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dc.contributor.authorCao, Zhenweien_US
dc.date.accessioned2013-02-19T22:35:52Z
dc.date.available2013-02-19T22:35:52Z
dc.date.issued2012-12-11en_US
dc.identifier.othervt_gsexam:98en_US
dc.identifier.urihttp://hdl.handle.net/10919/19205
dc.description.abstractOver the years, people have found Quantum Mechanics to be extremely useful in <br />explaining various physical phenomena from a microscopic point of view.<br />Anderson localization, named after physicist P. W. Anderson, states that<br />disorder in a crystal can cause non-spreading of wave packets, which is one possible mechanism (at single electron level) to explain metal-insulator transitions. The theory of quantum computation promises to bring greater computational power over classical computers by making use of<br />some special features of Quantum Mechanics.<br />The first part of this dissertation considers a 3D alloy-type<br />model, where the Hamiltonian is the sum of the finite difference Laplacian corresponding to free motion of an electron and a random potential generated by a sign-indefinite single-site potential.<br />The result shows that localization occurs in the weak disorder regime,<br />{\\it i.e.}, when the coupling parameter $\\lambda$ is very small, for energies<br />$E \\le -C\\lambda^2$.<br />The second part of this dissertation considers adiabatic quantum computing (AQC) algorithms for the unstructured search problem to the case when the number of marked items is unknown.<br />In an ideal situation,<br />an explicit quantum algorithm together with a counting subroutine are given that achieve the optimal Grover<br />speedup over classical algorithms, {\\it i.e.}, roughly speaking, reduce $O(2^n)$ to $O(2^{n/2})$, where $n$ is the size of the problem. <br />However, if one considers more realistic settings, the result shows this quantum speedup is achievable <br />only under a very rigid control precision requirement ({\\it e.g.}, exponentially small control error).<br />en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThe authors of the theses and dissertations are the copyright owners. Virginia Tech's Digital Library and Archives has their permission to store and provide access to these works.en_US
dc.subjectQuantum Mechanicsen_US
dc.subjectRandom Schren_US
dc.titleQuantum evolution: The case of weak localization for a 3D alloy-type Anderson model and application to Hamiltonian based quantum computationen_US
dc.typeOther - Dissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePHDen_US
thesis.degree.namePHDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairElgart, Alexanderen_US
dc.contributor.committeememberTauber, Uwe Cen_US
dc.contributor.committeememberHagedorn, George Aen_US
dc.contributor.committeememberStolz, Gunteren_US


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