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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 crystals 1–8 , in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions 9,10 , solid-state spin systems 11–15 , ultracold atoms 16,17 and superconducting qubits 18–20 . 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 processors 21 .more » « less
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Wang, Zhen ; Chen, Yanzhu ; Song, Zixuan ; Qin, Dayue ; Li, Hekang ; Guo, Qiujiang ; Wang, H. ; Song, Chao ; Li, Ying ( , Physical Review Letters)null (Ed.)
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Song, Chao ; Xu, Kai ; Liu, Wuxin ; Yang, Chui-ping ; Zheng, Shi-Biao ; Deng, Hui ; Xie, Qiwei ; Huang, Keqiang ; Guo, Qiujiang ; Zhang, Libo ; et al ( , Physical Review Letters)