We consider quantum random walks (QRW) on the integers, a subject that has been considered in the last few years in the framework of quantum computation. We show how the theory of CMV matrices gives a natural tool to study these processes and to give results that are analogous to those that Karlin and McGregor developed to study (classical) birth-and-death processes using orthogonal polynomials on the real line. In perfect analogy with the classical case the study of QRWs on the set of non… CONTINUE READING

Random walks and orthogonal polynomials: some challenges, in Probability, Geometry and Integrable systems, Mark Pinsky and Bjorn Birnir editors, MSRI publication vol 55

F A Grünbaum

Random walks and orthogonal polynomials: some challenges, in Probability, Geometry and Integrable systems, Mark Pinsky and Bjorn Birnir editors, MSRI publication vol 55 • 2007