Explore the intricacies of discrete quantum walks in this 55-minute lecture by Hanmeng Zhan from York University. Delve into topics such as graph matrices, coins of order two, state transfer mechanisms, and the concept of pretty good state transfer. Examine spectral correspondences, strong cospectrality reduction, and geodetic angles. Investigate quantum walk searches, including marked vertex scenarios and average search probability. Analyze distance regular graphs and compare discrete and continuous quantum walks. Gain insights into the one-quarter success probability theorem and participate in a concluding question session.
Transferring States in Discrete Quantum Walks
Overview
Syllabus
Intro
Outline
A graph and a matrix
A discrete quantum walk
Coins of order two
Transferring states
Pretty good state transfer
A spectral correspondence
Reduction of strong cospectrality
Example 1
A 'characterization
Geodetic angles
More examples
Quantum walk with a marked vertex
Quantum walk search
An averaging perspective
Average search probability
Distance regular graphs
Discrete bounded by continuous
Question
One quarter success probability
Taught by
Fields Institute
