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arXiv · 1801.06209

Phase measurement of quantum walks: application to structure theorem of the positive support of the Grover walk

Norio Konno·Iwao Sato·Etsuo Segawa
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Abstract

We obtain a structure theorem of the positive support of the $n$-th power of the Grover walk on $k$-regular graph whose girth is greater than $2(n-1)$. This structure theorem is provided by the parity of the amplitude of another quantum walk on the line which depends only on $k$. The phase pattern of this quantum walk has a curious regularity. We also exactly show how the spectrum of the $n$-th power of the Grover walk is obtained by lifting up that of the adjacency matrix to the complex plain.

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Norio Konno, Iwao Sato, Etsuo Segawa. 2018-01-18. Phase measurement of quantum walks: application to structure theorem of the positive support of the Grover walk. https://arxiv.org/abs/1801.06209

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