Thèse Conception et Exécution d'Algorithmes Adaptés aux Processeurs Quantiques à Atomes Neutres pour l'Exploration des Matériaux Quantiques 2D H/F - Doctorat.Gouv.Fr

Établissement : Institut Polytechnique de Paris École polytechnique École doctorale : Ecole Doctorale de l'Institut Polytechnique de Paris Laboratoire de recherche : Centre de Physique Théorique Direction de la thèse : Thomas AYRAL ORCID 0000000309604065 Début de la thèse : 2026-10-01 Date limite de candidature : 2026-09-30T23:59:59 Comprendre et prédire les propriétés des matériaux quantiques (aimants, électrons corrélés, etc.) constitue l'un des défis centraux de la physique de la matière condensée. Cette difficulté est inhérente à la mécanique quantique : la dimension de l'espace de Hilbert croît exponentiellement avec le nombre de constituants, de sorte que la description exacte d'un système quantique à N corps dépasse rapidement les capacités des ordinateurs classiques. Les méthodes classiques approchées ont connu des succès remarquables, mais chacune repose sur des hypothèses qui ne tiennent plus dans des régimes importants (aimants frustrés, dynamique en temps réel, ou électrons fortement corrélés). La simulation quantique, telle que proposée initialement par Feynman, offre une voie fondamentalement différente : utiliser un système quantique contrôlable pour simuler le modèle, et ainsi accéder à des régimes hors de portée du calcul classique. Ce projet de thèse CIFRE vise à développer de nouveaux algorithmes pour la simulation quantique de matériaux sur la plateforme à atomes neutres de PASQAL, couvrant les paradigmes analogique, digital-analogique et numérique, des aimants de spin aux systèmes fermioniques, en passant par des algorithmes hybrides quantique-classique pour la théorie du champ moyen dynamique. Quantum simulation comes in several paradigms with different hardware maturity levels. Analog
simulation, available today, encodes the target Hamiltonian directly in the native interactions of
the platform; it reaches large system sizes and long evolution times, at the price of limited
programmability. Digital-analog simulation, expected in the midterm, combines discrete gates
with analog evolution, allowing for flexible state preparation with the favorable scaling of analog
dynamics. Fully digital, gate-based simulation is universal and already available, but its
applications remain limited today by the noise of devices (NISQ era); its full power will be
unlocked only in the longer term, with fault-tolerant quantum computers. These paradigms thus
embody a trade-off between programmability and scale, with the balance shifting as the
hardware matures.
Neutral-atom platforms based on Rydberg interactions have driven much of the recent progress for quantum matter. Early experiments revealed quantum many-body scars in the dynamics of a 51-atom chain, followed by the analog simulation of two-dimensional antiferromagnets with hundreds of atoms and of the dipolar XY model. More recently, the question of quantum advantage for these simulators has come into focus, with large-scale benchmarks against state-of-the-art classical methods. A further milestone is the quantum simulation of the frustrated magnet TmMgGaO4, whose results were compared against experimental measurements performed at the MagLab.
These advances have been accompanied by a rapid industrialization of the devices. What used
to be a one-of-a-kind laboratory experiment is now an engineered machine, accessible through
a cloud interface. As a result, the platforms are no longer the exclusive domain of the
experimental groups that built them: theorists can now run their own problems directly on the
hardware, accelerating the pace of research. Progress on both hardware and algorithms is
needed, but the steady advance of the hardware makes the development of new algorithms
especially timely.
The goal of this thesis is to develop new algorithms for the quantum simulation of materials
across these three paradigms. These paradigms correspond to successive stages of hardware
maturity, but the algorithms can be designed in parallel, ahead of the hardware. In the short
term, we focus on analog algorithms for magnetic (spin) materials. In the midterm, we turn to
digital-analog schemes-combining digital state preparation with analog evolution-to address
both magnetic and fermionic systems through hybrid strategies such as the slave-spin
approach. In the long term, we target electronic materials with fully digital, fault-tolerant
algorithms. Throughout, the algorithms are hybrid quantum-classical: a well-defined subroutine
runs on the QPU, while the remaining computation is carried out on classical high-performance
computing facilities.

Maîtrise des outils numériques de simulation classique (Python).
Formation en mécanique quantique et en physique à N corps.
Appétence pour la modélisation des problèmes complexes.

• Python
• Chimie