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Quantum systems scramble information, delocalizing their state in Hilbert space. Random quantum circuits show this delocalization saturates logarithmically with system size, confirmed by simulations.

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Area of Science:

  • Quantum Information Science
  • Quantum Many-Body Physics
  • Statistical Mechanics

Background:

  • Unitary dynamics of quantum systems lead to superposition states.
  • Quantum information scrambling and coherence are linked to state delocalization.
  • Random quantum circuits model chaotic quantum many-body dynamics.

Purpose of the Study:

  • Analyze Hilbert space delocalization in random quantum circuits.
  • Investigate the time evolution of participation entropies.
  • Determine the scaling of delocalization with system size.

Main Methods:

  • Analytical methods: replica trick and Weingarten calculus.
  • Studied time evolution of participation entropies.
  • Corroborated findings with numerical simulations and tensor network techniques.

Main Results:

  • Participation entropies quantify Hilbert space delocalization.
  • Delocalization approaches saturation value with fixed accuracy.
  • Saturation time scales logarithmically with system size.

Conclusions:

  • Random quantum circuits exhibit efficient Hilbert space delocalization.
  • Logarithmic scaling of delocalization time is a key finding.
  • Theoretical and numerical results align, validating the model.