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dc.rights.licenseCC-BY-NC-ND
dc.contributor.advisorLeeuwen, E.J. van
dc.contributor.advisorCampos, C.P. de
dc.contributor.authorMeijer, R.H.A.J.
dc.date.accessioned2020-02-20T19:03:55Z
dc.date.available2020-02-20T19:03:55Z
dc.date.issued2019
dc.identifier.urihttps://studenttheses.uu.nl/handle/20.500.12932/34880
dc.description.abstractPersistent homology is a way to analyse the shape of a dataset rather than its semantics. This is done by assigning the dataset holes in different dimensions, borrowing this theory from the mathematical area of topology. The dataset is treated as being sampled from a topological space, which is in turn approximated at different resolutions. The persistent Betti numbers then count the number of holes in these spaces, registering for how long the holes persist as the resolution increases. Computing such features classically may prove costly, with some steps possibly requiring exponential time. In a 2016 paper, a polynomial time quantum algorithm for the approximation of persistent homology is promised. In this thesis it is shown these methods are generally incapable of uniquely determining the persistent Betti numbers in arbitrary dimensions. The algorithm does succeed in the zeroth dimension. After treating the prerequisites, the methods from this paper are explained, the above statements are proven, and finally the quantum algorithm is related to agglomerative hierarchical clustering and spectral clustering.
dc.description.sponsorshipUtrecht University
dc.language.isoen
dc.titleClustering using Quantum Persistent Homology
dc.type.contentMaster Thesis
dc.rights.accessrightsOpen Access
dc.subject.keywordsQuantum Computing; Quantum Mechanics; Quantum Machine Learning; Machine Learning; Clustering; Cluster Analysis; Hierarchical Clustering; Spectral Clustering; Complexity; Topology; Algebraic Topology; Homology; Persistent Homology; Topological Data Analysis
dc.subject.courseuuComputing Science


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