This article is cited in 8 papers

Phase Condition for the Grover Algorithm

D.-F. Li^a, X.-X. Li^b, H.-T. Huang<sup>c

a</sup> Tsinghua University
^b Wayne State University
^c Michigan State University

Abstract: 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, phase condition.

Received: 26.10.2003
Revised: 04.03.2005

DOI: 10.4213/tmf1871

 English version: Theoretical and Mathematical Physics, 2005, 144:3, 1279–1287

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