On alternating quantum walks

We study an inhomogeneous quantum walk on a line that evolves according to alternating coins, each a rotation matrix. For the quantum walk with the coin alternating between clockwise and counterclockwise rotations by the same angle, we derive a closed form solution for the propagation of probabiliti...

Full description

Saved in:
Bibliographic Details
Published in:Physica A 2017-03, Vol.470, p.309-320
Main Authors: Rousseva, Jenia, Kovchegov, Yevgeniy
Format: Article
Language:English
Subjects:
Quantum walk
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study an inhomogeneous quantum walk on a line that evolves according to alternating coins, each a rotation matrix. For the quantum walk with the coin alternating between clockwise and counterclockwise rotations by the same angle, we derive a closed form solution for the propagation of probabilities, and provide its asymptotic approximation via the method of stationary phase. Finally, we observe that for a π4 angle, this alternating rotation walk will replicate the renown Hadamard walk. •A class of quantum walks with an alternating coin operator is considered.•The case when the coin alternates between clockwise and counterclockwise rotations is analyzed.•A closed form solution for the propagation of probabilities is derived.•Asymptotic approximation is provided.•A connection with the Hadamard walk is established.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2016.11.138