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arXiv · 1701.08274

The spectra of the unitary marix of a 2-tessellable staggered quantum walk on a graph

Norio Konno·Iwao Sato·Etsuo Segawa
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Abstract

Recently, the staggered quantum walk (SQW) on a graph is discussed as a generalization of coined quantum walks on graphs and Szegedy walks. We present a formula for the time evolution matrix of a 2-tessellable SQW on a graph, and so directly give its spectra. Furthermore, we present a formula for the Szegedy matrix of a bipartite graph by the same method, and so give its spectra. As an application, we present a formula for the characteristic polynomial of the modified Szegedy matrix in the quantum search problem on a graph, and give its spectra.

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Norio Konno, Iwao Sato, Etsuo Segawa. 2017-01-28. The spectra of the unitary marix of a 2-tessellable staggered quantum walk on a graph. https://arxiv.org/abs/1701.08274

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