Observation of exact quantum critical states

Nature Physics (2026) Cite this article Anderson localization describes the suppression of wave transport in disordered media. In quantum systems, it gives rise to extended, localized and critical eigenstates, with the latter showing properties between the other two. Characterizing critical states is challenging because it requires analysis in the thermodynamic limit or a universal mechanism that identifies them. Here we experimentally realize critical states in a programmable quasiperiodic mosaic model with tunable couplings and on-site potentials using a system of superconducting qubits. By measuring time-evolving observables, we identify coexisting delocalized dynamics and incommensurately distributed zeros in the couplings, which characterize the critical states. We map the transition from localized to critical behaviour and show that critical states persist until strong long-range couplings remove the quasiperiodic zeros. 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Data for “Observation of exact quantum critical states”. Zenodo https://doi.org/10.5281/zenodo.19221385 (2026).Download referencesWe thank Q. Zhou and Y. Wang for helpful discussions. This work was supported by National Key Research and Development Program of China no. 2021YFA1400900 (X.-J.L.), Quantum Science and Technology-National Science and Technology Major Project nos. 2021ZD0302000 (X.-J.L.) and 2021ZD0301703 (Y. Zhong and S.L.), the Science, Technology and Innovation Commission of Shenzhen Municipality no. KQTD20210811090049034 (Y. Zhong), the National Natural Science Foundation of China nos. 12425401 (X.-J.L.), 12174178 (Y. Zhong) and 12261160368 (X.-J.L.), respectively, and Shanghai Municipal Science and Technology Major Project no. 2019SHZDZX01 (X.-J.L.). X.-J.L. was also supported by the New Cornerstone Science Foundation through the XPLORER PRIZE.These authors contributed equally: Wenhui Huang, Xin-Chi Zhou, Libo Zhang, Jiawei Zhang, Yuxuan Zhou, Bing-Chen Yao.International Quantum Academy, Shenzhen, ChinaWenhui Huang, Libo Zhang, Jiawei Zhang, Yuxuan Zhou, Zechen Guo, Peisheng Huang, Qixian Li, Yongqi Liang, Yiting Liu, Jiawei Qiu, Daxiong Sun, Xuandong Sun, Zilin Wang, Changrong Xie, Yuzhe Xiong, Xiaohan Yang, Jiajian Zhang, Zihao Zhang, Ji Chu, Weijie Guo, Ji Jiang, Xiayu Linpeng, Wenhui Ren, Yuefeng Yuan, Jingjing Niu, Ziyu Tao, Song Liu, Youpeng Zhong, Xiong-Jun Liu & Dapeng YuShenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, ChinaWenhui Huang, Libo Zhang, Jiawei Zhang, Zechen Guo, Qixian Li, Yongqi Liang, Yiting Liu, Jiawei Qiu, Daxiong Sun, Xuandong Sun, Changrong Xie, Yuzhe Xiong, Xiaohan Yang, Jiajian Zhang, Zihao Zhang, Ji Jiang, Song Liu & Youpeng ZhongGuangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, ChinaWenhui Huang, Libo Zhang, Jiawei Zhang, Zechen Guo, Qixian Li, Yongqi Liang, Yiting Liu, Jiawei Qiu, Daxiong Sun, Xuandong Sun, Changrong Xie, Yuzhe Xiong, Xiaohan Yang, Jiajian Zhang, Zihao Zhang, Ji Jiang & Song LiuInternational Center for Quantum Materials and School of Physics, Peking University, Beijing, ChinaXin-Chi Zhou, Bing-Chen Yao & Xiong-Jun LiuHefei National Laboratory, Hefei, ChinaXin-Chi Zhou & Xiong-Jun LiuSchool of Physics, Ningxia University, Yinchuan, ChinaPeisheng Huang & Zilin WangShenzhen Branch, Hefei National Laboratory, Shenzhen, ChinaJingjing Niu, Song Liu, Youpeng Zhong & Dapeng YuSearch 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 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 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 ScholarX.-J.L. conceived of the project. W.H. designed and tested the device under the supervision of Y. Zhong. Z.T. collected the data, and analysed the data with the help of X.-C.Z. X.-C.Z. and B.-C.Y. provided theoretical and numerical studies under the supervision of X.-J.L. L.Z. and Y. Zhou fabricated the device. Jiawei Zhang built the microwave electronics under the supervision of Y. Zhong. Y. Zhong, X.-J.L., and D.Y. supervised the project. All authors contributed to the discussion and preparation of the paper.Correspondence to Ziyu Tao, Song Liu, Youpeng Zhong, Xiong-Jun Liu or Dapeng Yu.The authors declare no competing interests.Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Figs. 1–23 and Discussion.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 permissionsHuang, W., Zhou, XC., Zhang, L. et al. Observation of exact quantum critical states. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03333-0Download citationReceived: 19 May 2025Accepted: 13 May 2026Published: 09 June 2026Version of record: 09 June 2026DOI: https://doi.org/10.1038/s41567-026-03333-0Anyone 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