Resolvent Methods for Quantum Walks with an Application to a Thue-Morse Quantum Walk
Spectral Theory
2017-04-25 v1 Mathematical Physics
math.MP
Abstract
In this expository note, we discuss spatially inhomogeneous quantum walks in one dimension and describe a genre of mathematical methods that enables one to translate information about the time-independent eigenvalue equation for the unitary generator into dynamical estimates for the corresponding quantum walk. To illustrate the general methods, we show how to apply them to a 1D coined quantum walk whose coins are distributed according to an element of the Thue--Morse subshift.
Keywords
Cite
@article{arxiv.1704.07328,
title = {Resolvent Methods for Quantum Walks with an Application to a Thue-Morse Quantum Walk},
author = {Jake Fillman},
journal= {arXiv preprint arXiv:1704.07328},
year = {2017}
}
Comments
This paper is part of the proceedings volume for the Workshop on "Quantum Simulation and Quantum Walks" held in Yokohama, Japan in November of 2015