Long-lived topological time-crystalline order on a quantum processor

Liang Xiang, Wenjie Jiang, Zehang Bao, Zixuan Song, Shibo Xu, Ke Wang, Jiachen Chen, Feitong Jin, Xuhao Zhu, Zitian Zhu, Fanhao Shen, Ning Wang, Chuanyu Zhang, Yaozu Wu, Yiren Zou, Jiarun Zhong, Zhengyi Cui, Aosai Zhang, Ziqi Tan, Tingting Li, Yu Gao, Jinfeng Deng, Xu Zhang, Hang Dong, Pengfei Zhang, Si Jiang, Weikang Li, Zhide Lu, Zheng-Zhi Sun, Hekang Li, Zhen Wang, Chao Song, Qiujiang Guo, Fangli Liu, Zhe-Xuan Gong, Alexey V. Gorshkov, Norman Y. Yao, Thomas Iadecola, Francisco Machado, H. Wang, Dong-Ling Deng
(2024)
arXiv:2401.04333

Abstract

Topologically ordered phases of matter elude Landau’s symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon – a prethermal topologically ordered time crystal – with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface-code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors.