Quantum walks and elliptic integrals

Abstract

Polya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional quantum walk.

8 pages, Journal-ref added

References in corpus (2)

• On the relationship between continuous- and discrete-time quantum walk
• Connecting the discrete and continuous-time quantum walks