TITLE:  ” Practical applications of quantum harmonic analysis  “

SPEAKER:  Pablo Bermejo (DIPC)

ABSTRACT:  A few key concepts from representation theory reveal central features that are common to random quantum circuits, challenges in quantum machine learning (QML), the classical simulability of QML models, and quantum resource theory. Using basic ideas from representation theory, we explore how to compute moments of local random quantum circuits via tensor networks exponentially faster than previous Monte Carlo methods. We show how these insights can be used to characterize barren plateaus in QML, as well as their consequences for classical simulability. In particular, we show why quantum convolutional neural networks are effectively classically simulable. We generalize the ideas underlying these works to develop a new framework for characterizing resources in quantum information, including multipartite entanglement, non-Gaussianity, spin coherence, and non-stabilizerness, with broader applications to entanglement witnesses, state compression, and simulation schemes. Finally, we take a closer look at the classical simulation of random quantum circuits by analyzing the so-called “quantum echos” experiment from Google Quantum AI using tensor networks and belief propagation

DATE: MONDAY , June 29th, 2026

TIME: 11:40 am

LOCATION: Theoretical Physics Seminar Room