The European Physical Journal D

, Volume 45, Issue 2, pp 335–340 | Cite as

Performance of equal phase-shift search for one iteration

Quantum Optics and Quantum Information

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.

PACS.

03.67.Lx Quantum computation 

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References

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  11. In the reviewer's report on this paper, the reviewer investigated fixed points of the phase-θ search algorithm as follows. The reviewer let f(epsilonn)=epsilonn+1=epsilon n[1+2(cosθ-1)(1-epsilonn)]2. Then the reviewer showed that the equation has 0 to be an attractive fixed point when 0<θ<π/2 because 0<f(0)<1, cosθ/(cosθ-1) to be an attractive fixed point when π/2<θ<2π/3 because |f(cosθ/(cosθ-1))|<1, and all the fixed points to be repulsive when 2π/3<θ<π. Following the reviewer's idea, we can show when θ=π/2, 0 is a semi-attractive fixed point because f(0)=1 and f′′(0)=-8 and when θ=2π/3, 1/3 is also a semi-attractive fixed-point because f(1/3)=-1 and f′′(1/3)=-6 Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Dept of mathematical sciences, Tsinghua UniversityBeijingP.R. China
  2. 2.Department of MathematicsUniversity of CaliforniaIrvineUSA
  3. 3.Electrical Engineering and Computer Science Department University of MichiganAnn ArborUSA
  4. 4.Dept. of computer science, Wayne State UniversityDetroitUSA

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