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Explore a technical colloquium talk that delves into Linear homotopy type theory (LHoTT) as a programming and certification language for quantum computers with classical control and topologically protected quantum gates. Learn about the categorical semantics of LHoTT, its extension of Proto-Quipper, and its relationship to quantum protocols. Discover how classical dependent type theory through Homotopy Type Theory (HoTT) serves as a certification language for topological logic gates, and understand the quantum enhancement of classical HoTT through parameterized stable homotopy theory. Examine how LHoTT provides monadic computational effects that implement classical control in quantum circuits, and see practical applications through QS programming language examples including quantum teleportation, error-correction, and repeat-until-success quantum gates. Note that this presentation ends early due to technical difficulties, with a follow-up session planned to complete the material.
