Geodesic
Phase measurement of quantum walks: application to structure theorem of the positive support of the Grover walk
Norio Konno1 ; Iwao Sato2 ; Etsuo Segawa3
1Yokohama National University
2Oyama National College of Technology
3Tohoku University
The electronic journal of combinatorics, Tome 26 (2019) no. 2
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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.
DOI : 10.37236/7618
Classification : 81S25, 60G50, 05C81, 05C50

Norio Konno  1   ; Iwao Sato  2   ; Etsuo Segawa  3

1 Yokohama National University
2 Oyama National College of Technology
3 Tohoku University 
@article{10_37236_7618,
     author = {Norio Konno and Iwao Sato and Etsuo Segawa},
     title = {Phase measurement of quantum walks: application to structure theorem of the positive support of the {Grover} walk},
     journal = {The electronic journal of combinatorics},
     year = {2019},
     volume = {26},
     number = {2},
     doi = {10.37236/7618},
     zbl = {1414.81145},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7618/}
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Norio Konno; Iwao Sato; Etsuo Segawa. Phase measurement of quantum walks: application to structure theorem of the positive support of the Grover walk. The electronic journal of combinatorics, Tome 26 (2019) no. 2. doi: 10.37236/7618

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