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

Hang Dong1, Pengfei Zhang1, Ceren B Dağ2,3

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We experimentally measured the spectral form factor (SFF) in quantum many-body systems using superconducting quantum processors. This method reveals signatures of quantum chaos, distinguishing chaotic phases from localized ones.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Quantum information science

Background:

  • The spectral form factor (SFF) is crucial for understanding quantum chaos and has applications in black hole physics and many-body systems.
  • Experimentally measuring the SFF in many-body systems is difficult due to exponentially small energy level spacings.

Purpose of the Study:

  • To develop and apply a novel experimental method for measuring the SFF in quantum many-body systems.
  • To probe quantum chaos and distinguish between chaotic and localized phases in these systems.
  • To utilize superconducting quantum processors for direct SFF measurements.

Main Methods:

  • Utilized the random measurement toolbox for direct experimental measurement of the SFF.
  • Performed measurements on superconducting quantum processors.
  • Measured a generalization of the SFF, the partial SFF, to probe eigenstate statistics.

Main Results:

  • Observed ramp-plateau behavior in the SFF for a Floquet chaotic system, indicating short- and long-range spectral correlations.
  • Observed dip-ramp-plateau behavior in the SFF for a Hamiltonian chaotic system, consistent with random matrix theory.
  • Distinguished between quantum many-body chaotic and prethermal many-body localized phases.
  • Observed distinct behaviors in the purity of reduced density matrices for chaotic and localized phases.

Conclusions:

  • The random measurement toolbox provides a new experimental pathway to extract universal signatures of many-body quantum chaos.
  • This technique allows for the investigation of spectral correlations and eigenstate statistics in quantum devices.
  • The findings contribute to a deeper understanding of quantum chaos in complex quantum systems.