Pieter Claeys

Congratulations both!

Amazing opportunities to start your own research group!

The office meme where Pam says "They're the same picture", but with a structured and a random quantum circuit.

Aha, thanks for letting me know!

All of this suggests that this description of OTOCs and the emergence of free cumulants should hold in more generic quantum systems -- exactly as predicted by ETH. Comments and feedback welcome!

We were able to exactly solve these dynamics by combining tools from free probability with results from dual-unitarity, allowing us to go beyond both. Also, remarkably, we can actually prove that all our predictions are stable even away from this solvable limit! (A rare thing in quantum systems.)

Free cumulants as Lorentzians.

In this way we can fully characterize free cumulants and make exact predictions for (higher-order) OTOCs and correlations in matrix elements -- fundamental quantities in ETH.

Here we introduce a structured model for quantum dynamics, termed boundary scrambling, for which we can exactly solve the OTOC dynamics, and show how our random-bath predictions naturally appears from structured scrambling!

While this clarified the role of free cumulants in quantum dynamics (to me), we were not able to relate these results to ETH: ETH tells us how structured systems lead to random matrix behavior, whereas in that work we used random matrices to obtain random matrix behavior. (Slightly less surprising.)

Free Probability in a Minimal Quantum Circuit Model Recent experimental and theoretical developments in many-body quantum systems motivate the study of their out-of-equilibrium properties through multi-time correlation functions. We consider the dynami...

Extensions of ETH are based on free cumulants from free probability, and it was unclear to me where these came from. In arxiv.org/abs/2506.11197 we made a first step in this direction, showing how coupling a quantum system to a random bath directly returns OTOC dynamics in terms of free cumulants.

Constructive interference at the edge of quantum ergodic dynamics Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables gen...

Such multi-time correlation functions include out-of-time-order correlation functions (OTOCs) and their higher-order generalizations, probes of quantum scrambling, with such higher-order OTOCs recently measured by Google Quantum AI in its 103-qubit quantum processor!
arxiv.org/abs/2506.10191

I've recently gotten interested in extensions of ETH, which tell us how complicated multi-time correlation functions equilibrate. This theory builds on free probability, extending probability theory and the notion of independent random variables to noncommuting variables (think: random matrices).

The eigenstate thermalization hypothesis (ETH) presents the main theoretical framework through which we understand how complex quantum systems can relax to simple equilibrium states. Much of this theory is based on treating highly complex quantum states as essentially random variables.

Drawing of a staircase quantum circuit and a plot showing the dynamics of an OTOC and its decomposition in free cumulant.

New paper on arXiv = good excuse for a first post on Bluesky! In arxiv.org/abs/2509.08060 we present a simple quantum circuit model in which we can characterize quantum scrambling and explicitly establish recent extensions of the eigenstate thermalization hypothesis. A short thread 🧵

Dit is de droom!