Resolvent Methods for Quantum Walks with an Application to a Thue-Morse Quantum Walk
arXiv:1704.07328 · doi:10.4036/iis.2017.A.04
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.
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
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