N. Konno: Quaternionic quantum walks


Norio Konno, Quantum Studies: Mathematics and Foundations, April 2015, Volume 2, Issue 1, pp 63-76, Date: 03 Mar 2015, DOI: 10.1007/s40509-015-0035-9

Abstract: The discrete-time quantum walk (QW) has been extensively and intensively investigated in 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.

Keywords: Quantum walks, Quaternionic quantum walk, Stationary measure
60F05, 60G50, 82B41, 81Q99.

Source: springer_AT_sci.scientific-direct.net, 22 May 2015, http://link.springer.com/article/10.1007/s40509-015-0035-9

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