Adiabatic quantum computation: Noise in the adiabatic theorem and using the Jordan-Wigner transform to find effective Hamiltonians

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dc.contributor.advisorO'Leary, Dianne Pen_US
dc.contributor.authorO'Hara, Michael Jamesen_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2008-06-20T05:34:59Z
dc.date.available2008-06-20T05:34:59Z
dc.date.issued2008-04-22en_US
dc.description.abstractThis thesis explores two mathematical aspects of adiabatic quantum computation. Adiabatic quantum computation depends on the adiabatic theorem of quantum mechanics, and (a) we provide a rigorous formulation of the adiabatic theorem with explicit definitions of constants, and (b) we bound error in the adiabatic approximation under conditions of noise and experimental error. We apply the new results to a standard example of violation of the adiabatic approximation, and to a superconducting flux qubit. Further, adiabatic quantum computation requires large ground-state energy gaps throughout a Hamiltonian evolution if it is to solve problems in polynomial time. We identify a class of random Hamiltonians with non-nearest-neighbor interactions and a ground-state energy gap of $\mathcal{O}(1/\sqrt{n})$, where $n$ is the number of qubits. We also identify two classes of Hamiltonians with non-nearest-neighbor interactions whose ground state can be found in polynomial time with adiabatic quantum computing. We then use the Jordan-Wigner transformation to derive equivalent results for Hamiltonians defined using Pauli operators.en_US
dc.format.extent827108 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/8113
dc.language.isoen_US
dc.subject.pqcontrolledPhysics, Theoryen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledPhysics, Generalen_US
dc.subject.pquncontrolledquantum mechanicsen_US
dc.subject.pquncontrolledadiabatic theoremen_US
dc.subject.pquncontrolledquantum computingen_US
dc.subject.pquncontrolledadiabatic quantum computingen_US
dc.subject.pquncontrolledquantum physicsen_US
dc.titleAdiabatic quantum computation: Noise in the adiabatic theorem and using the Jordan-Wigner transform to find effective Hamiltoniansen_US
dc.typeDissertationen_US

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