Geodesic
Phase Condition for the Grover Algorithm
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 3, pp. 472-483

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For the Grover algorithm, we derive the exact formula of the norm of the amplitude in the marked state in a sine-function form and use this formula to derive the necessary and sufficient phase condition условие $\sin\Delta\leq|\beta|$ for this algorithm with arbitrary phase rotations. We show that the condition of identical rotation angles $\theta=\phi$, which is a special case of our condition, is a sufficient but not necessary phase condition.
Keywords: Grover algorithm, quantum search algorithm
Mots-clés : phase condition. 
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     author = {D. Li and X. Li and H. Huang},
     title = {Phase {Condition} for the {Grover} {Algorithm}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {472--483},
     publisher = {mathdoc},
     volume = {144},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_3_a2/}
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D. Li; X. Li; H. Huang. Phase Condition for the Grover Algorithm. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 3, pp. 472-483. http://geodesic.mathdoc.fr/item/TMF_2005_144_3_a2/