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Performance of equal phase-shift search for one iteration

  • Quantum Optics and Quantum Information
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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.

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References

  • L.K. Grover, Phys. Rev. Lett. 80, 4329 (1998)

    Article  ADS  Google Scholar 

  • L.K. Grover, Phys. Rev. Lett. 95, 150501 (2005)

    Article  ADS  Google Scholar 

  • D. Li et al., Theor. Math. Phys. 144, 1279 (2005)

    Article  Google Scholar 

  • G. Brassard, Science 275, 627 (1997)

    Article  Google Scholar 

  • E. Farhi et al., Science 292, 472 (2001)

    MathSciNet  Google Scholar 

  • J. Roland, N.J. Cerf, Phys. Rev. A 65, 042308 (2002)

    Article  ADS  Google Scholar 

  • L.K. Grover et al., e-print arXiv:quant-ph/0603132

  • T. Tulsi, L. Grover, A. Patel, e-print arXiv:quant-ph/0505007; also, Quant. Inf. Comput. 6, 483 (2006)

    MathSciNet  Google Scholar 

  • M. Boyer et al., e-print arXiv:quant-ph/9605034, Fortschr. Phys. 46, 493 (1998)

    Article  ADS  Google Scholar 

  • D. Li et al., Phys. Lett. A 362, 260 (2007); also see e-print arXiv:quant-ph/0604062

    Article  MathSciNet  Google Scholar 

  • 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

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Authors and Affiliations

  1. Dept of mathematical sciences, Tsinghua University, Beijing, 100084, P.R. China

    D. Li & J. P. Chen

  2. Department of Mathematics, University of California, Irvine, CA, 92697-3875, USA

    X. Li

  3. Electrical Engineering and Computer Science Department University of Michigan, Ann Arbor, MI, 48109, USA

    H. Huang

  4. Dept. of computer science, Wayne State University, Detroit, MI, 48202, USA

    X. Li

Authors
  1. D. Li
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  2. J. P. Chen
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  3. X. Li
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  4. H. Huang
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  5. X. Li
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Correspondence to D. Li.

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Li, D., Chen, J., Li, X. et al. Performance of equal phase-shift search for one iteration. Eur. Phys. J. D 45, 335–340 (2007). https://doi.org/10.1140/epjd/e2007-00247-9

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  • DOI: https://doi.org/10.1140/epjd/e2007-00247-9

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