Reconfigurable non-Abelian braiding of nematic bits

Nature Materials (2026) Cite this article Non-Abelian braiding offers a route to information processing that is robust against local perturbations, yet its programmable realization in real space remains challenging. Here we present a room-temperature soft-matter platform for reconfigurable non-Abelian braiding based on the light-driven transformations of disclination lines in a nematic liquid crystal. By photonically manipulating the entangled colloids, we weave the lines into chiral double-helix entanglements and encode their topological states as nematic bits. We implement a complete set of braid operations and demonstrate their non-commutativity in three-line networks, a defining signature of non-Abelian behaviour. Repositioning colloidal gates enables in situ reprogramming, whereas the method extends to multiline architectures. Building on the scalability of this approach, we establish a predictive inverse-design framework that algebraically compiles target topological transformations into prescribed spatial routing and layer-by-layer phase corrections. These results establish a programmable classical platform for robust topological transformations and connect soft-matter physics with topological information processing. 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Cryst. 331, 49–57 (1999).Article Google Scholar Download referencesThis work was partially carried out at the Experimental Center for Engineering and Materials Science, University of Science and Technology of China (USTC). We also acknowledge support from the USTC Center for Micro and Nanoscale Research and Fabrication.C.P. acknowledges the Fundamental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry of Education of China (grant number JYB2025XDXM502) and the National Natural Science Foundation of China (grant numbers 62375254 and 62575275). J.J. acknowledges the National Natural Science Foundation of China (grant number 62305323) and the Chinese Academy of Sciences Pioneer Hundred Talents Program (grant number KJ2030007006). R.Z. acknowledges the Hong Kong Research Grants Council (grant number 26302320).These authors contributed equally: Zihan Lei, Xinda Zheng, Jing Zhang.Department of Physics, University of Science and Technology of China, Hefei, ChinaZihan Lei, Xinda Zheng, Jing Zhang, Kun Tian, Ganlin Song, Zhawure Asilehan, Zijun Chen, Fernando Vergara, Yu Guan, Jinghua Jiang & Chenhui PengDepartment of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, ChinaWentao Tang & Rui ZhangXinjiang Key Laboratory of Luminescence Minerals and Optical Functional Materials, School of Physics and Electronic Engineering, Xinjiang Normal University, Urumqi, ChinaZhawure AsilehanState Key Lab of Displays and Opto-electronics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, ChinaRui ZhangCenter for AI for Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, ChinaRui ZhangSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarJ.J. and C.P. directed the research. Z.L., G.S., Z.A. and Z.C. performed the experiments. Z.L., X.Z., J.Z., G.S. and Y.G. analysed the data. Z.L., X.Z., J.Z., W.T., K.T., F.V. and R.Z. performed the numerical modelling. All authors participated in discussing and writing the paper.Correspondence to Jinghua Jiang or Chenhui Peng.The authors declare no competing interests.Nature Materials thanks Uroš Tkalec and Xu-Lin Zhang for their contribution to the peer review of this work. Peer reviewer reports are available.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Figs. 1–16, Table 1 and References and captions for supplementary videos.Light-controlled formation of the left-twist double-helix colloidal entanglement. When the top director field reorients CCW, a left-twist double-helix colloidal entanglement structure is generated.Light-controlled formation of the right-twist double-helix colloidal entanglement. When the top director field reorients CW, a right-twist double-helix colloidal entanglement structure is generated.Light-controlled formation of the left-twist five-colloid double-helix entanglement. Through the manipulation of CCW LP light combined with optical tweezers, a left-twist five-colloid double-helix entanglement structure is formed.Light-controlled formation of the left-twist six-colloid double-helix entanglement. When the top director field reorients CCW, a left-twist six-colloid double-helix entanglement structure is generated.Light-controlled formation of the left-twist nine-colloid double-helix entanglement. Through the manipulation of CCW LP light combined with optical tweezers, a left-twist nine-colloid double-helix entanglement structure is formed.Light-controlled formation of the right-twist five-colloid double-helix entanglement. When the top director field reorients CW, a right-twist five-colloid double-helix entanglement structure is generated.Light-controlled formation of the right-twist six-colloid double-helix entanglement. When the top director field reorients CW, a right-twist six-colloid double-helix entanglement structure is generated.Light-controlled formation of the right-twist nine-colloid double-helix entanglement. When the top director field reorients CW, a right-twist nine-colloid double-helix entanglement structure is generated.Light-controlled formation of the double-helix entanglement with two chirality. By manipulating CW LP light and optical tweezers, a four-colloid double-helix entangled structure is obtained, which features the coexistence of left- and right-twist chirality.Dynamic reconfiguration of the braiding sequence. By simply arranging the positions of the colloids, the braiding sequence can be dynamically reconfigured.Structural robustness of the nematic braiding network against local perturbations. The braiding network is robust against small variations, such as colloid position and local disclination-line curvature.All custom Mathematica scripts used for generating main-text and supplementary figures.Statistical source data.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsLei, Z., Zheng, X., Zhang, J. et al. Reconfigurable non-Abelian braiding of nematic bits. Nat. Mater. (2026). https://doi.org/10.1038/s41563-026-02728-xDownload citationReceived: 20 April 2026Accepted: 30 July 2026Published: 22 September 2026Version of record: 22 September 2026DOI: https://doi.org/10.1038/s41563-026-02728-xAnyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative