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Simulation of a Floquet non-Abelian topological insulator with photonic quantum walks

Nature Photonics (2026)Cite this article

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Abstract

Floquet non-Abelian topological phases emerge in periodically driven systems and exhibit properties that are absent from their Abelian or static counterparts. Dubbed the Floquet non-Abelian topological insulators (FNATIs), they are characterized by non-Abelian topological charges with intricate bulk-boundary correspondence, making their experimental observation challenging. Here we simulate the FNATI using a higher-dimensional photonic quantum walk and develop dynamic measurement schemes to demonstrate key signatures of the FNATI. Importantly, combining a direct bulk-dynamic detection for the underlying quaternion topological charge, and a spatially resolved injection spectroscopy for the edge states, we experimentally confirm the bulk-boundary correspondence through a Floquet non-Abelian topological invariant, which is also capable of characterizing the observed anomalous non-Abelian phase. This study experimentally characterizes the FNATI, providing general insight into gapped non-Abelian topological phases.

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Fig. 1: Experimental set-up and bulk-boundary correspondence.
Fig. 2: Bulk-boundary correspondence: domain-wall states within a single gap.
Fig. 3: Bulk-boundary correspondence: domain-wall states within two gaps.
Fig. 4: Probing anomalous non-Abelian state.

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Data availability

The data that support the findings of this study are available via Zenodo at https://doi.org/10.5281/zenodo.18264637 (ref. 53). Source data are provided with this paper.

Code availability

The code that supports the findings of this study is available via Zenodo at https://doi.org/10.5281/zenodo.18264637 (ref. 53).

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Acknowledgements

This work has been supported by the National Key R&D Program of China (grant nos. 2023YFA1406701 and 2023YFA1406704) and National Natural Science Foundation of China (grant nos. 12025401, 92265209, 12374479, 12504587). Q.L. is supported by the China Postdoctoral Science Foundation (grant nos. BX20240065 and 2024M750405) and Basic Research Program of Jiangsu (grant no. BK20251297). T.L. is supported by National Natural Science Foundation of China (grant no. 12504189). H.H. is supported by National Key Research and Development Program of China no. 2022YFA1405800 and National Natural Science Foundation of China (grant no. 12474496). W. Y. is grateful to Xuan Tong and Wenshi Feng for their expertise and care during the revision of this work.

Author information

Author notes

  1. Peng Xue

    Present address: Beijing Computational Science Research Center, Beijing, China

  2. These authors contributed equally: Quan Lin, Tianyu Li.

Authors and Affiliations

  1. School of Physics, Southeast University, Nanjing, China

    Quan Lin & Peng Xue

  2. Key Laboratory of Quantum Materials and Devices of Ministry of Education, School of Physics, Southeast University, Nanjing, China

    Quan Lin

  3. Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou, China

    Tianyu Li

  4. Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou, China

    Tianyu Li

  5. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, China

    Haiping Hu

  6. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China

    Haiping Hu

  7. Laboratory of Quantum Information, University of Science and Technology of China, Hefei, China

    Wei Yi

  8. Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China, Hefei, China

    Wei Yi

  9. CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei, China

    Wei Yi

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Contributions

Q.L. performed the experiments and wrote part of the paper. T.L. and H.H. developed the theoretical aspects and wrote part of the paper. W.Y. performed the theoretical analysis and wrote part of the paper. P.X. supervised the project, designed the experiments, analysed the results and revised the paper.

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Correspondence to Wei Yi or Peng Xue.

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Nature Photonics thanks Guancong Ma and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Phase bands of discrete-time quantum walks.

A case with Q = J, corresponding to phase-band singularities satisfying \(J=\widetilde{k}\widetilde{i}\). Inset: locations of the Dirac points with quaternion charges in the (k, t) space. P denotes the base point for the encircling paths.

Supplementary information

Supplementary Information (download PDF )

Supplementary Figs. 1–9, Discussion and Table 1.

Source data

Source Data Fig. 2 (download XLSX )

Experimental and numerical data for eigenstate trajectories and domain-wall spectroscopy of single-gap domain-wall states.

Source Data Fig. 3 (download XLSX )

Experimental and numerical data for eigenstate trajectories and domain-wall spectroscopy of domain-wall states within two gaps.

Source Data Fig. 4 (download XLSX )

Experimental and numerical data for eigenstate trajectories and domain-wall spectroscopy of the anomalous non-Abelian state.

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Lin, Q., Li, T., Hu, H. et al. Simulation of a Floquet non-Abelian topological insulator with photonic quantum walks. Nat. Photon. (2026). https://doi.org/10.1038/s41566-026-01854-x

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