Title: Quantum Walks, State Transfer, and Entanglement
|Speaker:||Christopher van Bommel|
|Affiliation:||University of Waterloo|
Abstract: Quantum walks are the quantum analogues of classical random walks and can be used to model quantum computations. If a quantum walker starts at a vertex of a graph and after some length of time, has probability 1 of being found at a different vertex, we say there is perfect state transfer between the two vertices. If instead, there is a time for which probability can be made arbitrarily close to 1, we say there is pretty good state transfer between them. We consider the quantum walk model determined by the XY-Hamiltonian, which can be considered as based on the adjacency matrix of the graph and briefly review results for state transfer on paths between two vertices before discussing how to extend these ideas to starting states involving multiple qubits.