TL;DR
This paper introduces quaternionic quantum walks (QQWs), extending traditional quantum walks by using quaternion-valued unitary matrices, and explores their initial properties as a new research direction.
Contribution
It is the first study to define and analyze quaternionic quantum walks, expanding the mathematical framework of quantum walks with quaternionic components.
Findings
Defined quaternionic quantum walks (QQWs)
Presented initial properties of QQWs
Laid groundwork for future research on QQWs
Abstract
The discrete-time quantum walk (QW) has been extensively and intensively investigated for the last decade, whose coin operator is defined by a unitary matrix. We extend the QW to a walk determined by a unitary matrix whose component is quaternion. We call this model quaternionic quantum walk (QQW) and present some properties. This paper is the first step for the study on QQWs.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Quantum-Dot Cellular Automata · Quantum Information and Cryptography