Solving Mathematical Problems in Quantum Regime

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dc.contributor.advisorLomonaco, Samuel J
dc.contributor.authorShehab Uddin Ayub, Abu Mohammad Omar
dc.contributor.departmentComputer Science and Electrical Engineering
dc.contributor.programComputer Science
dc.date.accessioned2019-10-11T13:42:53Z
dc.date.available2019-10-11T13:42:53Z
dc.date.issued2016-01-01
dc.description.abstractIn this dissertations, I investigate a number of algorithmic approaches in the quantum computational regime to solve mathematical problems. My problems of interest are the graph isomorphism and the graph automorphism problems, and the complexity of memory recall of Hopfield network. I show that the hidden subgroup algorithm, quantum Fourier sampling, always fails, to construct the automorphism group for the class of the cycle graphs. I have discussed what we may infer for a few non-trivial classes of graphs from this result. This raises the question, I have discussed in this dissertations, whether the hidden subgroup algorithm is the best approach for these kinds of problems. I have given a correctness proof of the Hen-Young quantum adiabatic algorithm for graph isomorphism for cycle graphs. To the best of my knowledge this result is the first of its kind. I also report a proof-of-concept implementation of a quantum annealing algorithm for the graph isomorphism problem on a commercial quantum annealing device. This is also, to the best of my knowledge, the first of its kind. I have also discussed the worst-case for the algorithm. Finally, I have shown that quantum annealing helps us achieve exponential capacity for Hopfield networks.
dc.genredissertations
dc.identifierdoi:10.13016/m2agyp-fgc3
dc.identifier.other11519
dc.identifier.urihttp://hdl.handle.net/11603/15488
dc.languageen
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Computer Science and Electrical Engineering Department Collection
dc.relation.ispartofUMBC Theses and Dissertations Collection
dc.relation.ispartofUMBC Graduate School Collection
dc.relation.ispartofUMBC Student Collection
dc.rightsThis item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu
dc.sourceOriginal File Name: ShehabUddinAyub_umbc_0434D_11519.pdf
dc.subjectgraph automorphism
dc.subjectgraph isomorphism
dc.subjectquantum annealing
dc.subjectquantum complexity
dc.subjectquantum computing
dc.subjectquantum information
dc.titleSolving Mathematical Problems in Quantum Regime
dc.typeText
dcterms.accessRightsDistribution Rights granted to UMBC by the author.

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