Quantum Theory for Mathematicians

François Huveneers

These notes are based on a mini-course delivered at the Les Houches Summer School, Quantum Theory on All Scales, in August 2026. They introduce many-body localization to mathematicians, emphasizing the physical mechanisms that support or destabilize it. The mathematical discussion deals with how perturbative rotations, renormalization, and probabilistic estimates are used in a rigorous approach to many-body localization.

Paolo Bertozzini

Joseph M. Landsberg

M Batty, SL Braunstein, Andrew J. Duncan +1 more

We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.