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The ZX-Calculus: A graphical calculus for multipartite qubit systems
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.
2013 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In this thesis we will give a presentation of a graphical/diagrammatic calculus for quantum systems involving interacting quantum observables such as multi-partite systems of qubits, the ZX-Calculus. Unlike the Hilbert space formulation of quantum mechanics, the ZX-Calculus is based on category theory, more specically on the notion of a compact dagger symmetric monoidal category and as a consequence the graphical language associated with such a category is inherited by the calculus. This enables us to think about and deal with many calculations in quantum computation and information in a purely graphical and intuitive fashion. Although being formulated in a more general mathematical framework, huge parts of the Hilbert space formulation of quantum mechanics can be extracted from the ZX-calculus. In this thesis we will begin by giving a motivation for the need of such a calculus and then key concepts of category theory will be introduced in an intuitive manner in order to understand the ZX-calculus that will be presented afterwards. We then apply the calculus to'model' and describe certain quantum circuits and quantum teleportation.

Place, publisher, year, edition, pages
2013. , p. 59
Keyword [en]
categorical quantum mechanics, category theory, qubit systems, ZX-Calculus, diagrammatic calculus, quantum observables
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kau:diva-29552OAI: oai:DiVA.org:kau-29552DiVA, id: diva2:656815
Subject / course
Physics
Educational program
Bachelor Programme in Physics , 180 hp
Presentation
2013-06-17, Karlstad, 10:03 (English)
Supervisors
Examiners
Available from: 2013-10-29 Created: 2013-10-17 Last updated: 2013-10-29Bibliographically approved

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