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arXiv · 2505.01978

One- and two-dimensional cluster states for topological phase simulation and measurement-based quantum computation

Tao Jiang·Jianbin Cai·Junxiang Huang·Naibin Zhou·Yukun Zhang·Jiahao Bei·Guoqing Cai·Sirui Cao·Fusheng Chen·Jiang Chen·Kefu Chen·Xiawei Chen·Xiqing Chen·Zhe Chen·Zhiyuan Chen·Zihua Chen·Wenhao Chu·Hui Deng·Zhibin Deng·Pei Ding·Xun Ding·Zhuzhengqi Ding·Shuai Dong·Bo Fan·Daojin Fan·Yuanhao Fu·Dongxin Gao·Lei Ge·Jiacheng Gui·Cheng Guo·Shaojun Guo·Xiaoyang Guo·Lianchen Han·Tan He·Linyin Hong·Yisen Hu·He-Liang Huang·Yong-Heng Huo·Zuokai Jiang·Honghong Jin·Yunxiang Leng·Dayu Li·Dongdong Li·Fangyu Li·Jiaqi Li·Jinjin Li·Junyan Li·Junyun Li·Na Li·Shaowei Li·Wei Li·Yuhuai Li·Yuan Li·Futian Liang·Xuelian Liang·Nanxing Liao·Jin Lin·Weiping Lin·Dailin Liu·Hongxiu Liu·Maliang Liu·Xinyu Liu·Xuemeng Liu·Yancheng Liu·Haoxin Lou·Yuwei Ma·Lingxin Meng·Hao Mou·Kailiang Nan·Binghan Nie·Meijuan Nie·Jie Ning·Le Niu·Wenyi Peng·Haoran Qian·Hao Rong·Tao Rong·Huiyan Shen·Qiong Shen·Hong Su·Feifan Su·Chenyin Sun·Liangchao Sun·Tianzuo Sun·Yingxiu Sun·Yimeng Tan·Jun Tan·Longyue Tang·Wenbing Tu·Jiafei Wang·Biao Wang·Chang Wang·Chen Wang·Chu Wang·Jian Wang·Liangyuan Wang·Rui Wang·Shengtao Wang·Xiaomin Wang·Xinzhe Wang
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Abstract

Quantum entanglement is a fundamental resource for quantum information processing and serves as a critical benchmark for quantum hardware performance. Cluster states are a special class of entangled states that serve as universal resources for measurement-based quantum computation and possess an intrinsic symmetry-protected topological order, which confers robustness against symmetry-respecting noise. Here we report the scalable preparation and verification of genuine multipartite cluster states on the 105-qubit Zuchongzhi 3.1 superconducting processor. We achieve one-dimensional cluster states of up to 95 qubits and two-dimensional cluster states of up to 72 qubits. The symmetry-protected topological cluster states exhibit input-state-dependent robustness under symmetry-breaking perturbations due to an operational parity structure that enhances the performance of measurement-based quantum computation. Furthermore, we use our two-dimensional cluster states to implement the Deutsch-Jozsa algorithm within the measurement-based quantum computation framework, achieving higher output-state fidelity compared with traditional circuit-based models and a query efficiency advantage over classical approaches. Our work establishes a scalable platform that combines large-scale entanglement generation, symmetry-protected topological order and practical quantum algorithms to enable robust, fault-tolerant measurement-based quantum computation.

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Tao Jiang, Jianbin Cai, Junxiang Huang, Naibin Zhou, Yukun Zhang, Jiahao Bei, Guoqing Cai, Sirui Cao, Fusheng Chen, Jiang Chen, Kefu Chen, Xiawei Chen, Xiqing Chen, Zhe Chen, Zhiyuan Chen, Zihua Chen, Wenhao Chu, Hui Deng, Zhibin Deng, Pei Ding, Xun Ding, Zhuzhengqi Ding, Shuai Dong, Bo Fan, Daojin Fan, Yuanhao Fu, Dongxin Gao, Lei Ge, Jiacheng Gui, Cheng Guo, Shaojun Guo, Xiaoyang Guo, Lianchen Han, Tan He, Linyin Hong, Yisen Hu, He-Liang Huang, Yong-Heng Huo, Zuokai Jiang, Honghong Jin, Yunxiang Leng, Dayu Li, Dongdong Li, Fangyu Li, Jiaqi Li, Jinjin Li, Junyan Li, Junyun Li, Na Li, Shaowei Li, Wei Li, Yuhuai Li, Yuan Li, Futian Liang, Xuelian Liang, Nanxing Liao, Jin Lin, Weiping Lin, Dailin Liu, Hongxiu Liu, Maliang Liu, Xinyu Liu, Xuemeng Liu, Yancheng Liu, Haoxin Lou, Yuwei Ma, Lingxin Meng, Hao Mou, Kailiang Nan, Binghan Nie, Meijuan Nie, Jie Ning, Le Niu, Wenyi Peng, Haoran Qian, Hao Rong, Tao Rong, Huiyan Shen, Qiong Shen, Hong Su, Feifan Su, Chenyin Sun, Liangchao Sun, Tianzuo Sun, Yingxiu Sun, Yimeng Tan, Jun Tan, Longyue Tang, Wenbing Tu, Jiafei Wang, Biao Wang, Chang Wang, Chen Wang, Chu Wang, Jian Wang, Liangyuan Wang, Rui Wang, Shengtao Wang, Xiaomin Wang, Xinzhe Wang. 2026-09-13. One- and two-dimensional cluster states for topological phase simulation and measurement-based quantum computation. https://doi.org/10.1038/s41567-026-03179-6

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