Return probability of quantum and correlated random walks
arXiv:2203.07674 · doi:10.3390/e24050584
Abstract
The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer lattice by the path counting method. We show that the return probability of both quantum and correlated random walks can be expressed in terms of the Legendre polynomial. Moreover, the generating function of the return probability can be written in terms of elliptic integrals of the first and second kinds for the quantum walk.
arXiv comment15pages
References in corpus (11)
- A Quantum Random Walk Search Algorithm
- Quantum walks: a comprehensive review
- Spatial search by quantum walk
- Exploring Topological Phases With Quantum Walks
- Recurrence and Pólya number of quantum walks
- Recurrence properties of unbiased coined quantum walks on infinite -dimensional lattices
- Quantum Walks and discrete Gauge Theories
- Quantum walks and non-Abelian discrete gauge theory
- Recurrence of biased quantum walks on a line
- Discrete-time quantum walks on one-dimensional lattices
- A limit law of the return probability for a quantum walk on a hexagonal lattice