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Matchgate Circuits Deeply Thermalize.

Mircea Bejan1, Benjamin Béri1,2, Max McGinley1

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Projected ensembles from random quantum circuits exhibit deep thermalization, converging to a universal state uniform over Gaussian fermionic states. This convergence is measured using Wasserstein-1 distance, revealing insights into quantum statistical mechanics.

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Area of Science:

  • Quantum Information Science
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Random quantum circuits are crucial for studying quantum dynamics.
  • Projective measurements can alter the state of quantum systems.
  • Thermalization describes the approach of a system to equilibrium.

Purpose of the Study:

  • To rigorously analyze the "projected ensemble" generated by projective measurements on random quantum circuits.
  • To demonstrate deep thermalization in these projected ensembles.
  • To establish a computable metric for quantifying convergence in deep thermalization.

Main Methods:

  • Mathematical analysis of ensembles generated by projective measurements on random matchgate circuits.
  • Proof of momentwise convergence for projected ensembles.
  • Application of Wasserstein-1 distance to measure the proximity of projected and universal ensembles.

Main Results:

  • The projected ensemble converges to a universal ensemble uniform over Gaussian fermionic states for large system sizes.
  • The Wasserstein-1 distance is shown to be an appropriate and efficiently computable measure for deep thermalization.
  • Numerical simulations indicate deep thermalization occurs on a timescale proportional to L^2, linked to quantum information diffusion.

Conclusions:

  • Projected ensembles from random quantum circuits exhibit deep thermalization, converging to a universal Gaussian fermionic state.
  • Wasserstein-1 distance provides a robust method for quantifying deep thermalization.
  • The findings offer new experimental avenues for probing quantum statistical mechanics and benchmarking quantum simulators.