Colloquium Talk - Steve Kirkland (University of Manitoba, Canada): Perfect and Pretty Good State Transfer on Graphs
Transmitting a quantum state from one location to another is a key task within a quantum computer. This task can be realised through the use of a spin network, which can be modelled by an undirected graph G: vertices in G represent spins, and two edges are adjacent in G whenever the corresponding spins interact.
As the system evolves over time, the quality of the state transfer is measured by a function called the fidelity, which can be expressed in terms of the Hamiltonian for the system; that Hamiltonian is the adjacency matrix of G. The fidelity at time t, f(t), is a number between 0 and 1, and if it happens that f(t_0)=1 for some t_0>0, then we say that there is perfect state transfer (PST). Similarly if f(t) can be made arbitrarily close to 1 via suitable choice of t, then there is pretty good state transfer (PGST).
In this talk we will give an introduction to perfect and pretty good state transfer on graphs, with a focus on identifying some families of graphs that possess PST/PGST, and other families that don't. If time permits, there will also be a discussion of the effect of errors on the fidelity. Tools from matrix analysis, spectral graph theory and number theory will each play a role.
NB! Coffee/Tea/Biscuits from 14.00.