Measuring Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors

• URL: http://arxiv.org/abs/2403.16935v1
• Date: Mon, 25 Mar 2024 16:59:00 GMT
• Title: Measuring Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors
• Authors: Hang Dong, Pengfei Zhang, Ceren B. Dag, 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,
• Abstract summary: We experimentally measure the spectral form factor (SFF) to probe the presence or absence of chaos in quantum many-body systems. This work unveils a new way of extracting the universal signatures of many-body quantum chaos in quantum devices by probing the correlations in eigenenergies and eigenstates.
• Score: 22.983795509221974
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. However, the measurement of SFF in many-body systems is challenging due to the difficulty in resolving level spacings that become exponentially small with increasing system size. Here we experimentally measure the SFF to probe the presence or absence of chaos in quantum many-body systems using a superconducting quantum processor with a randomized measurement protocol. For a Floquet chaotic system, we observe signatures of spectral rigidity of random matrix theory in SFF given by the ramp-plateau behavior. For a Hamiltonian system, we utilize SFF to distinguish the 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. Furthermore, we probe the eigenstate statistics by measuring a generalization of the SFF, known as the partial SFF, and observe distinct behaviors in the purities of the reduced density matrix in the two phases. This work unveils a new way of extracting the universal signatures of many-body quantum chaos in quantum devices by probing the correlations in eigenenergies and eigenstates.

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