of the ENS

Welcome to the Data Science Colloquium of the ENS.

This colloquium is organized around data sciences in a broad sense with the goal of bringing together researchers with diverse backgrounds (including for instance mathematics, computer science, physics, chemistry and neuroscience) but a common interest in dealing with large scale or high dimensional data.

The colloquium is followed by an open buffet around which participants can meet and discuss collaborations.

These seminars are made possible by the support of the CFM-ENS
Chair “*Modèles et Sciences des Données*”.

You can check the list of the next seminars below and the list of past seminars.

Videos of some of the past seminars are available online.

The colloquium is organized by:

- Giulio Biroli (ENS): director ;
- Stéphane Mallat (Collège de France) ;
- Christian Lorenzi (CNRS and ENS) ;
- Gabriel Peyré (CNRS and ENS).

Thurs. April 29th, 2021, 16h00-17h00 (Paris time), room online (link here).

Giuseppe Carleo (EPFL)

**Title:** *Learning Solutions to the Schrödinger equation with Neural-Network Quantum States*

**Abstract:** The theoretical description of several complex quantum phenomena fundamentally relies on many-particle wave functions and our ability to represent and manipulate them. Variational methods in quantum mechanics aim at compact descriptions of many-body wave functions in terms of parameterised ansatz states, and are at present living exciting transformative developments informed by ideas developed in machine learning. In this presentation I will discuss variational representations of quantum states based on artificial neural networks [1] and their use in approximately solving the Schrödinger equation. I will further highlight the general representation properties of such states, the crucial role of physical symmetries, as well as the connection with other known representations based on tensor networks [2]. Finally, I will discuss how some classic ideas in machine learning, such as the Natural Gradient, are being used and re-purposed in quantum computing applications [3].

[1] Carleo and Troyer, Science 365, 602 (2017)

[2] Sharir, Shashua, and Carleo, arXiv:2103.10293 (2021)

[3] Stokes, Izaac, Killoran, and Carleo, Quantum 4, 269 (2020)