Digital quantum simulation of Floquet symmetry-protected topological phases

Xu Zhang, Wenjie Jiang, Jinfeng Deng, Ke Wang, Jiachen Chen, Pengfei Zhang, Wenhui Ren, Hang Dong, Shibo Xu, Yu Gao, Feitong Jin, Xuhao Zhu, Qiujiang Guo, Hekang Li, Chao Song, Alexey V. Gorshkov, Thomas Iadecola, Fangli Liu, Zhe-Xuan Gong, Zhen Wang (), Dong-Ling Deng () and H. Wang
Additional contact information
Xu Zhang: Zhejiang University
Wenjie Jiang: Tsinghua University
Jinfeng Deng: Zhejiang University
Ke Wang: Zhejiang University
Jiachen Chen: Zhejiang University
Pengfei Zhang: Zhejiang University
Wenhui Ren: Zhejiang University
Hang Dong: Zhejiang University
Shibo Xu: Zhejiang University
Yu Gao: Zhejiang University
Feitong Jin: Zhejiang University
Xuhao Zhu: Zhejiang University
Qiujiang Guo: Zhejiang University
Hekang Li: Zhejiang University
Chao Song: Zhejiang University
Alexey V. Gorshkov: University of Maryland and NIST
Thomas Iadecola: Iowa State University
Fangli Liu: University of Maryland and NIST
Zhe-Xuan Gong: Department of Physics, Colorado School of Mines
Zhen Wang: Zhejiang University
Dong-Ling Deng: Tsinghua University
H. Wang: Zhejiang University

Nature, 2022, vol. 607, issue 7919, 468-473

Abstract: Abstract Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals1–8, in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions9,10, solid-state spin systems11–15, ultracold atoms16,17 and superconducting qubits18–20. Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors21.

Date: 2022
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DOI: 10.1038/s41586-022-04854-3

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