Matchgate Circuits Deeply Thermalize

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.