in numerical simulation
CEA–EDF–Inria Summer Schools
Thus, many new low-order and high-order numerical methods have been developed in recent years that could meet these needs:
All of these methods have a rigourous mathematical analysis. Many of them have been extented to non-linear problems (and even to industrial problems)
first introductions to quantum computation and we will discuss notions such as error correction, the latest advances in quantum algorithms as well as the representation formalism of quantum circuits. In particular :
If it were to happen in its most promising form, the quantum computer would constitute a major breakthrough for many of the algorithms used within the industry. This concerns algorithms as varied as the resolution of partial differential equations, the simulation of molecules, combinatorial optimization, machine learning or financial mathematics.
The development of quantum algorithms follows drastically different rules and logic than those used in the development of classical algorithms.
Moreover, the maturity of the technology means that questions that a classical algorithmicist has stopped asking are once again relevant in the quantum world. Error correction, circuit representation formalism, data encoding or circuit compilation are all questions that are still open and that need to be adapted to the case under study. In the absence of machines, a deep theoretical work is carried out by the scientific community to address not only these questions, but also questions in quantum algorithms, quantum complexity classes, quantum information theory and quantum formal methods.
CEA is a French government-funded technological research organisation in four main areas: low-carbon energies, defense and security, information technologies and health technologies. A prominent player in the European Research Area, it is involved in setting up collaborative projects with many partners around the world.