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

TL;DR

This paper experimentally measures the spectral form factor in quantum processors to distinguish chaotic and localized phases, revealing universal spectral signatures and eigenstate correlations in many-body quantum systems.

Contribution

It introduces a randomized measurement protocol to measure SFF in quantum processors, distinguishing chaotic from localized phases through spectral and eigenstate analysis.

Findings

Observed ramp-plateau behavior in chaotic phases consistent with random matrix theory

Distinguished many-body chaotic and localized phases via SFF scaling and eigenstate purities

Proposed a new method to probe quantum chaos signatures in quantum devices

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.