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DTSTART;TZID=America/Toronto:20250414T113000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-gr
 aph-theory-tom-wong
SUMMARY:Algebraic Graph Theory-Tom Wong
CLASS:PUBLIC
DESCRIPTION:TITLE: Quantum Search with the Signless Laplacian\n\nSPEAKER:\
 n\nTom Wong\n\nAFFILIATION:\n\nCreighton University\n\nLOCATION:\n Please
  contact Sabrina Lato for Zoom link.\n\nABSTRACT: Continuous-time quantu
 m walks are typically effected by\neither the discrete Laplacian or the ad
 jacency matrix. In this paper\,\nwe explore a third option: the signless L
 aplacian\, which has\napplications in algebraic graph theory and may arise
  in layered\nantiferromagnetic materials. We explore spatial search on the
  complete\nbipartite graph\, which is generally irregular and breaks the\n
 equivalence of the three quantum walks for regular graphs\, and where\nthe
  search oracle breaks the equivalence of the Laplacian and signless\nLapla
 cian quantum walks on bipartite graphs without the oracle. We\nprove that 
 a uniform superposition over all the vertices of the graph\npartially evol
 ves to the marked vertices in one partite set\, with the\nchoice of set de
 pending on the jumping rate of the quantum walk. We\nboost this success pr
 obability to 1 by proving that a particular\nnon-uniform initial state com
 pletely evolves to the marked vertices in\none partite set\, again dependi
 ng on the jumping rate. For some\nparameter regimes\, the signless Laplaci
 an yields the fastest search\nalgorithm of the three\, suggesting that it 
 could be a new tool for\ndeveloping faster quantum algorithms.\n\nThis is 
 joint work with Molly McLaughlin.
DTSTAMP:20260403T071941Z
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