Eur. Phys. J. D 45, 335-340 (2007)
https://doi.org/10.1140/epjd/e2007-00247-9

Performance of equal phase-shift search for one iteration^*

¹ Dept of mathematical sciences, Tsinghua University, Beijing, 100084, P.R. China
² Department of Mathematics, University of California, Irvine, CA, 92697-3875, USA
³ Electrical Engineering and Computer Science Department University of Michigan, Ann Arbor, MI, 48109, USA
⁴ Dept. of computer science, Wayne State University, Detroit, MI, 48202, USA

Corresponding author: ^a dli@math.tsinghua.edu.cn

Received: 13 March 2007
Revised: 30 May 2007
Published online: 1 August 2007

Abstract

Grover presented the phase-shift search by replacing the selective inversions by selective phase shifts of π/3. In this paper, we investigate the phase-shift search with general equal phase shifts. We show that for small uncertainties, the failure probability of the phase-π/3 search is smaller than the general phase-shift search and for large uncertainties, the success probability of the large phase-shift search is larger than the phase-π/3 search. Therefore, the large phase-shift search is suitable for large-size of databases.