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The ZX-Calculus: A graphical calculus for multipartite qubit systems
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för ingenjörsvetenskap och fysik.
2013 (engelsk)Independent thesis Basic level (degree of Bachelor), 10 poäng / 15 hpOppgave
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.

sted, utgiver, år, opplag, sider
2013. , s. 59
Emneord [en]
categorical quantum mechanics, category theory, qubit systems, ZX-Calculus, diagrammatic calculus, quantum observables
HSV kategori
Identifikatorer
URN: urn:nbn:se:kau:diva-29552OAI: oai:DiVA.org:kau-29552DiVA, id: diva2:656815
Fag / kurs
Physics
Utdanningsprogram
Bachelor Programme in Physics , 180 hp
Presentation
2013-06-17, Karlstad, 10:03 (engelsk)
Veileder
Examiner
Tilgjengelig fra: 2013-10-29 Laget: 2013-10-17 Sist oppdatert: 2013-10-29bibliografisk kontrollert

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Totalt: 550 treff
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