal topological quantum computer based on a network of Majorana nanowires. Preprint at https://arxiv.org/abs/1509.07135 (2015).
Barkeshli, M., Jian, C.-M. & Qi, X.-L. Theory of defects in Abelian topological states. Phys. Rev. B 88, 235103 (2013).
Barkeshli, M., Jian, C.-M. & Qi, X.-L. Genons, twist defects, and projective non-Abelian braiding statistics. Phys. Rev. B 87, 045130 (2013).
Cong, I., Cheng, M. & Wang, Z. Universal quantum computation with gapped boundaries. Phys. Rev. Lett. 119, 170504 (2017).
Wineland, D. J. et al. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl Inst. Stand. Technol. 103, 259–328 (1998).
Kielpinski, D., Monroe, C. & Wineland, D. J. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002).
Moses, S. A. et al. A race track trapped-ion quantum processor. Phys. Rev. X 13, 041052 (2023).
Bravyi, S., Hastings, M. B. & Verstraete, F. Lieb–Robinson bounds and the generation of correlations and topological quantum order. Phys. Rev. Lett. 97, 050401 (2006).
Liu, Y.-J., Shtengel, K., Smith, A. & Pollmann, F. Methods for simulating string-net states and anyons on a digital quantum computer. PRX Quantum 3, 040315 (2022).
Aharonov, D. & Touati, Y. Quantum circuit depth lower bounds for homological codes. Preprint at https://arxiv.org/abs/1810.03912 (2018).
Raussendorf, R., Bravyi, S. & Harrington, J. Long-range quantum entanglement in noisy cluster states. Phys. Rev. A 71, 062313 (2005).
Bolt, A., Duclos-Cianci, G., Poulin, D. & Stace, T. Foliated quantum error-correcting codes. Phys. Rev. Lett. 117, 070501 (2016).
Piroli, L., Styliaris, G. & Cirac, J. I. Quantum circuits assisted by local operations and classical communication: transformations and phases of matter. Phys. Rev. Lett. 127, 220503 (2021).
Tantivasadakarn, N., Vishwanath, A. & Verresen, R. Hierarchy of topological order from finite-depth unitaries, measurement, and feedforward. PRX Quantum 4, 020339 (2023).
Shi, B. Seeing topological entanglement through the information convex. Phys. Rev. Res. 1, 033048 (2019).
Tantivasadakarn, N., Thorngren, R., Vishwanath, A. & Verresen, R. Long-range entanglement from measuring symmetry-protected topological phases. Preprint at https://arxiv.org/abs/2112.01519 (2022).
Verresen, R., Tantivasadakarn, N. & Vishwanath, A. Efficiently preparing Schrödinger’s cat, fractons and non-Abelian topological order in quantum devices. Preprint at https://arxiv.org/abs/2112.03061 (2022).
Bravyi, S., Kim, I., Kliesch, A. & Koenig, R. Adaptive constant-depth circuits for manipulating non-Abelian anyons. Preprint at https://arxiv.org/abs/2205.01933 (2022).
Tantivasadakarn, N., Verresen, R. & Vishwanath, A. Shortest route to non-Abelian topological order on a quantum processor. Phys. Rev. Lett. 131, 060405 (2023).
Yoshida, B. Topological phases with generalized global symmetries. Phys. Rev. B 93, 155131 (2016).
Potter, A. C. & Vasseur, R. Symmetry constraints on many-body localization. Phys. Rev. B 94, 224206 (2016).
Senthil, T. Symmetry-protected topological phases of quantum matter. Annu. Rev. Condensed Matter Phys. 6, 299–324 (2015).
Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001).
Wang, C. & Levin, M. Topological invariants for gauge theories and symmetry-protected topological phases. Phys. Rev. B 91, 165119 (2015).
Wang, J., Wen, X.-G. & Yau, S.-T. Quantum statistics and spacetime surgery. Phys. Lett. B 807, 135516 (2020).
Putrov, P., Wang, J. & Yau, S.-T. Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+1 and 3+1 dimensions. Ann. Phys. 384, 254–287 (2017).
Kulkarni, A., Mignard, M. & Schauenburg, P. A topological invariant for modular fusion categories. Preprint at https://arxiv.org/abs/1806.03158 (2021).
Dauphinais, G. & Poulin, D. Fault-tolerant quantum error correction for non-Abelian anyons. Commun. Math. Phys. 355, 519–560 (2017).
Lu, T.-C., Lessa, L. A., Kim, I. H. & Hsieh, T. H. Measurement as a shortcut to long-range entangled quantum matter. PRX Quantum 3, 040337 (2022).
Zhu, G.-Y., Tantivasadakarn, N., Vishwanath, A., Trebst, S. & Verresen, R. Nishimori’s cat: stable long-range entanglement from finite-depth unitaries and weak measurements. Phys. Rev. Lett. 131, 200201 (2023).
Lee, J. Y., Ji, W., Bi, Z. & Fisher, M. P. A. Decoding measurement-prepared quantum phases and transitions: from Ising model to gauge theory, and beyond. Preprint at https://arxiv.org/abs/2208.11699 (2022).
Lu, T.-C., Zhang, Z., Vijay, S. & Hsieh, T. H. Mixed-state long-range order and criticality from measurement and feedback. PRX Quantum 4, 030318 (2023).
Mochon, C. Anyon computers with smaller groups. Phys. Rev. A 69, 032306 (2004).