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dc.contributor.authorMancinska, Laura
dc.date.accessioned2009-12-16 19:15:54 (GMT)
dc.date.available2009-12-16 19:15:54 (GMT)
dc.date.issued2009-12-16T19:15:54Z
dc.date.submitted2009
dc.identifier.urihttp://hdl.handle.net/10012/4873
dc.description.abstractIt is known that almost all 2-qubit gates are universal for quantum computing (Lloyd 1995; Deutsch, Barenco, Eckert 1995). However, an explicit characterization of non-universal 2-qubit gates is not known. We consider a closely related problem of characterizing the set of non-universal 2-qubit Hamiltonians. We call a 2-qubit Hamiltonian n-universal if, when applied on different pairs of qubits, it can be used to approximate any unitary operation on n qubits. It follows directly from the results of Lloyd and Deutsch, Barenco, Eckert, that almost any 2-qubit Hamiltonian is 2-universal. Our main result is a complete characterization of 2-non-universal 2-qubit Hamiltonians. There are three cases when a 2-qubit Hamiltonian H is not universal: (1) H shares an eigenvector with the gate that swaps two qubits; (2) H acts on the two qubits independently (in any of a certain family of bases); (3) H has zero trace. The last condition rules out the Hamiltonians that generate SU(4)---it can be omitted if the global phase is not important. A Hamiltonian that is not 2-universal can still be 3-universal. We give a (possibly incomplete) list of 2-qubit Hamiltonians that are not 3-universal. If this list happens to be complete, it actually gives a classification of n-universal 2-qubit Hamiltonians for all n >= 3.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectHamiltonianen
dc.subjectuniversalen
dc.subjectquantumen
dc.subjectuniversalityen
dc.titleCharacterization of non-universal two-qubit Hamiltoniansen
dc.typeMaster Thesisen
dc.comment.hiddenCompared to the previous version in this one I included References in table of contents and changed the author's declaration. I don't know who is responsible for the uw-thesis.tex file that is recommended as a model for Master's thesis. In this file there is a problem with \addcontentsline{toc}{chapter}{\textbf{References}} command. If one uses bibtex, then in order for the page number of References to be correct one has to put \cleardoublepage command before \addcontentsline.en
dc.pendingfalseen
dc.subject.programCombinatorics and Optimizationen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


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