Abstract
Abstract
Monitored recurrence of a one-parameter set of three-state quantum walks on a line is investigated. The calculations are considerably simplified by choosing a suitable basis of the coin space. We show that the Polya number (i.e. the site recurrence probability) depends on the coin parameter and the probability that the walker is initially in a particular coin state for which the walk returns to the origin with certainty. Finally, we present a brief investigation of the exact quantum state recurrence.
Funder
Ministerstvo Školství, Mládeže a Tělovýchovy
European Commission
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics
Reference33 articles.
1. Quantum random walks;Aharonov;Phys. Rev. A,1993
2. From quantum cellular automata to quantum lattice gases;Meyer;J. Stat. Phys.,1996
3. Quantum computation and decision trees;Farhi;Phys. Rev. A,1998
4. Quantum mechanics and path integrals;Feynman,1965
5. Quantum graphic dynamics;Gudder;Found. Phys.,1988