Geometric pictures for quantum search algorithms

Geometric pictures for quantum search algorithms In this paper, we give the geometric pictures for quantum search algorithms in decomposed form, namely in terms of a phase rotation of the marked state and a phase rotation about the average. We apply this formalism to various quantum search algorithms, and give explicit interpretations of the standard Grover algorithm, arbitrary phase rotations, phase matching and fixed-point search algorithm. The pictures straightforwardly show how state vectors evolve during the search process. These results are helpful in understanding how the quantum search algorithms work. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Geometric pictures for quantum search algorithms

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Publisher
Springer US
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Physics; Physics, general; Theoretical, Mathematical and Computational Physics; Quantum Physics; Computer Science, general; Mathematics, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-011-0249-7
Publisher site
See Article on Publisher Site

Abstract

In this paper, we give the geometric pictures for quantum search algorithms in decomposed form, namely in terms of a phase rotation of the marked state and a phase rotation about the average. We apply this formalism to various quantum search algorithms, and give explicit interpretations of the standard Grover algorithm, arbitrary phase rotations, phase matching and fixed-point search algorithm. The pictures straightforwardly show how state vectors evolve during the search process. These results are helpful in understanding how the quantum search algorithms work.

Journal

Quantum Information ProcessingSpringer Journals

Published: May 21, 2011

References

  • Phase matching condition for quantum search with a generalized initial state
    Long, G.L.
  • Experimental NMR realization of a generalized quantum search algorithm
    Long, G.L.
  • Entanglement in the Grover search algorithm
    Fang, Y.; Kaszlikowski, D.; Chin, C.; Tay, K.; Kwek, L.C.; Oh, C.H.
  • Fixed-point quantum search for different phase shifts
    Li, D.; Li, X.; Huang, H.; Li, X.

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