Haoran Qian, Ming Gong, Jia-Hui Zhang, Shaojun Guo, Chen Zha, Fusheng Chen, Yangsen Ye, Yulin Wu, Sirui Cao, Chong Ying, Qingling Zhu, He-Liang Huang, Youwei Zhao, Shaowei Li, Jiale Yu, Daojin Fan, Dachao Wu, Hong Su, Hui Deng, Hao Rong, Yuan Li, Kaili Zhang, Tung-Hsun Chung, Futian Liang, Jing Lin, Yu Xu, Cheng Guo, Na Li, Kai Yan, Feifan Su, Gang Wu, Yong-Heng Huo, Cheng-Zhi Peng, Chao‐Yang Lu, Feng Mei, Suotang Jia, Xiaobo Zhu, Jian-Wei Pan
Topological phases of matter are of both fundamental and practical interest. In this study, we implemented both equilibrium and nonequilibrium higher-order topological phases using a two-dimensional programmable superconducting quantum processor. Quantum programming of nonequilibrium higher-order topological phases was achieved by constructing quantum circuits comprising >50 cycles of Floquet operators on a six-by-six qubit array. Additionally, we introduce a universal approach based on measuring the dynamics of chiral density to identify distinct nonequilibrium higher-order topological features, including Floquet corner topological invariants and π-energy topological corner modes. Our work may enable the use of programmable quantum processors to explore exotic higher-order nonequilibrium topological phases of matter.