1999/06/05 by Gui Lu Long, Yan Song Li, Wei Lin Zhang +1 · 151 citations
Computer Science · Physics and Astronomy · #Amplitude #Matching (statistics) #Phase (matter) #Phase matching #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum error correction #Rotation (mathematics) #Scientific Research and Discoveries #Simple (philosophy) #quant-ph
paper · pdf · doi:10.1016/s0375-9601(99)00631-3
published in Physics Letters A 262(1), 27-34 (Elsevier BV) · 13 pages, 7 figures
arxiv created 1999/06/05 · openalex publication_date 1999/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Each iteration in Grover's original quantum search algorithm contains 4 steps: two Hadamard-Walsh transformations and two amplitudes inversions. When the inversion of the marked state is replaced by arbitrary phase rotation θand the inversion for the prepared state |γ> is replaced by rotation through ϕ, we found that these phase rotations must satisfy a matching condition θ=ϕ. Approximate formula for the amplitude of the marked state after an arbitrary number of iterations are also derived. We give also a simple explanation of the phase matching requirement.