Hopf Algebras in Quantum Computation
نویسنده
چکیده
In this thesis, we use string diagrams to study the theory of Hopf algebras in the context of Categorical Quantum Mechanics. First, we treat the theory of representations of a Hopf algebra diagrammatically. The category of representations of a quasitriangular Hopf algebra Rep(H) is a braided tensor category and can be understood as a process theory of particles in Topological Quantum theory. We provide diagrammatic proofs of equivalences relating the Drinfeld center construction on Rep(H) to the category of Quantum double modules Rep(DH). We then use similar tools to generalize Kitaev’s lattice models for Topological Quantum computation and give a categorical perspective on Permutational Quantum computation. Finally, we discuss functorial semantics in the context of quantum computation, by constructing a braided language for stabilizer quantum gates.
منابع مشابه
Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras
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