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dc.contributor.authorMirjalalieh Shirazi, Mirhamed 14:02:27 (GMT) 14:02:27 (GMT)
dc.description.abstractIt is not hard to see that the number of equiangular lines in a complex space of dimension $d$ is at most $d^{2}$. A set of $d^{2}$ equiangular lines in a $d$-dimensional complex space is of significant importance in Quantum Computing as it corresponds to a measurement for which its statistics determine completely the quantum state on which the measurement is carried out. The existence of $d^{2}$ equiangular lines in a $d$-dimensional complex space is only known for a few values of $d$, although physicists conjecture that they do exist for any value of $d$. The main results in this thesis are: \begin{enumerate} \item Abelian covers of complete graphs that have certain parameters can be used to construct sets of $d^2$ equiangular lines in $d$-dimen\-sion\-al space; \item we exhibit infinitely many parameter sets that satisfy all the known necessary conditions for the existence of such a cover; and \item we find the decompose of the space into irreducible modules over the Terwilliger algebra of covers of complete graphs. \end{enumerate} A few techniques are known for constructing covers of complete graphs, none of which can be used to construct covers that lead to sets of $d^{2}$ equiangular lines in $d$-dimensional complex spaces. The third main result is developed in the hope of assisting such construction.en
dc.publisherUniversity of Waterlooen
dc.subjectAlgebraic Combinatoricsen
dc.subjectQuantum Computingen
dc.subjectGraph Theoryen
dc.titleEquiangular Lines and Antipodal Coversen
dc.typeDoctoral Thesisen
dc.subject.programCombinatorics and Optimizationen and Optimizationen
uws-etd.degreeDoctor of Philosophyen

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