Dong, Hang and Zhang, Pengfei and Dağ, Ceren B. and Gao, Yu and Wang, Ning and Deng, Jinfeng and Zhang, Xu and Chen, Jiachen and Xu, Shibo and Wang, Ke and Wu, Yaozu and Zhang, Chuanyu and Jin, Feitong and Zhu, Xuhao and Zhang, Aosai and Zou, Yiren and Tan, Ziqi and Cui, Zhengyi and Zhu, Zitian and Shen, Fanhao and Li, Tingting and Zhong, Jiarun and Bao, Zehang and Li, Hekang and Wang, Zhen and Guo, Qiujiang and Song, Chao and Liu, Fangli and Chan, Amos and Ying, Lei and Wang, H. (2025) Measuring the Spectral Form Factor in Many-Body Chaotic and Localized Phases of Quantum Processors. Physical review letters, 134 (1): 010402. ISSN 0031-9007
Full text not available from this repository.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. 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.