Category Theoretical Physics RIKEN ECL Research Unit

We study and exploit quantum field theory, the universal framework underlying physics from particle physics to condensed matter and quantum information, using mathematical structures such as category theory and higher algebra. Building on the recently discovered generalized and non-invertible symmetries, we develop a systematic framework that translates desired macroscopic behaviors of matter into the microscopic quantum models that realize them. Combined with tensor networks and lattice models, our aim is an "algebraic calculus" that guides the design and simulation of quantum systems with desired properties.