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Categorical quantum mechanics is a research programme which aims to axiomatise (finite dimensional) quantum theory as an algebraic theory inside an abstract symmetric monoidal category. The central idea is that quantum observables can be
axiomatised as certain Frobenius algebras, and that two observables are (strongly) complementary when their Frobenius algebras jointly form a Hopf algebra. The resulting theory is surprisingly powerful, especially when combined with its graphical notation. In this talk
I'll introduce the main concepts and present some applications to quantum computation.