Ulysse Rémond
Supervisors : Fabrice Debbasch, Kyryl Kazymyrenko
Team : MIS-PLASMAS
The development of quantum computers has offered new perspectives towards the simulation of quantum-like and classical partial differential equations (PDEs). The aim of this thesis is to provide such quantum algorithms and techniques for efficient simulations while taking into account the hardware implementation, including the shortcomings of the current noisy intermediate-scale quantum computers. One quantum approach to simulation is the quantum walks framework, where the differential operators are discretized into unitary evolution steps on a lattice. Another approach allows us to discretize via FEM classical problems parabolic PDEs. While working under the supervision of Fabrice Debbasch, Kyryl Kazymyrenko and Joseph Mikael, I aim at studying a minimal version of 2+1D quantum walks and discretizations of various structural mechanics and thermal problems. Emphasis is also being put on applying classical simulation techniques, such as remeshing, to these quantum simulations.
