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The potential of quantum algorithms for solving optimization problems has been explored since the early days of quantum computing. This course introduces some of the key ideas and algorithms developed in this context, along with their fundamental limitations. Depending on the available time, topics covered may include: quantum optimization algorithms inspired by physics (adiabatic algorithms, variational algorithms, QAOA, quantum annealing, etc.), quantum algorithms for convex optimization (acceleration of first- and second-order methods, oracular problems, etc.), applications to combinatorial optimization (graph problems, quadratic binary optimization, etc.). Recording during the CEMRACS Summer School : «Quantum Computing» the July 15, 2025 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area