Explore the intricacies of spatial search on Johnson graphs using continuous-time quantum walks in this 54-minute lecture by Hajime Tanaka from Tohoku University. Delivered as part of the Workshop on Algebraic Graph Theory and Quantum Information at the Fields Institute, delve into topics such as Hamiltonian setup, invariant subspaces, matrix representation, and perturbation theory. Gain insights into the search algorithm, success probability, and time scale, while also examining other graph families and negative examples. Enhance your understanding of quantum information and algebraic graph theory through this comprehensive presentation.
Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk
Overview
Syllabus
Introduction
Who am I
General setup
Hamiltonian setup
Previous work
Invariant subspace
General strategy
Matrix representation
Normalized Hamiltonian
Eigenvectors
Technical proposition
Perturbation theory
Implicit function theorem
Search algorithm
Success probability
Hamiltonian
Search time scale
Other families
Negative examples
Taught by
Fields Institute
