Random quantum circuits, chaos and quantum thermalization

Abstract:These notes accompany lectures given in June 2025 at the summer school \emph{Fundamental Problems in Statistical Physics XVI}. They offer a short introduction to random quantum circuits as simple models for generic many-body quantum systems. They give an outline of the motivation for introducing these models, starting from ideas of random matrix theory. They also provide a sketch of calculations of some of the quantities of most physical interest, based on an average over an ensemble of systems. These quantities give insights into operator spreading, entanglement dynamics and spectral correlations.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2608.21303 [quant-ph]

(or arXiv:2608.21303v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.21303 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

J. Stat. Mech. (2026) 064003

https://doi.org/10.1088/1742-5468/ae7424 Focus to learn more DOI(s) linking to related resources

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