Together with Giuseppe Di Giulio and Saskia Demulder we are putting together a special issue of J. Phys. A on "Krylov Complexity Across Scales: From Quantum Many-Body Systems to Black Holes". Let me know if you're interested in contributing! Details here: iopscience.iop.org/collections/...
Illustration of information spreading on a tree geometry.
Our paper on Solvable Quantum Circuits in Tree+1 Dimensions is now published in @prxquantum.bsky.social ! Very happy with how this work turned out, possibly even happier that the title made it through peer review.
journals.aps.org/prxquantum/a...
Nice article about either magic potions or Google’s recent OTOC experiment — only one way to find out which. Plus, a few words from me!
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.)
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.
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!
