Phase matching condition for quantum search with a generalized initial state

Authors:
Gui-Lu Long;Xiao Li;Yang Sun
Affiliations:
Dept. Phys., Tsinghua University, Beijing and Key Lab. for Quantum Information and Measurements, Min. Ed., PR China and Inst. of Theor. Phys., Chinese Acad. Sci. and Center of Atomic and Molecular ...;Department of Physics, Tsinghua University, Beijing and Key Laboratory for Quantum Information and Measurements, Ministry of Education, PR China;Department of Physics and Astronomy, University of Tennessee, Knoxville, TN and Dept. Phys., Tsinghua University, Beijing and Key Lab. for Quantum Information and Measurements, Min. Ed., PR China
Venue:
Physics Letters A
Year:
2002

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Abstract

We present a general phase matching condition for the quantum search algorithm with arbitrary unitary transformation and arbitrary phase rotations in the case of a general initial state. We show by an explicit expression that the phase matching condition depends both on the unitary transformation U and the initial state. We show that several phase conditions previously discussed in the literature are special cases of this general one, which clarifies the question of which condition should be regarded as exact.