Algebraic Graph Theory Seminar - Gabriel Coutinho

Title: State transfer and the size of the graph

Abstract:

If there is perfect state transfer between two vertices at distance d, how small can the graph be compared to d? This question is motivated by the fact that the known infinite families of graphs admitting state transfer at increasingly large distances are all obtained from graph products, thus their sizes grow exponentially compared to their diameter. On the other hand, building quantum systems with many qubits can be expensive. I will show that the size of graphs admitting state transfer is at least cubic in the diameter, and I will also discuss some improvements in the exponential upper bound due to A. Kay. Nevertheless, the question that motivates this talk remains open, and in the end we will discuss some possible research directions.