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dc.contributorBall, Simeon Michael
dc.contributor.authorCentelles Tarrés, Aina
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2020-05-25T09:10:58Z
dc.date.available2020-05-25T09:10:58Z
dc.date.issued2020-05
dc.identifier.urihttp://hdl.handle.net/2117/188779
dc.description.abstractThe aim of this project is to bring together quantum error-correcting codes theory and the study of finite geometries. A quantum code is used to protect quantum information from errors that may occur due to quantum decoherence. We give a geometric interpretation of the codes as sets of lines in certain finite projective spaces. We exploit the geometric aspect of codes to rewrite proofs in a more intuitive way and explore their properties through visualization. Some examples of stabiliser codes and their associated quantum sets of lines are presented. We also discuss how to build nonadditive codes as the union of stabiliser codes. Finite geometry has proved to be a powerful tool to work on quantum error-correcting codes. Some of its applications include finding new codes or proving the non-existence of codes with certain parameters.
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
dc.subject.lcshGeometry
dc.subject.otherCoding theory
dc.subject.otherStabiliser codes
dc.subject.otherFinite geometry
dc.subject.otherQuantum error-correction
dc.titleThe geometry of quantum stabiliser codes
dc.typeBachelor thesis
dc.subject.lemacGeometria finita
dc.subject.amsClassificació AMS::51 Geometry::51E Finite geometry and special incidence structures
dc.identifier.slugFME-1915
dc.rights.accessOpen Access
dc.date.updated2020-05-20T05:22:12Z
dc.audience.educationlevelGrau
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeGRAU EN MATEMÀTIQUES (Pla 2009)


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