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dc.contributor.advisorEdward H. Farhi.en_US
dc.contributor.authorChilds, Andrew MacGregor, 1977-en_US
dc.contributor.otherMassachusetts Institute of Technology. Dept. of Physics.en_US
dc.date.accessioned2005-05-17T14:50:52Z
dc.date.available2005-05-17T14:50:52Z
dc.date.copyright2004en_US
dc.date.issued2004en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/16663
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2004.en_US
dc.descriptionIncludes bibliographical references (p. 127-138) and index.en_US
dc.descriptionThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.en_US
dc.description.abstractQuantum mechanical computers can solve certain problems asymptotically faster than any classical computing device. Several fast quantum algorithms are known, but the nature of quantum speedup is not well understood, and inventing new quantum algorithms seems to be difficult. In this thesis, we explore two approaches to designing quantum algorithms based on continuous-time Hamiltonian dynamics. In quantum computation by adiabatic evolution, the computer is prepared in the known ground state of a simple Hamiltonian, which is slowly modified so that its ground state encodes the solution to a problem. We argue that this approach should be inherently robust against low-temperature thermal noise and certain control errors, and we support this claim using simulations. We then show that any adiabatic algorithm can be implemented in a different way, using only a sequence of measurements of the Hamiltonian. We illustrate how this approach can achieve quadratic speedup for the unstructured search problem. We also demonstrate two examples of quantum speedup by quantum walk, a quantum mechanical analog of random walk. First, we consider the problem of searching a region of space for a marked item. Whereas a classical algorithm for this problem requires time proportional to the number of items regardless of the geometry, we show that a simple quantum walk algorithm can find the marked item quadratically faster for a lattice of dimension greater than four, and almost quadratically faster for a four-dimensional lattice. We also show that by endowing the walk with spin degrees of freedom, the critical dimension can be lowered to two. Second, we construct an oracular problem that a quantum walk can solve exponentially faster than any classical algorithm.en_US
dc.description.abstract(cont.) This constitutes the only known example of exponential quantum speedup not based on the quantum Fourier transform. Finally, we consider bipartite Hamiltonians as a model of quantum channels and study their ability to process information given perfect local control. We show that any interaction can simulate any other at a nonzero rate, and that tensor product Hamiltonians can simulate each other reversibly. We also calculate the optimal asymptotic rate at which certain Hamiltonians can generate entanglement.en_US
dc.description.statementofresponsibilityby Andrew MacGregor Childs.en_US
dc.format.extent140 p.en_US
dc.format.extent1318731 bytes
dc.format.extent2096468 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582
dc.subjectPhysics.en_US
dc.titleQuantum information processing in continuous timeen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Dept. of Physics.en_US
dc.identifier.oclc56558690en_US


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