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dc.contributor.authorZhan, Hanmeng 18:22:37 (GMT) 18:22:37 (GMT)
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.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.subject.programCombinatorics and Optimizationen and Optimizationen
uws-etd.degreeMaster of Mathematicsen

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