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Antoine Tilloy

Antoine Tilloy

Researcher Scientist

Center · CAS

Keywords

Awards & distinctions

  • 2022 ERC for his research as part of the Quantic team on the “QFT.zip” project

Team

QUANTIC

Biography

Antoine Tilloy is a researcher in theoretical physics whose work focuses on the intersection of quantum mechanics, field theories, and open dynamical systems. His research explores innovative methods for solving complex problems in quantum physics, notably through the use of continuous tensor networks (CTNS, RCMPS) and their application to quantum field theories in 1+1 dimensions. He has contributed to the study of hybrid quantum-classical dynamics by deriving stochastic equations and models of spontaneous collapse, while analyzing their implications for semiclassical gravity and decoherence. His work also addresses fundamental questions, such as continuous measurement in quantum mechanics, critical phase transitions, and the emergence of macroscopic behavior from microscopic systems. His expertise includes methodological developments for simulating and interpreting quantum phenomena, often in connection with experimental or conceptual challenges.

Publication(s)

Teaching

Quantum Physics (Phys1)

Lecturer

The detailed syllabus for the Quantum Physics and Relativity course, which combines lectures and small-group sessions, is as follows: The Lagrangian and Hamiltonian formulations of mechanics; spacetime in special relativity, Lorentz transformations; the relativistic Lagrangian, four-vectors, mass–energy equivalence; the strange world of atoms, wave–particle duality; relativistic kinematics (PC) The postulates of quantum mechanics, the quantum formalism; the Schrödinger equation, the algebra of operators; the quantum well and the tunnel effect (PC) The Dirac formalism—quantization of angular momentum; atomic orbitals, the hydrogen atom; spin, bosons, and fermions; half-spin and measurement (PC) The complete classification of atoms, the structure of matter; the quantum harmonic oscillator (PC) Quantum entanglement, the EPR paradox, the nature of reality; quantum cryptography, quantum molecules (PC)

Statistical Physics (Phys2)

Lecturer

The detailed syllabus for the Statistical Physics course, which combines lectures and small-group sessions, is as follows: From Mechanics to Statistical Physics – Deterministic Chaos: Micro-states, Macro-states, Individual States – State Density From Microscopic Reversibility to Macroscopic Irreversibility: entropy; H’s theorem; the ideal gas, entropy, and state equations—the Gibbs paradox; paramagnetism and ferromagnetism in metals (PC) Diffusion, motion without force Statistical physics of non-isolated systems The Stokes–Einstein relation (PC) Statistical physics in the canonical ensemble, the ideal gas Einstein’s model of solids, classical fluids Thermostatically balanced systems – classical fluids (PC) Statistical physics of quantum systems, superconductivity Bose-Einstein condensation (PC) Matter and radiation, the Big Bang Semiconductors (PC)

Optimization

Lecturer

This optimization course covers finite-dimensional nonlinear convex optimization. It begins by presenting the fundamentals of convex analysis and the sufficient and necessary conditions for optimality. Next, optimization algorithms—first for unconstrained problems and then for constrained problems—are discussed in detail, along with detailed proofs of convergence guarantees. Finally, elements of advanced convex analysis are covered to provide an introduction to non-smooth optimization methods. This course includes lectures (10 hours), tutorials (8 hours), and practical sessions conducted in Python (6 hours). Detailed ContentChapter 1: Optimality Conditions and Convex Analysis (3 hours)Definitions, optimality conditions, convex analysis (convex function, subdifferential, optimality conditions, strong convexity)Chapter 2: Numerical Methods for Differentiable Optimization (15 hours)2.1 Unconstrained Optimization Gradient methods (optimal step, linear search, stochastic gradient)Newton and quasi-Newton (BFGS)2.2 Constrained OptimizationLagrange multipliers, stationarity conditionsKKT conditions, active constraint algorithmsDuality and saddle points, Uzawa’s algorithmChapter 3: Introduction to Non-Smooth Optimization (6 hours) Advanced convex analysis: Fechner transform, proximal operator; subgradient methods, proximal gradient method, bundle methods

PhD supervision

  • 2024 Problem solving for open quantum N-body systems using semi-definite relaxation methods ROBICHON Gustave
  • 2021 From theory to experiment: continuous quantum measurement with filtered and digitized signals GUILMIN Pierre