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Non-Abelian topological order and anyons on a trapped-ion processor

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  • 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).

    Article 
    ADS 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • Moore, G. & Seiberg, N. Classical and quantum conformal field theory. Commun. Math. Phys. 123, 177–254 (1989).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Moore, G. & Read, N. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Wen, X. G. Non-Abelian statistics in the fractional quantum Hall states. Phys. Rev. Lett. 66, 802–805 (1991).

    Article 
    ADS 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

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

    Article 
    ADS 
    MathSciNet 
    CAS 

    Google Scholar
     

  • 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).

    Article 
    ADS 
    MathSciNet 
    CAS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

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

    Article 
    ADS 
    MathSciNet 
    CAS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).

    Article 
    CAS 

    Google Scholar
     

  • Bartolomei, H. et al. Fractional statistics in anyon collisions. Science 368, 173–177 (2020).

    Article 
    ADS 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • Satzinger, K. J. et al. Realizing topologically ordered states on a quantum processor. Science 374, 1237–1241 (2021).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Semeghini, G. et al. Probing topological spin liquids on a programmable quantum simulator. Science 374, 1242–1247 (2021).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • 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).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Banerjee, M. et al. Observation of half-integer thermal Hall conductance. Nature 559, 205–210 (2018).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • 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).

    CAS 

    Google Scholar
     

  • Feldman, D. E. & Halperin, B. I. Fractional charge and fractional statistics in the quantum Hall effects. Rep. Prog. Phys. 84, 076501 (2021).

    Article 
    MathSciNet 

    Google Scholar
     

  • Kitaev, A. Unpaired Majorana fermions in quantum wires. Phys. Uspekhi 44, 131–136 (2001).

    Article 
    ADS 

    Google Scholar
     

  • Microsoft Quantum InAs–Al hybrid devices passing the topological gap protocol. Phys. Rev. B 107, 245423 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Bombin, H. Topological order with a twist: Ising anyons from an Abelian model. Phys. Rev. Lett. 105, 030403 (2010).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Andersen, T. I. et al. Non-Abelian braiding of graph vertices in a superconducting processor. Nature 618, 264–269 (2023).

    Article 

    Google Scholar
     

  • Xu, S. et al. Digital simulation of projective non-Abelian anyons with 68 superconducting qubits. Chin. Phys. Lett. 40, 060301 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Cui, S. X., Hong, S.-M. & Wang, Z. Universal quantum computation with weakly integral anyons. Quantum Inf. Process. 14, 2687–2727 (2015).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • Barkeshli, M., Jian, C.-M. & Qi, X.-L. Genons, twist defects, and projective non-Abelian braiding statistics. Phys. Rev. B 87, 045130 (2013).

    Article 
    ADS 

    Google Scholar
     

  • Cong, I., Cheng, M. & Wang, Z. Universal quantum computation with gapped boundaries. Phys. Rev. Lett. 119, 170504 (2017).

    Article 
    ADS 
    MathSciNet 
    PubMed 

    Google Scholar
     

  • 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).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Kielpinski, D., Monroe, C. & Wineland, D. J. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • 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).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • Bolt, A., Duclos-Cianci, G., Poulin, D. & Stace, T. Foliated quantum error-correcting codes. Phys. Rev. Lett. 117, 070501 (2016).

    Article 
    ADS 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • 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).

    Article 
    ADS 
    MathSciNet 
    CAS 
    PubMed 

    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
     

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

    Article 
    CAS 

    Google Scholar
     

  • 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).

    Article 
    ADS 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • Yoshida, B. Topological phases with generalized global symmetries. Phys. Rev. B 93, 155131 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Potter, A. C. & Vasseur, R. Symmetry constraints on many-body localization. Phys. Rev. B 94, 224206 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Senthil, T. Symmetry-protected topological phases of quantum matter. Annu. Rev. Condensed Matter Phys. 6, 299–324 (2015).

    Article 
    ADS 
    CAS 

    Google Scholar
     

  • Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001).

    Article 
    ADS 
    CAS 
    PubMed 

    Google Scholar
     

  • Wang, C. & Levin, M. Topological invariants for gauge theories and symmetry-protected topological phases. Phys. Rev. B 91, 165119 (2015).

    Article 
    ADS 

    Google Scholar
     

  • Wang, J., Wen, X.-G. & Yau, S.-T. Quantum statistics and spacetime surgery. Phys. Lett. B 807, 135516 (2020).

    Article 
    MathSciNet 
    CAS 

    Google Scholar
     

  • 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).

    Article 
    ADS 
    MathSciNet 
    CAS 

    Google Scholar
     

  • 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).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

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