Applications of abelian algebraic structures in quantum computation
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2016
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| Online Access: | http://hdl.handle.net/1721.1/106102 |
| _version_ | 1826207763941818368 |
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| author | Zatloukal, Kevin C. (Kevin Chaffee) |
| author2 | Aram W. Harrow. |
| author_facet | Aram W. Harrow. Zatloukal, Kevin C. (Kevin Chaffee) |
| author_sort | Zatloukal, Kevin C. (Kevin Chaffee) |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016. |
| first_indexed | 2024-09-23T13:54:35Z |
| format | Thesis |
| id | mit-1721.1/106102 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:54:35Z |
| publishDate | 2016 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1061022019-04-12T19:24:01Z Applications of abelian algebraic structures in quantum computation Zatloukal, Kevin C. (Kevin Chaffee) Aram W. Harrow. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Electrical Engineering and Computer Science. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016. Cataloged from PDF version of thesis. Includes bibliographical references (pages 163-168). Shor's groundbreaking algorithms for integer factoring and discrete logarithm [58], along with their later generalizations 116, 35, 49, 18], demonstrated a unique ability of quantum computers to solve problems defined on abelian groups. In this thesis, we study ways in which that ability can be leveraged in order to solve problems on more complex structures such as non-abelian groups and hypergroups. This leads to new quantum algorithms for the hidden subgroup problem on nilpotent groups whose order is a product of large primes, the hidden subhypergroup problem on both strongly integral hypergroups and ultragroups, testing equivalence of group extensions, and computing the component parts of the cohomology groups of both group extensions and a generalization of simplicial complexes, amongst other problems. For each of those listed, we also show that no classical algorithm can achieve similar efficiency under standard cryptographic assumptions. by Kevin C. Zatloukal. Ph. D. 2016-12-22T16:29:05Z 2016-12-22T16:29:05Z 2016 2016 Thesis http://hdl.handle.net/1721.1/106102 965445128 eng M.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. http://dspace.mit.edu/handle/1721.1/7582 168 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Electrical Engineering and Computer Science. Zatloukal, Kevin C. (Kevin Chaffee) Applications of abelian algebraic structures in quantum computation |
| title | Applications of abelian algebraic structures in quantum computation |
| title_full | Applications of abelian algebraic structures in quantum computation |
| title_fullStr | Applications of abelian algebraic structures in quantum computation |
| title_full_unstemmed | Applications of abelian algebraic structures in quantum computation |
| title_short | Applications of abelian algebraic structures in quantum computation |
| title_sort | applications of abelian algebraic structures in quantum computation |
| topic | Electrical Engineering and Computer Science. |
| url | http://hdl.handle.net/1721.1/106102 |
| work_keys_str_mv | AT zatloukalkevinckevinchaffee applicationsofabelianalgebraicstructuresinquantumcomputation |