Krystal Guo (UvA) — State transfer in continuous-time quantum walks on graphs скачать в хорошем качестве

Krystal Guo (UvA) — State transfer in continuous-time quantum walks on graphs

Title: State transfer in continuous-time quantum walks on graphs Abstract: A quantum walk is a quantum process on an underlying graph. For a graph-theorist, the transition matrix of a continuous-time quantum walk on a graph is a matrix-valued function in time, denoted U(t), whose rows and columns are indexed by the combinatorial information of a graph. Thus it is an example of a combinatorial matrix and could be studied with classical tools from algebraic graph theory. In 2004, Christandl, Datta, Ekert, and Landahl introduced the study of perfect state transfer in quantum spin networks under the nearest-neighbour XY-coupling model, which has since attracted widespread attention in both physics and mathematics. Loosely speaking, perfect state transfer happens if you start the quantum walk at vertex u and, after some amount of time, your likelihood of measuring at some other vertex v is 100%. In this introductory, overview talk (where no prior knowledge of quantum walks nor of algebraic graph theory will be assumed), we will give an overview how the spectral characterization of perfect state transfer was derived, and discuss some more recent results on related notions of state transfer. We will see many examples of perfect state transfer, including one implemented in Qiskit and run on an IBM quantum computer. Date of talk: 2025-01-17