{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:18Z","timestamp":1753893858736,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.37236\/7618","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:14:21Z","timestamp":1578640461000},"source":"Crossref","is-referenced-by-count":1,"title":["Phase Measurement of Quantum Walks: Application to Structure Theorem of the Positive Support of the Grover Walk"],"prefix":"10.37236","volume":"26","author":[{"given":"Norio","family":"Konno","sequence":"first","affiliation":[]},{"given":"Iwao","family":"Sato","sequence":"additional","affiliation":[]},{"given":"Etsuo","family":"Segawa","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,5,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p26\/7840","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p26\/7840","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:14:27Z","timestamp":1579234467000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,17]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7618","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,5,17]]},"article-number":"P2.26"}}