The Quantum Walk of F. Riesz
F. A. Grunbaum, L. Velazquez

TL;DR
This paper introduces a novel method to associate quantum walks with probability measures on the unit circle, exemplified by the Riesz measure, expanding the traditional framework of quantum walks.
Contribution
It presents a new approach linking quantum walks to arbitrary measures on the unit circle, including unconventional transition steps, with a detailed example involving the Riesz measure.
Findings
Established a method to connect quantum walks with measures on the unit circle
Demonstrated the approach using the Riesz measure as a key example
Extended the framework of quantum walks to include non-traditional transitions
Abstract
We exhibit a way to associate a quantum walk (QW) on the non-negative integers to any probability measure on the unit circle. This forces us to consider one step transitions that are not traditionally allowed. We illustrate this in the case of a very interesting measure, originally proposed by F. Riesz for a different purpose.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture
