# Meeting Details

Title: Abstract Structures in the Design and Analysis of Quantum Algorithms Applied Algebra and Network Theory Seminar William Zeng, Oxford University Despite almost two decades of research, there is still a need to find new and useful quantum algorithms. This is of interest in cases where the usefulness ranges from able to generate experimental evidence against the extended Church-Turing thesis" to commercially viable". Better languages, frameworks, and techniques for analyzing the structure of quantum algorithms will aid in these attempts. One such programme, initiated by Abramsky, Coecke, et. al, abstracts the setting of quantum information away from Hilbert spaces and linear maps into abstract process theories: dagger symmetric monoidal categories. This talk will have three goals: [0] Introduce how this abstract semantics applies to quantum computation [1] Show how this abstract setting has been used to design and analyze quantum algorithms in the traditional setting of finite Hilbert spaces and linear maps [2] Describe some current work that uses this framework to construct a model of quantum algorithms in the category of relations. See: W. J. Zeng. Models of quantum algorithms in sets and relations: (in preparation), W. J. Zeng & Jamie Vicary. Abstract structure of unitary oracles for quantum algorithms: arxiv.org/abs/1406.1278, Jamie Vicary. The Topology of of Quantum Algorithms: arxiv.org/abs/1209.3917