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dc.contributor.authorSijher, Sumit 16:29:12 (GMT) 16:29:12 (GMT)
dc.description.abstractThis thesis serves to give a mathematical overview of topological quantum computation and to apply the theory to characterize desirable fault-tolerant operations called protected gates. Topological quantum computation is a novel paradigm for quantum computation which seeks to harness certain exotic quantum systems known as topological phases of matter that exhibit unique physical phenomena such as the manifestation of quasiparticle excitations called anyons. The low energy effective field theories of these systems can be expressed by certain topological quantum field theories, which in turn are described in terms of unitary modular tensor categories that capture the essential properties of a topological phase of matter and its corresponding anyon model. An overview of the relevant category theoretic concepts is given, and the axioms of a unitary modular tensor category are made explicit. A topological quantum field theory is then defined and used to describe topological quantum computation. Having developed the necessary theoretical background, the theory is then applied to characterize protected gates. The main result is a no-go theorem which states that, for any model, the set of protected gates is finite, and hence, cannot be used to do universal quantum computation using protected gates alone.en
dc.publisherUniversity of Waterlooen
dc.subjectQuantum Conputationen
dc.subjectTopological Quantum Computationen
dc.subjectTopological Quantum Field Theoryen
dc.titleTopological Quantum Computation and Protected Gatesen
dc.typeMaster Thesisen
dc.pendingfalse Mathematicsen Mathematics (Quantum Information)en of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorKoenig, Robert
uws.contributor.affiliation1Faculty of Mathematicsen

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