QLunch: Pedro Baptista
Speaker: Pedro Baptista
Title: Irrational Quantum Walks
Abstract: The study of continuous-time quantum walks on graphs often require knowledge about the eigenvalues of the matrix representing the graph. For the adjacency matrix, although its entries are integers, its eigenvalues are generally irrational and this results in non-periodic behaviours of the quantum walk. To analyze these behaviours, one usually computes numerical approximations of the eigenvalues. In this talk, we show how it is possible to decide exactly if pretty good state transfer happens. Moreover, we show some relations between the geometric properties of curves of the entries of a quantum walk matrix and the linear dependencies of the eigenvalues.