Postdoctoral researcher in EDP and quantum computation

Descrizione

Testo originale dell'annuncio (in inglese)

Assigned Lab : ICB Department : UFR Sciences et Techniques Laboratory description : Laboratoire Interdisciplinaire Carnot de Bourgogne As part of the LabCom TeleMAQ (Testing the Limits of Quantum Machines and Algorithms) project, established between the start-up ColibriTD ( https://www.colibritd.com/ ) and the DiTeQ team (ICB, UMR 6303), we are recruiting a postdoctoral researcher to work on solving partial differential equations using quantum approaches, with a particular focus on the Burgers equation. The main responsibility of the successful candidate will be the theoretical and numerical study of the Burgers equation [HR Jauslin, HO Kreiss, and J Moser. On the forced Burgers equation with periodic boundary conditions. Differential Equations: La Pietra 1996, 65:133–153, 1998.] with a view to solving it on a quantum computer [Baumann et al. Solving nonlinear differential equations on noisy 156-qubit quantum computers. arXiv preprint arXiv:2601.04439, 2026] The research will focus in particular on the following areas: • study of the inviscid Burgers equation via its Hamilton–Jacobi formulation, as well as its Carleman linearisation, with a view to analysing the solution to the linearised problem using quantum methods; • study of the viscous Burgers equation via the Cole–Hopf transformation and the associated linear problem; • quantum circuit simulation of the dynamics associated with a classical Hamiltonian via the Koopman–von Neumann (KvN) formulation [Ilon Joseph. Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics. Physical Review Research, 2(4):043102, 2020]; • study of variational strategies for real-time simulation, in particular via Variational Quantum Simulation (VQS) [Hamza Jaffali et al. H-des: a quantum-classical hybrid differential equation solver. Physica Scripta, 2026]