Abstracts
Poster Abstracts | Talk Abstracts
Quantum walk search on the complete bipartite graph
Presenting Author: Mason Rhodes, Creighton University
Contributing Author(s): Thomas Wong
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of N vertices for one of k marked vertices with different initial states. We prove intriguing dependence on the number of marked and unmarked vertices in each partite set. For example, when the graph is irregular and the initial state is the typical uniform superposition over the vertices, then the success probability can vary greatly from one timestep to the next, even alternating between 0 and 1, so the precise time at which measurement occurs is crucial. When the initial state is a uniform superposition over the edges, however, the success probability evolves smoothly. As another example, if the complete bipartite graph is regular, then the two initial states are equivalent. Then if two marked vertices are in the same partite set, the success probability reaches 1/2, but if they are in different partite sets, it instead reaches 1. This differs from the complete graph, which is the quantum walk formulation of Grover’s algorithm, where the success probability with two marked vertices is 8/9. This reveals a contrast to the continuous-time quantum walk, whose evolution is governed by Schrödinger’s equation, since its success probability reaches 1 for either arrangement of marked vertices and also for the complete graph.
- Home
- SQuInT
- Registration
- Program
- Instructions for Presenters
- Survey
- Lodging and Transportation
- Hotel Floor Maps (.pdf)
- Faculty Favorites at Old Town
- Past SQuInT Meetings
SQuInT Chief Organizer
Akimasa Miyake, Associate Professor
amiyake@unm.edu
Rafael Alexander, Postdoctoral Fellow
Chris Jackson, Postdoctoral Fellow
SQuInT Administrator
Gloria Cordova
gjcordo1@unm.edu
505 277-1850
SQuInT Assistant
Wendy Jay
SQuInT Founder
Ivan Deutsch, Regents' Professor, CQuIC Director
ideutsch@unm.edu