Measuring the Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors.
Hang Dong, Pengfei Zhang, Ceren B Da��, Yu Gao, Ning Wang, Jinfeng Deng, Xu Zhang, Jiachen Chen, Shibo Xu, Ke Wang, Yaozu Wu, Chuanyu Zhang, Feitong Jin, Xuhao Zhu, Aosai Zhang, Yiren Zou, Ziqi Tan, Zhengyi Cui, Zitian Zhu, Fanhao Shen, Tingting Li, Jiarun Zhong, Zehang Bao, Hekang Li, Zhen Wang, Qiujiang Guo, Chao Song, Fangli Liu, Amos Chan, Lei Ying, H Wang
Author Information
Hang Dong: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Pengfei Zhang: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Ceren B Da��: Harvard-Smithsonian Center for Astrophysics, ITAMP, Cambridge, Massachusetts 02138, USA.
Yu Gao: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Ning Wang: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Jinfeng Deng: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Xu Zhang: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Jiachen Chen: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Shibo Xu: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Ke Wang: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Yaozu Wu: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Chuanyu Zhang: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Feitong Jin: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Xuhao Zhu: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Aosai Zhang: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Yiren Zou: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Ziqi Tan: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Zhengyi Cui: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Zitian Zhu: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Fanhao Shen: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Tingting Li: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Jiarun Zhong: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Zehang Bao: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Hekang Li: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Zhen Wang: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Qiujiang Guo: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Chao Song: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
Fangli Liu: QuEra Computing Inc., 1284 Soldiers Field Road, Boston, Massachusetts 02135, USA.
Amos Chan: Lancaster University, Department of Physics, Lancaster LA1 4YB, United Kingdom.
Lei Ying: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
H Wang: Zhejiang University, School of Physics, ZJU-Hangzhou Global Scientific and Technological Innovation Center, and Zhejiang Key Laboratory of Micro-nano Quantum Chips and Quantum Control, Hangzhou, China.
The spectral form factor (SFF) captures universal spectral fluctuations as signatures of quantum chaos, and has been instrumental in advancing multiple frontiers of physics including the studies of black holes and quantum many-body systems. The measurement of the SFF in many-body systems is however challenging due to the difficulty in resolving level spacings that become exponentially small with increasing system size. Here, we utilize the random measurement toolbox to perform a direct experimental measurement of the SFF, and hence probe the presence or absence of chaos in quantum many-body systems on superconducting quantum processors. For a Floquet chaotic system, we observe signatures of both short- and long-range spectral correlations in the SFF given by the ramp-plateau behavior. Furthermore, for a Hamiltonian system we utilize the SFF to distinguish a quantum many-body chaotic phase and the prethermal many-body localization. We observe the dip-ramp-plateau behavior of random matrix theory in the chaotic phase and contrast the scaling of the plateau time in system size between the many-body chaotic and localized phases. Finally, we probe the eigenstate statistics by measuring a generalization of the SFF, known as the partial SFF, and observe distinct behaviors in the purity of the reduced density matrices in these two phases. This work unveils a new experimental way of extracting the universal signatures of many-body quantum chaos in quantum devices by probing short- and long-range correlations in the energy spectrum and eigenstates.
