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 () and Dong-Ling Deng ()
Additional contact information
Liang Xiang: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Wenjie Jiang: Tsinghua University
Zehang Bao: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Zixuan Song: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Shibo Xu: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Ke Wang: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Jiachen Chen: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Feitong Jin: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Xuhao Zhu: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Zitian Zhu: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Fanhao Shen: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Ning Wang: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Chuanyu Zhang: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Yaozu Wu: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Yiren Zou: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Jiarun Zhong: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Zhengyi Cui: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Aosai Zhang: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Ziqi Tan: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Tingting Li: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Yu Gao: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Jinfeng Deng: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Xu Zhang: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Hang Dong: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Pengfei Zhang: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Si Jiang: Tsinghua University
Weikang Li: Tsinghua University
Zhide Lu: Tsinghua University
Zheng-Zhi Sun: Tsinghua University
Hekang Li: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Zhen Wang: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Chao Song: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Qiujiang Guo: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Fangli Liu: NIST and University of Maryland
Zhe-Xuan Gong: Colorado School of Mines
Alexey V. Gorshkov: NIST and University of Maryland
Norman Y. Yao: Harvard University
Thomas Iadecola: Iowa State University
Francisco Machado: Harvard University
H. Wang: and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control
Dong-Ling Deng: Tsinghua University

Nature Communications, 2024, vol. 15, issue 1, 1-9

Abstract: 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.

Date: 2024
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DOI: 10.1038/s41467-024-53077-9

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