Show simple item record

dc.contributor.authorZhan, Hanmeng
dc.date.accessioned2014-05-22 18:22:37 (GMT)
dc.date.available2014-05-22 18:22:37 (GMT)
dc.date.issued2014-05-22
dc.date.submitted2014
dc.identifier.urihttp://hdl.handle.net/10012/8499
dc.description.abstractThis thesis investigates uniform mixing on Cayley graphs over Z_3^d. We apply Mullin's results on Hamming quotients, and characterize the 2(d+2)-regular connected Cayley graphs over Z_3^d that admit uniform mixing at time 2pi/9. We generalize Chan's construction on the Hamming scheme H(d,2) to the scheme H(d,3), and find some distance graphs of the Hamming graph H(d,3) that admit uniform mixing at time 2pi/3^k for any k≥2. To restrict the mixing time, we derive a sufficient and necessary condition for uniform mixing to occur on a Cayley graph over Z_3^d at a given time. Using this, we obtain three results. First, we give a lower bound of the valency of a Cayley graph over Z_3^d that could admit uniform mixing at some time. Next, we prove that no Hamming quotient H(d,3)/<1> admits uniform mixing at time earlier than 2pi/9. Finally, we explore the connected Cayley graphs over Z_3^3 with connected complements, and show that five complementary graphs admit uniform mixing with earliest mixing time 2pi/9.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectQuantum Walksen
dc.subjectUniform Mixingen
dc.titleUniform Mixing on Cayley Graphs over Z_3^den
dc.typeMaster Thesisen
dc.comment.hiddenI accidentally removed the entire submission, so I had to start it over. Sorry about that!en
dc.pendingfalse
dc.subject.programCombinatorics and Optimizationen
uws-etd.degree.departmentCombinatorics and Optimizationen
uws-etd.degreeMaster of Mathematicsen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record


UWSpace

University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages